draft-ietf-tsvwg-rlc-fec-scheme-09.txt   draft-ietf-tsvwg-rlc-fec-scheme-10.txt 
TSVWG V. Roca TSVWG V. Roca
Internet-Draft B. Teibi Internet-Draft B. Teibi
Intended status: Standards Track INRIA Intended status: Standards Track E. Baccelli
Expires: March 23, 2019 September 19, 2018 Expires: July 21, 2019 INRIA
January 17, 2019
Sliding Window Random Linear Code (RLC) Forward Erasure Correction (FEC) Sliding Window Random Linear Code (RLC) Forward Erasure Correction (FEC)
Schemes for FECFRAME Schemes for FECFRAME
draft-ietf-tsvwg-rlc-fec-scheme-09 draft-ietf-tsvwg-rlc-fec-scheme-10
Abstract Abstract
This document describes two fully-specified Forward Erasure This document describes two fully-specified Forward Erasure
Correction (FEC) Schemes for Sliding Window Random Linear Codes Correction (FEC) Schemes for Sliding Window Random Linear Codes
(RLC), one for RLC over the Galois Field (A.K.A. Finite Field) (RLC), one for RLC over the Galois Field (A.K.A. Finite Field)
GF(2), a second one for RLC over the Galois Field GF(2^^8), each time GF(2), a second one for RLC over the Galois Field GF(2^^8), each time
with the possibility of controlling the code density. They can with the possibility of controlling the code density. They can
protect arbitrary media streams along the lines defined by FECFRAME protect arbitrary media streams along the lines defined by FECFRAME
extended to sliding window FEC codes, as defined in [fecframe-ext]. extended to sliding window FEC codes, as defined in [fecframe-ext].
skipping to change at page 1, line 43 skipping to change at page 1, line 44
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Table of Contents Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Limits of Block Codes with Real-Time Flows . . . . . . . 3 1.1. Limits of Block Codes with Real-Time Flows . . . . . . . 4
1.2. Lower Latency and Better Protection of Real-Time Flows 1.2. Lower Latency and Better Protection of Real-Time Flows
with the Sliding Window RLC Codes . . . . . . . . . . . . 4 with the Sliding Window RLC Codes . . . . . . . . . . . . 4
1.3. Small Transmission Overheads with the Sliding Window RLC 1.3. Small Transmission Overheads with the Sliding Window RLC
FEC Scheme . . . . . . . . . . . . . . . . . . . . . . . 5 FEC Scheme . . . . . . . . . . . . . . . . . . . . . . . 5
1.4. Document Organization . . . . . . . . . . . . . . . . . . 6 1.4. Document Organization . . . . . . . . . . . . . . . . . . 6
2. Definitions and Abbreviations . . . . . . . . . . . . . . . . 6 2. Definitions and Abbreviations . . . . . . . . . . . . . . . . 6
3. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 7 3. Common Procedures . . . . . . . . . . . . . . . . . . . . . . 7
3.1. Possible Parameter Derivations . . . . . . . . . . . . . 7 3.1. Codec Parameters . . . . . . . . . . . . . . . . . . . . 7
3.1.1. Case of a CBR Real-Time Flow . . . . . . . . . . . . 8 3.2. ADU, ADUI and Source Symbols Mappings . . . . . . . . . . 9
3.1.2. Other Types of Real-Time Flow . . . . . . . . . . . . 10 3.3. Encoding Window Management . . . . . . . . . . . . . . . 10
3.1.3. Case of a Non Real-Time Flow . . . . . . . . . . . . 11 3.4. Source Symbol Identification . . . . . . . . . . . . . . 11
3.2. ADU, ADUI and Source Symbols Mappings . . . . . . . . . . 11 3.5. Pseudo-Random Number Generator (PRNG) . . . . . . . . . . 11
3.3. Encoding Window Management . . . . . . . . . . . . . . . 13 3.6. Coding Coefficients Generation Function . . . . . . . . . 17
3.4. Pseudo-Random Number Generator (PRNG) . . . . . . . . . . 13 3.7. Finite Fields Operations . . . . . . . . . . . . . . . . 19
3.5. Coding Coefficients Generation Function . . . . . . . . . 15 3.7.1. Finite Field Definitions . . . . . . . . . . . . . . 19
3.6. Finite Fields Operations . . . . . . . . . . . . . . . . 17 3.7.2. Linear Combination of Source Symbols Computation . . 19
3.6.1. Finite Field Definitions . . . . . . . . . . . . . . 17
3.6.2. Linear Combination of Source Symbols Computation . . 17
4. Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary 4. Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary
Packet Flows . . . . . . . . . . . . . . . . . . . . . . . . 18 Packet Flows . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 18 4.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 20
4.1.1. FEC Framework Configuration Information . . . . . . . 18 4.1.1. FEC Framework Configuration Information . . . . . . . 20
4.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 19 4.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 22
4.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 20 4.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 22
4.1.4. Additional Procedures . . . . . . . . . . . . . . . . 21 4.2. Procedures . . . . . . . . . . . . . . . . . . . . . . . 24
5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary Packet 5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary Packet
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 21 5.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 24
5.1.1. FEC Framework Configuration Information . . . . . . . 22 5.1.1. FEC Framework Configuration Information . . . . . . . 24
5.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 22 5.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 24
5.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 22 5.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 24
5.1.4. Additional Procedures . . . . . . . . . . . . . . . . 22
6. FEC Code Specification . . . . . . . . . . . . . . . . . . . 22 5.2. Procedures . . . . . . . . . . . . . . . . . . . . . . . 25
6.1. Encoding Side . . . . . . . . . . . . . . . . . . . . . . 22 6. FEC Code Specification . . . . . . . . . . . . . . . . . . . 25
6.2. Decoding Side . . . . . . . . . . . . . . . . . . . . . . 23 6.1. Encoding Side . . . . . . . . . . . . . . . . . . . . . . 25
7. Implementation Status . . . . . . . . . . . . . . . . . . . . 24 6.2. Decoding Side . . . . . . . . . . . . . . . . . . . . . . 25
8. Security Considerations . . . . . . . . . . . . . . . . . . . 24 7. Implementation Status . . . . . . . . . . . . . . . . . . . . 26
8.1. Attacks Against the Data Flow . . . . . . . . . . . . . . 24 8. Security Considerations . . . . . . . . . . . . . . . . . . . 27
8.1.1. Access to Confidential Content . . . . . . . . . . . 24 8.1. Attacks Against the Data Flow . . . . . . . . . . . . . . 27
8.1.2. Content Corruption . . . . . . . . . . . . . . . . . 25 8.1.1. Access to Confidential Content . . . . . . . . . . . 27
8.2. Attacks Against the FEC Parameters . . . . . . . . . . . 25 8.1.2. Content Corruption . . . . . . . . . . . . . . . . . 27
8.3. When Several Source Flows are to be Protected Together . 26 8.2. Attacks Against the FEC Parameters . . . . . . . . . . . 27
8.4. Baseline Secure FEC Framework Operation . . . . . . . . . 26 8.3. When Several Source Flows are to be Protected Together . 29
8.4. Baseline Secure FEC Framework Operation . . . . . . . . . 29
8.5. Additional Security Considerations for Numerical 8.5. Additional Security Considerations for Numerical
Computations . . . . . . . . . . . . . . . . . . . . . . 27 Computations . . . . . . . . . . . . . . . . . . . . . . 29
9. Operations and Management Considerations . . . . . . . . . . 27 9. Operations and Management Considerations . . . . . . . . . . 30
9.1. Operational Recommendations: Finite Field GF(2) Versus 9.1. Operational Recommendations: Finite Field GF(2) Versus
GF(2^^8) . . . . . . . . . . . . . . . . . . . . . . . . 27 GF(2^^8) . . . . . . . . . . . . . . . . . . . . . . . . 30
9.2. Operational Recommendations: Coding Coefficients Density 9.2. Operational Recommendations: Coding Coefficients Density
Threshold . . . . . . . . . . . . . . . . . . . . . . . . 28 Threshold . . . . . . . . . . . . . . . . . . . . . . . . 30
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 28 10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 31
11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 28 11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 31
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 28 12. References . . . . . . . . . . . . . . . . . . . . . . . . . 31
12.1. Normative References . . . . . . . . . . . . . . . . . . 28 12.1. Normative References . . . . . . . . . . . . . . . . . . 31
12.2. Informative References . . . . . . . . . . . . . . . . . 29 12.2. Informative References . . . . . . . . . . . . . . . . . 32
Appendix A. TinyMT32 Pseudo-Random Number Generator . . . . . . 31 Appendix A. TinyMT32 Validation Criteria (Normative) . . . . . . 34
Appendix B. Decoding Beyond Maximum Latency Optimization . . . . 35 Appendix B. Assessing the PRNG Adequacy (Informational) . . . . 35
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 36 Appendix C. Possible Parameter Derivation (Informational) . . . 37
C.1. Case of a CBR Real-Time Flow . . . . . . . . . . . . . . 38
C.2. Other Types of Real-Time Flow . . . . . . . . . . . . . . 40
C.3. Case of a Non Real-Time Flow . . . . . . . . . . . . . . 41
Appendix D. Decoding Beyond Maximum Latency Optimization
(Informational) . . . . . . . . . . . . . . . . . . 41
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 42
1. Introduction 1. Introduction
Application-Level Forward Erasure Correction (AL-FEC) codes, or Application-Level Forward Erasure Correction (AL-FEC) codes, or
simply FEC codes, are a key element of communication systems. They simply FEC codes, are a key element of communication systems. They
are used to recover from packet losses (or erasures) during content are used to recover from packet losses (or erasures) during content
delivery sessions to a potentially large number of receivers delivery sessions to a potentially large number of receivers
(multicast/broadcast transmissions). This is the case with the (multicast/broadcast transmissions). This is the case with the
FLUTE/ALC protocol [RFC6726] when used for reliable file transfers FLUTE/ALC protocol [RFC6726] when used for reliable file transfers
over lossy networks, and the FECFRAME protocol when used for reliable over lossy networks, and the FECFRAME protocol when used for reliable
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The present document only focuses on the FECFRAME protocol, used in The present document only focuses on the FECFRAME protocol, used in
multicast/broadcast delivery mode, in particular for contents that multicast/broadcast delivery mode, in particular for contents that
feature stringent real-time constraints: each source packet has a feature stringent real-time constraints: each source packet has a
maximum validity period after which it will not be considered by the maximum validity period after which it will not be considered by the
destination application. destination application.
1.1. Limits of Block Codes with Real-Time Flows 1.1. Limits of Block Codes with Real-Time Flows
With FECFRAME, there is a single FEC encoding point (either a end- With FECFRAME, there is a single FEC encoding point (either a end-
host/server (source) or a middlebox) and a single FEC decoding point host/server (source) or a middlebox) and a single FEC decoding point
(either a end-host (receiver) or middlebox). In this context, per receiver (either a end-host (receiver) or middlebox). In this
currently standardized AL-FEC codes for FECFRAME like Reed-Solomon context, currently standardized AL-FEC codes for FECFRAME like Reed-
Solomon [RFC6865], LDPC-Staircase [RFC6816], or Raptor/RaptorQ, are
[RFC6865], LDPC-Staircase [RFC6816], or Raptor/RaptorQ, are all all linear block codes: they require the data flow to be segmented
linear block codes: they require the data flow to be segmented into into blocks of a predefined maximum size.
blocks of a predefined maximum size.
To define this block size, it is required to find an appropriate To define this block size, it is required to find an appropriate
balance between robustness and decoding latency: the larger the block balance between robustness and decoding latency: the larger the block
size, the higher the robustness (e.g., in front of long packet size, the higher the robustness (e.g., in case of long packet erasure
erasure bursts), but also the higher the maximum decoding latency bursts), but also the higher the maximum decoding latency (i.e., the
(i.e., the maximum time required to recover a lost (erased) packet maximum time required to recover a lost (erased) packet thanks to FEC
thanks to FEC protection). Therefore, with a multicast/broadcast protection). Therefore, with a multicast/broadcast session where
session where different receivers experience different packet loss different receivers experience different packet loss rates, the block
rates, the block size should be chosen by considering the worst size should be chosen by considering the worst communication
communication conditions one wants to support, but without exceeding conditions one wants to support, but without exceeding the desired
the desired maximum decoding latency. This choice then impacts the maximum decoding latency. This choice then impacts the FEC-related
FEC-related latency of all receivers, even those experiencing a good latency of all receivers, even those experiencing a good
communication quality, since no FEC encoding can happen until all the communication quality, since no FEC encoding can happen until all the
source data of the block is available at the sender, which directly source data of the block is available at the sender, which directly
depends on the block size. depends on the block size.
1.2. Lower Latency and Better Protection of Real-Time Flows with the 1.2. Lower Latency and Better Protection of Real-Time Flows with the
Sliding Window RLC Codes Sliding Window RLC Codes
This document introduces two fully-specified FEC Schemes that follow This document introduces two fully-specified FEC Schemes that do not
a totally different approach: the Sliding Window Random Linear Codes follow the block code approach: the Sliding Window Random Linear
(RLC) over either Galois Fields (A.K.A. Finite Fields) GF(2) (the Codes (RLC) over either Galois Fields (A.K.A. Finite Fields) GF(2)
"binary case") or GF(2^^8), each time with the possibility of (the "binary case") or GF(2^^8), each time with the possibility of
controlling the code density. These FEC Schemes are used to protect controlling the code density. These FEC Schemes are used to protect
arbitrary media streams along the lines defined by FECFRAME extended arbitrary media streams along the lines defined by FECFRAME extended
to sliding window FEC codes [fecframe-ext]. These FEC Schemes, and to sliding window FEC codes [fecframe-ext]. These FEC Schemes, and
more generally Sliding Window FEC codes, are recommended for instance more generally Sliding Window FEC codes, are recommended for
with media that feature real-time constraints sent within a instance, with media that feature real-time constraints sent within a
multicast/broadcast session [Roca17]. multicast/broadcast session [Roca17].
The RLC codes belong to the broad class of sliding window AL-FEC The RLC codes belong to the broad class of sliding-window AL-FEC
codes (A.K.A. convolutional codes) [RFC8406]. The encoding process codes (A.K.A. convolutional codes) [RFC8406]. The encoding process
is based on an encoding window that slides over the set of source is based on an encoding window that slides over the set of source
packets (in fact source symbols as we will see in Section 3.2), this packets (in fact source symbols as we will see in Section 3.2), this
window being either of fixed size or variable size (A.K.A. an elastic window being either of fixed size or variable size (A.K.A. an elastic
window). Repair symbols are generated on-the-fly, by computing a window). Repair symbols are generated on-the-fly, by computing a
random linear combination of the source symbols present in the random linear combination of the source symbols present in the
current encoding window, and passed to the transport layer. current encoding window, and passed to the transport layer.
At the receiver, a linear system is managed from the set of received At the receiver, a linear system is managed from the set of received
source and repair packets. New variables (representing source source and repair packets. New variables (representing source
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by each repair symbol received) are added upon receiving new packets. by each repair symbol received) are added upon receiving new packets.
Variables and the equations they are involved in are removed when Variables and the equations they are involved in are removed when
they are too old with respect to their validity period (real-time they are too old with respect to their validity period (real-time
constraints) . Lost source symbols are then recovered thanks to this constraints) . Lost source symbols are then recovered thanks to this
linear system whenever its rank permits to solve it (at least linear system whenever its rank permits to solve it (at least
partially). partially).
The protection of any multicast/broadcast session needs to be The protection of any multicast/broadcast session needs to be
dimensioned by considering the worst communication conditions one dimensioned by considering the worst communication conditions one
wants to support. This is also true with RLC (more generally any wants to support. This is also true with RLC (more generally any
sliding window) code. However the receivers experiencing a good to sliding window) code. However, the receivers experiencing a good to
medium communication quality will observe a reduced FEC-related medium communication quality will observe a reduced FEC-related
latency compared to block codes [Roca17] since an isolated lost latency compared to block codes [Roca17] since an isolated lost
source packet is quickly recovered with the following repair packet. source packet is quickly recovered with the following repair packet.
On the opposite, with a block code, recovering an isolated lost On the opposite, with a block code, recovering an isolated lost
source packet always requires waiting for the first repair packet to source packet always requires waiting for the first repair packet to
arrive after the end of the block. Additionally, under certain arrive after the end of the block. Additionally, under certain
situations (e.g., with a limited FEC-related latency budget and with situations (e.g., with a limited FEC-related latency budget and with
constant bitrate transmissions after FECFRAME encoding), sliding constant bitrate transmissions after FECFRAME encoding), sliding
window codes can more efficiently achieve a target transmission window codes can more efficiently achieve a target transmission
quality (e.g., measured by the residual loss after FEC decoding) by quality (e.g., measured by the residual loss after FEC decoding) by
skipping to change at page 5, line 45 skipping to change at page 6, line 7
in the linear combination are not individually listed in the repair in the linear combination are not individually listed in the repair
packet header. Instead, each FEC Repair Packet header contains: packet header. Instead, each FEC Repair Packet header contains:
o the Encoding Symbol Identifier (ESI) of the first source symbol in o the Encoding Symbol Identifier (ESI) of the first source symbol in
the encoding window as well as the number of symbols (since this the encoding window as well as the number of symbols (since this
number may vary with a variable size, elastic window). These two number may vary with a variable size, elastic window). These two
pieces of information enable each receiver to reconstruct the set pieces of information enable each receiver to reconstruct the set
of source symbols considered during encoding, the only constraint of source symbols considered during encoding, the only constraint
being that there cannot be any gap; being that there cannot be any gap;
o the seed and density threshold parameters used by a coding o the seed and density threshold parameters used by a coding
coefficients generation function (Section 3.5). These two pieces coefficients generation function (Section 3.6). These two pieces
of information enable each receiver to generate the same set of of information enable each receiver to generate the same set of
coding coefficients over GF(2^^m) as the sender; coding coefficients over GF(2^^m) as the sender;
Therefore, no matter the number of source symbols present in the Therefore, no matter the number of source symbols present in the
encoding window, each FEC Repair Packet features a fixed 64-bit long encoding window, each FEC Repair Packet features a fixed 64-bit long
header, called Repair FEC Payload ID (Figure 7). Similarly, each FEC header, called Repair FEC Payload ID (Figure 8). Similarly, each FEC
Source Packet features a fixed 32-bit long trailer, called Explicit Source Packet features a fixed 32-bit long trailer, called Explicit
Source FEC Payload ID (Figure 5), that contains the ESI of the first Source FEC Payload ID (Figure 6), that contains the ESI of the first
source symbol (Section 3.2). source symbol (Section 3.2).
1.4. Document Organization 1.4. Document Organization
This fully-specified FEC Scheme follows the structure required by This fully-specified FEC Scheme follows the structure required by
[RFC6363], section 5.6. "FEC Scheme Requirements", namely: [RFC6363], section 5.6. "FEC Scheme Requirements", namely:
3. Procedures: This section describes procedures specific to this 3. Procedures: This section describes procedures specific to this
FEC Scheme, namely: RLC parameters derivation, ADUI and source FEC Scheme, namely: RLC parameters derivation, ADUI and source
symbols mapping, pseudo-random number generator, and coding symbols mapping, pseudo-random number generator, and coding
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In this document, m is equal to 1 or 8 In this document, m is equal to 1 or 8
ADU: Application Data Unit ADU: Application Data Unit
ADUI: Application Data Unit Information (includes the F, L and ADUI: Application Data Unit Information (includes the F, L and
padding fields in addition to the ADU) padding fields in addition to the ADU)
E: size of an encoding symbol (i.e., source or repair symbol), E: size of an encoding symbol (i.e., source or repair symbol),
assumed fixed (in bytes) assumed fixed (in bytes)
br_in: transmission bitrate at the input of the FECFRAME sender, br_in: transmission bitrate at the input of the FECFRAME sender,
assumed fixed (in bits/s) assumed fixed (in bits/s)
br_out: transmission bitrate at the output of the FECFRAME sender, br_out: transmission bitrate at the output of the FECFRAME sender,
assumed fixed (in bits/s) assumed fixed (in bits/s)
max_lat: maximum FEC-related latency within FECFRAME (in seconds) max_lat: maximum FEC-related latency within FECFRAME (a decimal
number expressed in seconds)
cr: RLC coding rate, ratio between the total number of source cr: RLC coding rate, ratio between the total number of source
symbols and the total number of source plus repair symbols symbols and the total number of source plus repair symbols
ew_size: encoding window current size at a sender (in symbols) ew_size: encoding window current size at a sender (in symbols)
ew_max_size: encoding window maximum size at a sender (in symbols) ew_max_size: encoding window maximum size at a sender (in symbols)
dw_max_size: decoding window maximum size at a receiver (in symbols) dw_max_size: decoding window maximum size at a receiver (in symbols)
ls_max_size: linear system maximum size (or width) at a receiver (in ls_max_size: linear system maximum size (or width) at a receiver (in
symbols) symbols)
WSR: window size ratio parameter used to derive ew_max_size
(encoder) and ls_max_size (decoder).
PRNG: pseudo-random number generator PRNG: pseudo-random number generator
tinymt32_rand(maxv): PRNG defined in Section 3.4 and used in this TinyMT32: PRNG defined in Section 3.5 and used in this
specification, that returns a new random integer in [0; maxv-1] specification.
DT: coding coefficients density threshold, an integer between 0 and DT: coding coefficients density threshold, an integer between 0 and
15 (inclusive) the controls the fraction of coefficients that are 15 (inclusive) the controls the fraction of coefficients that are
non zero non zero
3. Procedures 3. Common Procedures
This section introduces the procedures that are used by these FEC This section introduces the procedures that are used by these FEC
Schemes. Schemes.
3.1. Possible Parameter Derivations 3.1. Codec Parameters
The Sliding Window RLC FEC Scheme relies on several parameters: A codec implementing the Sliding Window RLC FEC Scheme relies on
several parameters:
Maximum FEC-related latency budget, max_lat (in seconds) with real- Maximum FEC-related latency budget, max_lat (a decimal number
time flows: expressed in seconds) with real-time flows:
a source ADU flow can have real-time constraints, and therefore a source ADU flow can have real-time constraints, and therefore
any FECFRAME related operation should take place within the any FECFRAME related operation should take place within the
validity period of each ADU (Appendix B describes an exception to validity period of each ADU (Appendix D describes an exception to
this rule). When there are multiple flows with different real- this rule). When there are multiple flows with different real-
time constraints, we consider the most stringent constraints (see time constraints, we consider the most stringent constraints (see
[RFC6363], Section 10.2, item 6, for recommendations when several [RFC6363], Section 10.2, item 6, for recommendations when several
flows are globally protected). The maximum FEC-related latency flows are globally protected). The maximum FEC-related latency
budget, max_lat, accounts for all sources of latency added by FEC budget, max_lat, accounts for all sources of latency added by FEC
encoding (at a sender) and FEC decoding (at a receiver). Other encoding (at a sender) and FEC decoding (at a receiver). Other
sources of latency (e.g., added by network communications) are out sources of latency (e.g., added by network communications) are out
of scope and must be considered separately (said differently, they of scope and must be considered separately (said differently, they
have already been deducted from max_lat). max_lat can be regarded have already been deducted from max_lat). max_lat can be regarded
as the latency budget permitted for all FEC-related operations. as the latency budget permitted for all FEC-related operations.
This is an input parameter that enables a FECFRAME sender to This is an input parameter that enables a FECFRAME sender to
derive other internal parameters as explained below; derive other internal parameters (see Appendix C);
Encoding window current (resp. maximum) size, ew_size (resp. Encoding window current (resp. maximum) size, ew_size (resp.
ew_max_size) (in symbols): ew_max_size) (in symbols):
at a FECFRAME sender, during FEC encoding, a repair symbol is at a FECFRAME sender, during FEC encoding, a repair symbol is
computed as a linear combination of the ew_size source symbols computed as a linear combination of the ew_size source symbols
present in the encoding window. The ew_max_size is the maximum present in the encoding window. The ew_max_size is the maximum
size of this window, while ew_size is the current size. For size of this window, while ew_size is the current size. For
instance, at session start, upon receiving new source ADUs, the instance, at session start, upon receiving new source ADUs, the
ew_size progressively increases until it reaches its maximum ew_size progressively increases until it reaches its maximum
value, ew_max_size. We have: value, ew_max_size. We have:
skipping to change at page 8, line 18 skipping to change at page 8, line 32
or lost source symbols that are still within their latency budget; or lost source symbols that are still within their latency budget;
Linear system maximum size, ls_max_size (in symbols): at a FECFRAME Linear system maximum size, ls_max_size (in symbols): at a FECFRAME
receiver, the linear system maximum size, ls_max_size, is the receiver, the linear system maximum size, ls_max_size, is the
maximum number of received or lost source symbols in the linear maximum number of received or lost source symbols in the linear
system (i.e., the variables). It SHOULD NOT be smaller than system (i.e., the variables). It SHOULD NOT be smaller than
dw_max_size since it would mean that, even after receiving a dw_max_size since it would mean that, even after receiving a
sufficient number of FEC Repair Packets, a lost ADU may not be sufficient number of FEC Repair Packets, a lost ADU may not be
recovered just because the associated source symbols have been recovered just because the associated source symbols have been
prematurely removed from the linear system, which is usually prematurely removed from the linear system, which is usually
counter-productive. On the opposite, the linear system MAY grow counter-productive. On the opposite, the linear system MAY grow
beyond the dw_max_size (Appendix B); beyond the dw_max_size (Appendix D);
Symbol size, E (in bytes): the E parameter determines the source and Symbol size, E (in bytes): the E parameter determines the source and
repair symbol sizes (necessarily equal). This is an input repair symbol sizes (necessarily equal). This is an input
parameter that enables a FECFRAME sender to derive other internal parameter that enables a FECFRAME sender to derive other internal
parameters, as explained below. An implementation at a sender parameters, as explained below. An implementation at a sender
SHOULD fix the E parameter and communicate it as part of the FEC MUST fix the E parameter and MUST communicate it as part of the
Scheme-Specific Information (Section 4.1.1.2). FEC Scheme-Specific Information (Section 4.1.1.2).
Code rate, cr: The code rate parameter determines the amount of Code rate, cr: The code rate parameter determines the amount of
redundancy added to the flow. More precisely the cr is the ratio redundancy added to the flow. More precisely the cr is the ratio
between the total number of source symbols and the total number of between the total number of source symbols and the total number of
source plus repair symbols and by definition: 0 < cr <= 1. This source plus repair symbols and by definition: 0 < cr <= 1. This
is an input parameter that enables a FECFRAME sender to derive is an input parameter that enables a FECFRAME sender to derive
other internal parameters, as explained below. However there is other internal parameters, as explained below. However, there is
no need to communicate the cr parameter per see (it's not required no need to communicate the cr parameter per see (it's not required
to process a repair symbol at a receiver). This code rate to process a repair symbol at a receiver). This code rate
parameter can be static. However, in specific use-cases (e.g., parameter can be static. However, in specific use-cases (e.g.,
with unicast transmissions in presence of a feedback mechanism with unicast transmissions in presence of a feedback mechanism
that estimates the communication quality, out of scope of that estimates the communication quality, out of scope of
FECFRAME), the code rate may be adjusted dynamically. FECFRAME), the code rate may be adjusted dynamically.
The FEC Schemes can be used in various manners. They can be used to Appendix C proposes non normative technics to derive those
protect a source ADU flow having real-time constraints, or a non- parameters, depending on the use-case specificities.
realtime source ADU flow. The source ADU flow may be a Constant
Bitrate (CBR) or Variable BitRate (VBR) flow. The flow's minimum/
maximum bitrate might or might not be known. The FEC Schemes can
also be used over the Internet or over a CBR communication path. It
follows that the FEC Scheme parameters can be derived in different
ways, as described in the following sections.
3.1.1. Case of a CBR Real-Time Flow
In the following, we consider a real-time flow with max_lat latency
budget. The encoding symbol size, E, is constant. The code rate,
cr, is also constant, its value depending on the expected
communication loss model (this choice is out of scope of this
document).
In a first configuration, the source ADU flow bitrate at the input of
the FECFRAME sender is fixed and equal to br_in (in bits/s), and this
value is known by the FECFRAME sender. It follows that the
transmission bitrate at the output of the FECFRAME sender will be
higher, depending on the added repair flow overhead. In order to
comply with the maximum FEC-related latency budget, we have:
dw_max_size = (max_lat * br_in) / (8 * E)
In a second configuration, the FECFRAME sender generates a fixed
bitrate flow, equal to the CBR communication path bitrate equal to
br_out (in bits/s), and this value is known by the FECFRAME sender,
as in [Roca17]. The maximum source flow bitrate needs to be such
that, with the added repair flow overhead, the total transmission
bitrate remains inferior or equal to br_out. We have:
dw_max_size = (max_lat * br_out * cr) / (8 * E)
For decoding to be possible within the latency budget, it is required
that the encoding window maximum size be smaller than or at most
equal to the decoding window maximum size, the exact value having no
impact on the the FEC-related latency budget. For the FEC Schemes
specified in this document, in line with [Roca17], the ew_max_size
SHOULD be computed with:
ew_max_size = dw_max_size * 0.75
The ew_max_size is the main parameter at a FECFRAME sender. It is
RECOMMENDED to check that the ew_max_size value stays within
reasonnable bounds in order to avoid hazardous behaviours.
The dw_max_size is computed by a FECFRAME sender but not explicitly
communicated to a FECFRAME receiver. However a FECFRAME receiver can
easily evaluate the ew_max_size by observing the maximum Number of
Source Symbols (NSS) value contained in the Repair FEC Payload ID of
received FEC Repair Packets (Section 4.1.3). A receiver can then
easily compute dw_max_size:
dw_max_size = max_NSS_observed / 0.75
A receiver can then chose an appropriate linear system maximum size:
ls_max_size >= dw_max_size
It is good practice to use a larger value for ls_max_size as
explained in Appendix B, which does not impact maximum latency nor
interoperability. However the linear system size should not be too
large for practical reasons (e.g., in order to limit computation
complexity). It is RECOMMENDED to check that the ls_max_size value
stays within reasonnable bounds in order to avoid hazardous
behaviours.
The particular case of session start needs to be managed
appropriately. Here ew_size increases each time a new source ADU is
received by the FECFRAME sender, until it reaches the ew_max_size
value. A FECFRAME receiver SHOULD continuously observe the received
FEC Repair Packets, since the NSS value carried in the Repair FEC
Payload ID will increase too, and adjust its ls_max_size accordingly
if need be.
3.1.2. Other Types of Real-Time Flow
In other configurations, a real-time source ADU flow, with a max_lat
latency budget, features a variable bitrate (VBR). A first approach
consists in considering the smallest instantaneous bitrate of the
source ADU flow, when this parameter is known, and to reuse the
derivation of Section 3.1.1. Considering the smallest bitrate means
that the encoding window and decoding window maximum sizes estimation
are pessimistic: these windows have the smallest size required to
enable a decoding on-time at a FECFRAME receiver. If the
instantaneous bitrate is higher than this smallest bitrate, this
approach leads to an encoding window that is unnecessarily small,
which reduces robustness in front of long erasure bursts.
Another approach consists in using ADU timing information (e.g.,
using the timestamp field of an RTP packet header, or registering the
time upon receiving a new ADU). From the global FEC-related latency
budget the FECFRAME sender can derive a practical maximum latency
budget for encoding operations, max_lat_for_encoding. For the FEC
Schemes specified in this document, this latency budget SHOULD be
computed with:
max_lat_for_encoding = max_lat * 0.75
It follows that any source symbols associated to an ADU that has
timed-out with respect to max_lat_for_encoding SHOULD be removed from
the encoding window. With this approach there is no pre-determined
ew_size value: this value fluctuates over the time according to the
instantaneous source ADU flow bitrate. For practical reasons, a
FECFRAME sender may still require that ew_size does not increase
beyond a maximum value (Section 3.1.3).
With both approaches, and no matter the choice of the FECFRAME
sender, a FECFRAME receiver can still easily evaluate the ew_max_size
by observing the maximum Number of Source Symbols (NSS) value
contained in the Repair FEC Payload ID of received FEC Repair
Packets. A receiver can then compute dw_max_size and derive an
appropriate ls_max_size as explained in Section 3.1.1.
When the observed NSS fluctuates significantly, a FECFRAME receiver
may want to adapt its ls_max_size accordingly. In particular when
the NSS is significantly reduced, a FECFRAME receiver may want to
reduce the ls_max_size too in order to limit computation complexity.
However it is usually preferable to use a ls_max_size "too large"
(which can increase computation complexity and memory requirements)
than the opposite (which can reduce recovery performance).
Beyond these general guidelines, the details of how to manage these
situations at a FECFRAME sender and receiver can depend on additional
considerations that are out of scope of this document.
3.1.3. Case of a Non Real-Time Flow
Finally there are configurations where a source ADU flow has no real-
time constraints. FECFRAME and the FEC Schemes defined in this
document can still be used. The choice of appropriate parameter
values can be directed by practical considerations. For instance it
can derive from an estimation of the maximum memory amount that could
be dedicated to the linear system at a FECFRAME receiver, or the
maximum computation complexity at a FECFRAME receiver, both of them
depending on the ls_max_size parameter. The same considerations also
apply to the FECFRAME sender, where the maximum memory amount and
computation complexity depend on the ew_max_size parameter.
Here also, the NSS value contained in FEC Repair Packets is used by a
FECFRAME receiver to determine the current coding window size and
ew_max_size by observing its maximum value over the time.
Beyond these general guidelines, the details of how to manage these
situations at a FECFRAME sender and receiver can depend on additional
considerations that are out of scope of this document.
3.2. ADU, ADUI and Source Symbols Mappings 3.2. ADU, ADUI and Source Symbols Mappings
At a sender, an ADU coming from the application cannot directly be At a sender, an ADU coming from the application is not directly
mapped to source symbols. When multiple source flows (e.g., media mapped to source symbols. When multiple source flows (e.g., media
streams) are mapped onto the same FECFRAME instance, each flow is streams) are mapped onto the same FECFRAME instance, each flow is
assigned its own Flow ID value (see below). At a sender, this assigned its own Flow ID value (see below). This Flow ID is then
identifier is prepended to each ADU before FEC encoding. This way, prepended to each ADU before FEC encoding. This way, FEC decoding at
FEC decoding at a receiver also recovers this Flow ID and a recovered a receiver also recovers this Flow ID and the recovered ADU can be
ADU can be assigned to the right source flow (note that transport assigned to the right source flow (note that the 5-tuple used to
port numbers and IP addresses cannot be used to that purpose as they identify the right source flow of a received ADU is absent with a
are not recovered during FEC decoding). recovered ADU since it is not FEC protected).
Additionally, since ADUs are of variable size, padding is needed so Additionally, since ADUs are of variable size, padding is needed so
that each ADU (with its flow identifier) contribute to an integral that each ADU (with its flow identifier) contribute to an integral
number of source symbols. This requires adding the original ADU number of source symbols. This requires adding the original ADU
length to each ADU before doing FEC encoding. Because of these length to each ADU before doing FEC encoding. Because of these
requirements, an intermediate format, the ADUI, or ADU Information, requirements, an intermediate format, the ADUI, or ADU Information,
is considered [RFC6363]. is considered [RFC6363].
For each incoming ADU, an ADUI MUST created as follows. First of For each incoming ADU, an ADUI MUST created as follows. First of
all, 3 bytes are prepended (Figure 1): all, 3 bytes are prepended (Figure 1):
skipping to change at page 12, line 36 skipping to change at page 9, line 48
fields. fields.
Then, zero padding is added to the ADU if needed: Then, zero padding is added to the ADU if needed:
Padding (Pad) (variable size field): this field contains zero Padding (Pad) (variable size field): this field contains zero
padding to align the F, L, ADU and padding up to a size that is padding to align the F, L, ADU and padding up to a size that is
multiple of E bytes (i.e., the source and repair symbol length). multiple of E bytes (i.e., the source and repair symbol length).
The data unit resulting from the ADU and the F, L, and Pad fields is The data unit resulting from the ADU and the F, L, and Pad fields is
called ADUI. Since ADUs can have different sizes, this is also the called ADUI. Since ADUs can have different sizes, this is also the
case for ADUIs. However an ADUI always contributes to an integral case for ADUIs. However, an ADUI always contributes to an integral
number of source symbols. number of source symbols.
symbol length, E E E symbol length, E E E
< ------------------ >< ------------------ >< ------------------ > < ------------------ >< ------------------ >< ------------------ >
+-+--+---------------------------------------------+-------------+ +-+--+---------------------------------------------+-------------+
|F| L| ADU | Pad | |F| L| ADU | Pad |
+-+--+---------------------------------------------+-------------+ +-+--+---------------------------------------------+-------------+
Figure 1: ADUI Creation example (here 3 source symbols are created Figure 1: ADUI Creation example (here 3 source symbols are created
for this ADUI). for this ADUI).
skipping to change at page 13, line 25 skipping to change at page 10, line 39
ew_max_size. In that case the oldest symbol MUST be removed ew_max_size. In that case the oldest symbol MUST be removed
before adding a new symbol, so that the current encoding window before adding a new symbol, so that the current encoding window
size always remains inferior or equal to the maximum size: ew_size size always remains inferior or equal to the maximum size: ew_size
<= ew_max_size; <= ew_max_size;
o when an ADU has reached its maximum validity duration in case of a o when an ADU has reached its maximum validity duration in case of a
real-time flow. When this happens, all source symbols real-time flow. When this happens, all source symbols
corresponding to the ADUI that expired SHOULD be removed from the corresponding to the ADUI that expired SHOULD be removed from the
encoding window; encoding window;
Source symbols are added to the sliding encoding window each time a Source symbols are added to the sliding encoding window each time a
new ADU arrives, once the ADU to source symbols mapping has been new ADU arrives, once the ADU-to-source symbols mapping has been
performed (Section 3.2). The current size of the encoding window, performed (Section 3.2). The current size of the encoding window,
ew_size, is updated after adding new source symbols. This process ew_size, is updated after adding new source symbols. This process
may require to remove old source symbols so that: ew_size <= may require to remove old source symbols so that: ew_size <=
ew_max_size. ew_max_size.
Note that a FEC codec may feature practical limits in the number of Note that a FEC codec may feature practical limits in the number of
source symbols in the encoding window (e.g., for computational source symbols in the encoding window (e.g., for computational
complexity reasons). This factor may further limit the ew_max_size complexity reasons). This factor may further limit the ew_max_size
value, in addition to the maximum FEC-related latency budget value, in addition to the maximum FEC-related latency budget
(Section 3.1). (Section 3.1).
3.4. Pseudo-Random Number Generator (PRNG) 3.4. Source Symbol Identification
The RLC FEC Schemes defined in this document rely on the TinyMT32 Each source symbol is identified by an Encoding Symbol ID (ESI), an
PRNG, a small-sized variant of the Mersenne Twister PRNG, as defined unsigned integer. The ESI of source symbols MUST start with value 0
in the reference implementation version 1.1 (2015/04/24) by Mutsuo for the first source symbol and MUST be managed sequentially.
Saito (Hiroshima University) and Makoto Matsumoto (The University of Wrapping to zero happens after reaching the maximum value made
possible by the ESI field size (this maximum value is FEC Scheme
dependant, for instance, 2^32-1 with FEC Schemes XXX and YYY).
No such consideration applies to repair symbols.
3.5. Pseudo-Random Number Generator (PRNG)
In order to compute coding coefficients (see Section 3.6), the RLC
FEC Schemes defined in this document rely on the TinyMT32 PRNG (a
small-sized variant of the Mersenne Twister PRNG), as defined in the
reference implementation version 1.1 (2015/04/24) by Mutsuo Saito
(Hiroshima University) and Makoto Matsumoto (The University of
Tokyo). Tokyo).
o Official web site: <http://www.math.sci.hiroshima-u.ac.jp/~m- o Official web site: <http://www.math.sci.hiroshima-u.ac.jp/~m-
mat/MT/TINYMT/> mat/MT/TINYMT/>
o Official github site and reference implementation: o Official github site and reference implementation:
<https://github.com/MersenneTwister-Lab/TinyMT> <https://github.com/MersenneTwister-Lab/TinyMT>
For the RLC FEC Schemes defined in this document, the tinymt32 32-bit For the RLC FEC Schemes defined in this document, the TinyMT32 32-bit
version (rather than the 64-bit version) MUST be used. This PRNG version (rather than the 64-bit version) MUST be used. This PRNG
requires a parameter set that needs to be pre-calculated. For the requires a parameter set that needs to be pre-calculated. For the
RLC FEC Schemes defined in this document, the following parameter set RLC FEC Schemes defined in this document, the following parameter set
MUST be used: MUST be used:
o mat1 = 0x8f7011ee = 2406486510; o mat1 = 0x8f7011ee = 2406486510
o mat2 = 0xfc78ff1f = 4235788063; o mat2 = 0xfc78ff1f = 4235788063
o tmat = 0x3793fdff = 932445695. o tmat = 0x3793fdff = 932445695
This parameter set is the first entry of the precalculated parameter This parameter set is the first entry of the precalculated parameter
sets in file tinymt32dc.0.1048576.txt, by Kenji Rikitake, and sets in file tinymt32dc.0.1048576.txt, by Kenji Rikitake, and
available at: available at <https://github.com/jj1bdx/tinymtdc-
longbatch/blob/master/tinymt32dc/tinymt32dc.0.1048576.txt>. This is
o <https://github.com/jj1bdx/tinymtdc- also the parameter set used in [KR12].
longbatch/blob/master/tinymt32dc/tinymt32dc.0.1048576.txt>.
This is also the parameter set used in [KR12].
The PRNG reference implementation is distributed under a BSD license
and excerpts of it are reproduced in Appendix A. In order to
validate an implementation of this PRNG, using seed 1, the 10,000th
value returned by: tinymt32_rand(s, 0xffff) MUST be equal to 0x7c37.
This PRNG MUST first be initialized with a 32-bit unsigned integer, This PRNG MUST first be initialized with a 32-bit unsigned integer,
used as a seed. The following function is used to this purpose: used as a seed. The following function is used to this purpose:
void tinymt32_init (tinymt32_t * s, uint32_t seed); void tinymt32_init (tinymt32_t * s, uint32_t seed);
With the FEC Schemes defined in this document, the seed is in With the FEC Schemes defined in this document, the seed is in
practice restricted to a value between 0 and 0xFFFF inclusive (note practice restricted to a value between 0 and 0xFFFF inclusive (note
that this PRNG accepts a seed equal to 0), since this is the that this PRNG accepts a seed value equal to 0), since this is the
Repair_Key 16-bit field value of the Repair FEC Payload ID Repair_Key 16-bit field value of the Repair FEC Payload ID
(Section 4.1.3). In addition to the seed, this function takes as (Section 4.1.3). In addition to the seed, this function takes as
parameter a pointer to an instance of a tinymt32_t structure that is parameter a pointer to an instance of a tinymt32_t structure that is
used to keep the internal state of the PRNG. used to keep the internal state of the PRNG.
Then, each time a new pseudo-random integer between 0 and maxv-1 Then, each time a new pseudo-random integer between 0 and 15
inclusive is needed, the following function is used: inclusive (4-bit pseudo-random integer) is needed, the following
function is used:
uint32_t tinymt32_rand (tinymt32_t * s, uint32_t maxv); uint32_t tinymt32_rand16 (tinymt32_t * s);
This function takes as parameter both a pointer to the same This function takes as parameter a pointer to the same tinymt32_t
tinymt32_t structure (that needs to be left unchanged between structure (that needs to be left unchanged between successive calls
successive calls to the function) and the maxv value. to the function). Similarly, each time a new pseudo-random integer
between 0 and 255 inclusive (8-bit pseudo-random integer) is needed,
the following function is used:
3.5. Coding Coefficients Generation Function uint32_t tinymt32_rand256 (tinymt32_t * s);
These two functions keep respectively the 4 or 8 less significant
bits of the 32-bit pseudo-random number generated by the
tinymt32_generate_uint32() TinyMT32 function. Test results discussed
in Appendix B show that this simple technique, applied to this PRNG,
is in line with the RLC FEC Schemes needs.
The TinyMT32 PRNG reference implementation is reproduced in Figure 2,
with the following differences with respect to the original source
code:
o the source code initially spread over the tinymt32.h and
tinymt32.c files has been merged;
o the unused parts of the original source code have been removed;
o the unused constants TINYMT32_MEXP and TINYMT32_MUL have been
removed;
o the appropriate parameter set has been added to the initialization
function;
o the function order has been changed;
o certain internal variables have been renamed for compactness
purposes;
o the constant definitions use the const qualifier;
o the tinymt32_rand16() and tinymt32_rand256() functions have been
added in order to scale the initial 32-bit value over a smaller
interval;
o the IETF Trusteed copyright has been added to this derived work.
<CODE BEGINS>
/**
* Tiny Mersenne Twister only 127 bit internal state
*
* Authors : Mutsuo Saito (Hiroshima University)
* Makoto Matsumoto (University of Tokyo)
*
* Copyright (c) 2011, 2013 Mutsuo Saito, Makoto Matsumoto,
* Hiroshima University and The University of Tokyo.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials
* provided with the distribution.
* - Neither the name of the Hiroshima University nor the names of
* its contributors may be used to endorse or promote products
* derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
* TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
* TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
* THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
/**
* The derived work of this document is:
* Copyright (c) 2018 IETF Trust and the persons identified as the
* document authors. All rights reserved.
*/
#include <stdint.h>
/**
* tinymt32 internal state vector and parameters
*/
typedef struct {
uint32_t status[4];
uint32_t mat1;
uint32_t mat2;
uint32_t tmat;
} tinymt32_t;
static void tinymt32_next_state (tinymt32_t * s);
static uint32_t tinymt32_temper (tinymt32_t * s);
static uint32_t tinymt32_generate_uint32 (tinymt32_t * s);
/**
* Parameter set to use for the IETF RLC FEC Schemes specification.
* Do not change.
* This parameter set is the first entry of the precalculated
* parameter sets in file tinymt32dc.0.1048576.txt, by Kenji
* Rikitake, available at:
* https://github.com/jj1bdx/tinymtdc-longbatch/blob/master/
* tinymt32dc/tinymt32dc.0.1048576.txt
* It is also the parameter set used:
* Rikitake, K., "TinyMT Pseudo Random Number Generator for
* Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
* September, 2012.
*/
const uint32_t TINYMT32_MAT1_PARAM = UINT32_C(0x8f7011ee);
const uint32_t TINYMT32_MAT2_PARAM = UINT32_C(0xfc78ff1f);
const uint32_t TINYMT32_TMAT_PARAM = UINT32_C(0x3793fdff);
/**
* This function initializes the internal state array with a 32-bit
* unsigned integer seed.
* @param s pointer to tinymt internal state.
* @param seed a 32-bit unsigned integer used as a seed.
*/
void tinymt32_init (tinymt32_t * s, uint32_t seed)
{
const uint32_t MIN_LOOP = 8;
const uint32_t PRE_LOOP = 8;
s->status[0] = seed;
s->status[1] = s->mat1 = TINYMT32_MAT1_PARAM;
s->status[2] = s->mat2 = TINYMT32_MAT2_PARAM;
s->status[3] = s->tmat = TINYMT32_TMAT_PARAM;
for (int i = 1; i < MIN_LOOP; i++) {
s->status[i & 3] ^= i + UINT32_C(1812433253)
* (s->status[(i - 1) & 3]
^ (s->status[(i - 1) & 3] >> 30));
}
for (int i = 0; i < PRE_LOOP; i++) {
tinymt32_next_state(s);
}
}
/**
* This function outputs a pseudo-random integer in [0 .. 15] range.
*
* @param s pointer to tinymt internal state.
* @return unsigned integer between 0 and 15 inclusive.
*/
uint32_t tinymt32_rand16(tinymt32_t *s)
{
return (tinymt32_generate_uint32(s) & 0xF);
}
/**
* This function outputs a pseudo-random integer in [0 .. 255] range.
*
* @param s pointer to tinymt internal state.
* @return unsigned integer between 0 and 255 inclusive.
*/
uint32_t tinymt32_rand256(tinymt32_t *s)
{
return (tinymt32_generate_uint32(s) & 0xFF);
}
/**
* Internal tinymt32 constants and functions.
* Users should not call these functions directly.
*/
const uint32_t TINYMT32_SH0 = 1;
const uint32_t TINYMT32_SH1 = 10;
const uint32_t TINYMT32_SH8 = 8;
const uint32_t TINYMT32_MASK = UINT32_C(0x7fffffff);
/**
* This function changes internal state of tinymt32.
* @param s pointer to tinymt internal state.
*/
static void tinymt32_next_state (tinymt32_t * s)
{
uint32_t x;
uint32_t y;
y = s->status[3];
x = (s->status[0] & TINYMT32_MASK)
^ s->status[1]
^ s->status[2];
x ^= (x << TINYMT32_SH0);
y ^= (y >> TINYMT32_SH0) ^ x;
s->status[0] = s->status[1];
s->status[1] = s->status[2];
s->status[2] = x ^ (y << TINYMT32_SH1);
s->status[3] = y;
s->status[1] ^= -((int32_t)(y & 1)) & s->mat1;
s->status[2] ^= -((int32_t)(y & 1)) & s->mat2;
}
/**
* This function outputs 32-bit unsigned integer from internal state.
* @param s pointer to tinymt internal state.
* @return 32-bit unsigned pseudos number
*/
static uint32_t tinymt32_temper (tinymt32_t * s)
{
uint32_t t0, t1;
t0 = s->status[3];
t1 = s->status[0] + (s->status[2] >> TINYMT32_SH8);
t0 ^= t1;
t0 ^= -((int32_t)(t1 & 1)) & s->tmat;
return t0;
}
/**
* This function outputs 32-bit unsigned integer from internal state.
* @param s pointer to tinymt internal state.
* @return 32-bit unsigned integer r (0 <= r < 2^32)
*/
static uint32_t tinymt32_generate_uint32 (tinymt32_t * s) {
tinymt32_next_state(s);
return tinymt32_temper(s);
}
<CODE ENDS>
Figure 2: TinyMT32 Reference Implementation
In addition to that, any implementation of this TinyMT32 PRNG MUST
fulfill three validation criteria detailed in Appendix A. These
criteria consist in several random number sequences that MUST be
matched. The first criteria focusses on the internal TinyMT32
unsigned 32-bit integer generator, the two others include the mapping
to 4-bit and 8-bit intervals.
Finally, the deterministic behavior of the implementation of Figure 2
has been checked across several platforms, from high-end 64-bit Mac
OSX and Linux/Ubuntu laptops, to various low-end embedded cards based
on 32-bit, 16-bit and 8-bit microcontrollers running RIOT
[Baccelli18] (details in Appendix A).
3.6. Coding Coefficients Generation Function
The coding coefficients, used during the encoding process, are The coding coefficients, used during the encoding process, are
generated at the RLC encoder by the generate_coding_coefficients() generated at the RLC encoder by the generate_coding_coefficients()
function each time a new repair symbol needs to be produced. The function each time a new repair symbol needs to be produced. The
fraction of coefficients that are non zero (i.e., the density) is fraction of coefficients that are non zero (i.e., the density) is
controlled by the DT (Density Threshold) parameter. When DT equals controlled by the DT (Density Threshold) parameter. DT has values
15, the maximum value, the function guaranties that all coefficients between 0 (the minimum value) and 15 (the maximum value), and the
are non zero (i.e., maximum density). When DT is between 0 (minimum average probability of having a non zero coefficient equals (DT + 1)
value) and strictly inferior to 15, the average probability of having / 16. In particular, when DT equals 15 the function guaranties that
a non zero coefficient equals (DT +1) / 16. all coefficients are non zero (i.e., maximum density).
These considerations apply both the RLC over GF(2) and RLC over These considerations apply to both the RLC over GF(2) and RLC over
GF(2^^8), the only difference being the value of the m parameter. GF(2^^8), the only difference being the value of the m parameter.
With the RLC over GF(2) FEC Scheme (Section 5), m MUST be equal to 1. With the RLC over GF(2) FEC Scheme (Section 5), m is equal to 1.
With RLC over GF(2^^8) FEC Scheme (Section 4), m MUST be equal to 8. With RLC over GF(2^^8) FEC Scheme (Section 4), m is equal to 8.
<CODE BEGINS> <CODE BEGINS>
/* /*
* Fills in the table of coding coefficients (of the right size) * Fills in the table of coding coefficients (of the right size)
* provided with the appropriate number of coding coefficients to * provided with the appropriate number of coding coefficients to
* use for the repair symbol key provided. * use for the repair symbol key provided.
* *
* (in) repair_key key associated to this repair symbol. This * (in) repair_key key associated to this repair symbol. This
* parameter is ignored (useless) if m=2 and dt=15 * parameter is ignored (useless) if m=1 and dt=15
* (in) cc_tab[] pointer to a table of the right size to store * (in/out) cc_tab[] pointer to a table of the right size to store
* coding coefficients. All coefficients are * coding coefficients. All coefficients are
* stored as bytes, regardless of the m parameter, * stored as bytes, regardless of the m parameter,
* upon return of this function. * upon return of this function.
* (in) cc_nb number of entries in the table. This value is * (in) cc_nb number of entries in the table. This value is
* equal to the current encoding window size. * equal to the current encoding window size.
* (in) dt integer between 0 and 15 (inclusive) that * (in) dt integer between 0 and 15 (inclusive) that
* controls the density. With value 15, all * controls the density. With value 15, all
* coefficients are guaranteed to be non zero * coefficients are guaranteed to be non zero
* (i.e. equal to 1 with GF(2) and equal to a * (i.e. equal to 1 with GF(2) and equal to a
* value in {1,... 255} with GF(2^^8)), otherwise * value in {1,... 255} with GF(2^^8)), otherwise
* a fraction of them will be 0. * a fraction of them will be 0.
* (in) m Finite Field GF(2^^m) parameter. In this * (in) m Finite Field GF(2^^m) parameter. In this
* document only values 1 and 8 are considered. * document only values 1 and 8 are considered.
* (out) returns an error code * (out) returns 0 in case of success, an error code
* different than 0 otherwise.
*/ */
int generate_coding_coefficients (uint16_t repair_key, int generate_coding_coefficients (uint16_t repair_key,
uint8_t cc_tab[], uint8_t cc_tab[],
uint16_t cc_nb, uint16_t cc_nb,
uint8_t dt, uint8_t dt,
uint8_t m) uint8_t m)
{ {
uint32_t i; uint32_t i;
tinymt32_t s; /* PRNG internal state */ tinymt32_t s; /* PRNG internal state */
if (dt > 15) { if (dt > 15) {
return SOMETHING_WENT_WRONG; /* bad dt parameter */ return -1; /* error, bad dt parameter */
} }
switch (m) { switch (m) {
case 1: case 1:
if (dt == 15) { if (dt == 15) {
/* all coefficients are 1 */ /* all coefficients are 1 */
memset(cc_tab, 1, cc_nb); memset(cc_tab, 1, cc_nb);
} else { } else {
/* here coefficients are either 0 or 1 */ /* here coefficients are either 0 or 1 */
tinymt32_init(&s, repair_key); tinymt32_init(&s, repair_key);
for (i = 0 ; i < cc_nb ; i++) { for (i = 0 ; i < cc_nb ; i++) {
if (tinymt32_rand(&s, 16) <= dt) { cc_tab[i] = (tinymt32_rand16(&s) <= dt) ? 1 : 0;
cc_tab[i] = (uint8_t) 1;
} else {
cc_tab[i] = (uint8_t) 0;
}
} }
} }
break; break;
case 8: case 8:
tinymt32_init(&s, repair_key); tinymt32_init(&s, repair_key);
if (dt == 15) { if (dt == 15) {
/* coefficient 0 is avoided here in order to include /* coefficient 0 is avoided here in order to include
* all the source symbols */ * all the source symbols */
for (i = 0 ; i < cc_nb ; i++) { for (i = 0 ; i < cc_nb ; i++) {
do { do {
cc_tab[i] = (uint8_t) tinymt32_rand(&s, 256); cc_tab[i] = (uint8_t) tinymt32_rand256(&s);
} while (cc_tab[i] == 0); } while (cc_tab[i] == 0);
} }
} else { } else {
/* here a certain fraction of coefficients should be 0 */ /* here a certain number of coefficients should be 0 */
for (i = 0 ; i < cc_nb ; i++) { for (i = 0 ; i < cc_nb ; i++) {
if (tinymt32_rand(&s, 16) <= dt) { if (tinymt32_rand16(&s) <= dt) {
do { do {
cc_tab[i] = (uint8_t) tinymt32_rand(&s, 256); cc_tab[i] = (uint8_t) tinymt32_rand256(&s);
} while (cc_tab[i] == 0); } while (cc_tab[i] == 0);
} else { } else {
cc_tab[i] = 0; cc_tab[i] = 0;
} }
} }
} }
break; break;
default: default:
return -2; /* error, bad parameter m */
/* bad parameter m */
return SOMETHING_WENT_WRONG;
} }
return EVERYTHING_IS_OKAY; return 0 /* success */
} }
<CODE ENDS> <CODE ENDS>
Figure 2: Coding Coefficients Generation Function pseudo-code Figure 3: Coding Coefficients Generation Function Reference
Implementation
3.6. Finite Fields Operations 3.7. Finite Fields Operations
3.6.1. Finite Field Definitions 3.7.1. Finite Field Definitions
The two RLC FEC Schemes specified in this document reuse the Finite The two RLC FEC Schemes specified in this document reuse the Finite
Fields defined in [RFC5510], section 8.1. More specifically, the Fields defined in [RFC5510], section 8.1. More specifically, the
elements of the field GF(2^^m) are represented by polynomials with elements of the field GF(2^^m) are represented by polynomials with
binary coefficients (i.e., over GF(2)) and degree lower or equal to binary coefficients (i.e., over GF(2)) and degree lower or equal to
m-1. The addition between two elements is defined as the addition of m-1. The addition between two elements is defined as the addition of
binary polynomials in GF(2), which is equivalent to a bitwise XOR binary polynomials in GF(2), which is equivalent to a bitwise XOR
operation on the binary representation of these elements. operation on the binary representation of these elements.
With GF(2^^8), multiplication between two elements is the With GF(2^^8), multiplication between two elements is the
multiplication modulo a given irreducible polynomial of degree 8. multiplication modulo a given irreducible polynomial of degree 8.
The following irreducible polynomial MUST be used for GF(2^^8): The following irreducible polynomial MUST be used for GF(2^^8):
x^^8 + x^^4 + x^^3 + x^^2 + 1 x^^8 + x^^4 + x^^3 + x^^2 + 1
With GF(2), multiplication corresponds to a logical AND operation. With GF(2), multiplication corresponds to a logical AND operation.
3.6.2. Linear Combination of Source Symbols Computation 3.7.2. Linear Combination of Source Symbols Computation
The two RLC FEC Schemes require the computation of a linear The two RLC FEC Schemes require the computation of a linear
combination of source symbols, using the coding coefficients produced combination of source symbols, using the coding coefficients produced
by the generate_coding_coefficients() function and stored in the by the generate_coding_coefficients() function and stored in the
cc_tab[] array. cc_tab[] array.
With the RLC over GF(2^^8) FEC Scheme, a linear combination of the With the RLC over GF(2^^8) FEC Scheme, a linear combination of the
ew_size source symbol present in the encoding window, say src_0 to ew_size source symbol present in the encoding window, say src_0 to
src_ew_size_1, in order to generate a repair symbol, is computed as src_ew_size_1, in order to generate a repair symbol, is computed as
follows. For each byte of position i in each source and the repair follows. For each byte of position i in each source and the repair
symbol, where i belongs to {0; E-1}, compute: symbol, where i belongs to {0; E-1}, compute:
repair[i] = cc_tab[0] * src_0[i] + cc_tab[1] * src_1[i] + ... + repair[i] = cc_tab[0] * src_0[i] XOR cc_tab[1] * src_1[i] XOR ...
cc_tab[ew_size - 1] * src_ew_size_1[i] XOR cc_tab[ew_size - 1] * src_ew_size_1[i]
where * is the multiplication over GF(2^^8) and + is an XOR where * is the multiplication over GF(2^^8). In practice various
operation. In practice various optimizations need to be used in optimizations need to be used in order to make this computation
order to make this computation efficient (see in particular [PGM13]). efficient (see in particular [PGM13]).
With the RLC over GF(2) FEC Scheme (binary case), a linear With the RLC over GF(2) FEC Scheme (binary case), a linear
combination is computed as follows. The repair symbol is the XOR sum combination is computed as follows. The repair symbol is the XOR sum
of all the source symbols corresponding to a coding coefficient of all the source symbols corresponding to a coding coefficient
cc_tab[j] equal to 1 (i.e., the source symbols corresponding to zero cc_tab[j] equal to 1 (i.e., the source symbols corresponding to zero
coding coefficients are ignored). The XOR sum of the byte of coding coefficients are ignored). The XOR sum of the byte of
position i in each source is computed and stored in the corresponding position i in each source is computed and stored in the corresponding
byte of the repair symbol, where i belongs to {0; E-1}. In practice, byte of the repair symbol, where i belongs to {0; E-1}. In practice,
the XOR sums will be computed several bytes at a time (e.g., on 64 the XOR sums will be computed several bytes at a time (e.g., on 64
bit words, or on arrays of 16 or more bytes when using SIMD CPU bit words, or on arrays of 16 or more bytes when using SIMD CPU
skipping to change at page 19, line 4 skipping to change at page 21, line 12
When SDP is used to communicate the FFCI, this FEC Encoding ID is When SDP is used to communicate the FFCI, this FEC Encoding ID is
carried in the 'encoding-id' parameter. carried in the 'encoding-id' parameter.
4.1.1.2. FEC Scheme-Specific Information 4.1.1.2. FEC Scheme-Specific Information
The FEC Scheme-Specific Information (FSSI) includes elements that are The FEC Scheme-Specific Information (FSSI) includes elements that are
specific to the present FEC Scheme. More precisely: specific to the present FEC Scheme. More precisely:
Encoding symbol size (E): a non-negative integer that indicates the Encoding symbol size (E): a non-negative integer that indicates the
size of each encoding symbol in bytes; size of each encoding symbol in bytes;
Window Size Ratio (WSR) parameter: a non-negative integer between 0
and 255 (both inclusive) used to initialize window sizes. A value
of 0 indicates this parameter is not considered (e.g., a fixed
encoding window size may be chosen). A value between 1 and 255
inclusive is required by certain of the parameter derivation
techniques described in Appendix C;
This element is required both by the sender (RLC encoder) and the This element is required both by the sender (RLC encoder) and the
receiver(s) (RLC decoder). receiver(s) (RLC decoder).
When SDP is used to communicate the FFCI, this FEC Scheme-specific When SDP is used to communicate the FFCI, this FEC Scheme-specific
information is carried in the 'fssi' parameter in textual information is carried in the 'fssi' parameter in textual
representation as specified in [RFC6364]. For instance: representation as specified in [RFC6364]. For instance:
fssi=E:1400 fssi=E:1400,WSR:191
In that case the name values "E" and "WSR" are used to convey the E
and WSR parameters respectively.
If another mechanism requires the FSSI to be carried as an opaque If another mechanism requires the FSSI to be carried as an opaque
octet string (for instance, after a Base64 encoding), the encoding octet string, the encoding format consists of the following three
format consists of the following 2 octets: octets, where the E field is carried in "big-endian" or "network
order" format, that is, most significant byte first:
Encoding symbol length (E): 16-bit field. Encoding symbol length (E): 16-bit field;
Window Size Ratio Parameter (WSR): 8-bit field.
0 1 These three octets can be communicated as such, or for instance, be
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 subject to an additional Base64 encoding.
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: FSSI Encoding Format 0 1 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) | WSR |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: FSSI Encoding Format
4.1.2. Explicit Source FEC Payload ID 4.1.2. Explicit Source FEC Payload ID
A FEC Source Packet MUST contain an Explicit Source FEC Payload ID A FEC Source Packet MUST contain an Explicit Source FEC Payload ID
that is appended to the end of the packet as illustrated in Figure 4. that is appended to the end of the packet as illustrated in Figure 5.
+--------------------------------+ +--------------------------------+
| IP Header | | IP Header |
+--------------------------------+ +--------------------------------+
| Transport Header | | Transport Header |
+--------------------------------+ +--------------------------------+
| ADU | | ADU |
+--------------------------------+ +--------------------------------+
| Explicit Source FEC Payload ID | | Explicit Source FEC Payload ID |
+--------------------------------+ +--------------------------------+
Figure 4: Structure of an FEC Source Packet with the Explicit Source Figure 5: Structure of an FEC Source Packet with the Explicit Source
FEC Payload ID FEC Payload ID
More precisely, the Explicit Source FEC Payload ID is composed of the More precisely, the Explicit Source FEC Payload ID is composed of the
following field (Figure 5): following field, carried in "big-endian" or "network order" format,
that is, most significant byte first (Figure 6):
Encoding Symbol ID (ESI) (32-bit field): this unsigned integer Encoding Symbol ID (ESI) (32-bit field): this unsigned integer
identifies the first source symbol of the ADUI corresponding to identifies the first source symbol of the ADUI corresponding to
this FEC Source Packet. The ESI is incremented for each new this FEC Source Packet. The ESI is incremented for each new
source symbol, and after reaching the maximum value (2^32-1), source symbol, and after reaching the maximum value (2^32-1),
wrapping to zero occurs. wrapping to zero occurs.
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol ID (ESI) | | Encoding Symbol ID (ESI) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: Source FEC Payload ID Encoding Format Figure 6: Source FEC Payload ID Encoding Format
4.1.3. Repair FEC Payload ID 4.1.3. Repair FEC Payload ID
A FEC Repair Packet MAY contain one or more repair symbols. When A FEC Repair Packet MAY contain one or more repair symbols. When
there are several repair symbols, all of them MUST have been there are several repair symbols, all of them MUST have been
generated from the same encoding window, using Repair_Key values that generated from the same encoding window, using Repair_Key values that
are managed as explained below. A receiver can easily deduce the are managed as explained below. A receiver can easily deduce the
number of repair symbols within a FEC Repair Packet by comparing the number of repair symbols within a FEC Repair Packet by comparing the
received FEC Repair Packet size (equal to the UDP payload size when received FEC Repair Packet size (equal to the UDP payload size when
UDP is the underlying transport protocol) and the symbol size, E, UDP is the underlying transport protocol) and the symbol size, E,
communicated in the FFCI. communicated in the FFCI.
A FEC Repair Packet MUST contain a Repair FEC Payload ID that is A FEC Repair Packet MUST contain a Repair FEC Payload ID that is
prepended to the repair symbol as illustrated in Figure 6. prepended to the repair symbol as illustrated in Figure 7.
+--------------------------------+ +--------------------------------+
| IP Header | | IP Header |
+--------------------------------+ +--------------------------------+
| Transport Header | | Transport Header |
+--------------------------------+ +--------------------------------+
| Repair FEC Payload ID | | Repair FEC Payload ID |
+--------------------------------+ +--------------------------------+
| Repair Symbol | | Repair Symbol |
+--------------------------------+ +--------------------------------+
Figure 6: Structure of an FEC Repair Packet with the Repair FEC Figure 7: Structure of an FEC Repair Packet with the Repair FEC
Payload ID Payload ID
More precisely, the Repair FEC Payload ID is composed of the More precisely, the Repair FEC Payload ID is composed of the
following fields (Figure 7): following fields where all integer fields are carried in "big-endian"
or "network order" format, that is, most significant byte first
(Figure 8):
Repair_Key (16-bit field): this unsigned integer is used as a seed Repair_Key (16-bit field): this unsigned integer is used as a seed
by the coefficient generation function (Section 3.5) in order to by the coefficient generation function (Section 3.6) in order to
generate the desired number of coding coefficients. When a FEC generate the desired number of coding coefficients. This repair
key may be a monotonically increasing integer value that loops
back to 0 after reaching 65535 (see Section 6.1). When a FEC
Repair Packet contains several repair symbols, this repair key Repair Packet contains several repair symbols, this repair key
value is that of the first repair symbol. The remaining repair value is that of the first repair symbol. The remaining repair
keys can be deduced by incrementing by 1 this value, up to a keys can be deduced by incrementing by 1 this value, up to a
maximum value of 65535 after which it loops back to 0. maximum value of 65535 after which it loops back to 0.
Density Threshold for the coding coefficients, DT (4-bit field): Density Threshold for the coding coefficients, DT (4-bit field):
this unsigned integer carries the Density Threshold (DT) used by this unsigned integer carries the Density Threshold (DT) used by
the coding coefficient generation function Section 3.5. More the coding coefficient generation function Section 3.6. More
precisely, it controls the probability of having a non zero coding precisely, it controls the probability of having a non zero coding
coefficient, which equals (DT+1) / 16. When a FEC Repair Packet coefficient, which equals (DT+1) / 16. When a FEC Repair Packet
contains several repair symbols, the DT value applies to all of contains several repair symbols, the DT value applies to all of
them; them;
Number of Source Symbols in the encoding window, NSS (12-bit field): Number of Source Symbols in the encoding window, NSS (12-bit field):
this unsigned integer indicates the number of source symbols in this unsigned integer indicates the number of source symbols in
the encoding window when this repair symbol was generated. When a the encoding window when this repair symbol was generated. When a
FEC Repair Packet contains several repair symbols, this NSS value FEC Repair Packet contains several repair symbols, this NSS value
applies to all of them; applies to all of them;
skipping to change at page 21, line 33 skipping to change at page 24, line 16
FSS_ESI value applies to all of them; FSS_ESI value applies to all of them;
0 1 2 3 0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Repair_Key | DT |NSS (# src symb in ew) | | Repair_Key | DT |NSS (# src symb in ew) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| FSS_ESI | | FSS_ESI |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: Repair FEC Payload ID Encoding Format Figure 8: Repair FEC Payload ID Encoding Format
4.1.4. Additional Procedures
The following procedure applies: 4.2. Procedures
o The ESI of source symbols MUST start with value 0 for the first All the procedures of Section 3 apply to this FEC Scheme.
source symbol and MUST be managed sequentially. Wrapping to zero
happens after reaching the maximum 32-bit value.
5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary Packet Flows 5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary Packet Flows
This fully-specified FEC Scheme defines the Sliding Window Random This fully-specified FEC Scheme defines the Sliding Window Random
Linear Codes (RLC) over GF(2) (binary case). Linear Codes (RLC) over GF(2) (binary case).
5.1. Formats and Codes 5.1. Formats and Codes
5.1.1. FEC Framework Configuration Information 5.1.1. FEC Framework Configuration Information
5.1.1.1. FEC Encoding ID 5.1.1.1. FEC Encoding ID
o FEC Encoding ID: the value assigned to this fully specified FEC o FEC Encoding ID: the value assigned to this fully specified FEC
Scheme MUST be YYYY, as assigned by IANA (Section 10). Scheme MUST be YYYY, as assigned by IANA (Section 10).
When SDP is used to communicate the FFCI, this FEC Encoding ID is When SDP is used to communicate the FFCI, this FEC Encoding ID is
carried in the 'encoding-id' parameter. carried in the 'encoding-id' parameter.
skipping to change at page 22, line 20 skipping to change at page 24, line 45
When SDP is used to communicate the FFCI, this FEC Encoding ID is When SDP is used to communicate the FFCI, this FEC Encoding ID is
carried in the 'encoding-id' parameter. carried in the 'encoding-id' parameter.
5.1.1.2. FEC Scheme-Specific Information 5.1.1.2. FEC Scheme-Specific Information
All the considerations of Section 4.1.1.2 apply here. All the considerations of Section 4.1.1.2 apply here.
5.1.2. Explicit Source FEC Payload ID 5.1.2. Explicit Source FEC Payload ID
All the considerations of Section 4.1.1.2 apply here. All the considerations of Section 4.1.2 apply here.
5.1.3. Repair FEC Payload ID 5.1.3. Repair FEC Payload ID
All the considerations of Section 4.1.1.2 apply here, with the only All the considerations of Section 4.1.3 apply here, with the only
exception that the Repair_Key field is useless if DT = 15 (indeed, in exception that the Repair_Key field is useless if DT = 15 (indeed, in
that case all the coefficients are necessarily equal to 1 and the that case all the coefficients are necessarily equal to 1 and the
coefficient generation function does not use any PRNG). When DT = 15 coefficient generation function does not use any PRNG). When DT = 15
it is RECOMMENDED that the sender use value 0 for the Repair_Key the FECFRAME sender MUST set the Repair_Key field to zero on
field, but a receiver SHALL ignore this field. transmission and a receiver MUST ignore it on receipt.
5.1.4. Additional Procedures 5.2. Procedures
All the considerations of Section 4.1.1.2 apply here. All the procedures of Section 3 apply to this FEC Scheme.
6. FEC Code Specification 6. FEC Code Specification
6.1. Encoding Side 6.1. Encoding Side
This section provides a high level description of a Sliding Window This section provides a high level description of a Sliding Window
RLC encoder. RLC encoder.
Whenever a new FEC Repair Packet is needed, the RLC encoder instance Whenever a new FEC Repair Packet is needed, the RLC encoder instance
first gathers the ew_size source symbols currently in the sliding first gathers the ew_size source symbols currently in the sliding
encoding window. Then it chooses a repair key, which can be a encoding window. Then it chooses a repair key, which can be a
monotonically increasing integer value, incremented for each repair monotonically increasing integer value, incremented for each repair
symbol up to a maximum value of 65535 (as it is carried within a symbol up to a maximum value of 65535 (as it is carried within a
16-bit field) after which it loops back to 0. This repair key is 16-bit field) after which it loops back to 0. This repair key is
communicated to the coefficient generation function (Section 3.5) in communicated to the coefficient generation function (Section 3.6) in
order to generate ew_size coding coefficients. Finally, the FECFRAME order to generate ew_size coding coefficients. Finally, the FECFRAME
sender computes the repair symbol as a linear combination of the sender computes the repair symbol as a linear combination of the
ew_size source symbols using the ew_size coding coefficients ew_size source symbols using the ew_size coding coefficients
(Section 3.6). When E is small and when there is an incentive to (Section 3.7). When E is small and when there is an incentive to
pack several repair symbols within the same FEC Repair Packet, the pack several repair symbols within the same FEC Repair Packet, the
appropriate number of repair symbols are computed. In that case the appropriate number of repair symbols are computed. In that case the
repair key for each of them MUST be incremented by 1, keeping the repair key for each of them MUST be incremented by 1, keeping the
same ew_size source symbols, since only the first repair key will be same ew_size source symbols, since only the first repair key will be
carried in the Repair FEC Payload ID. The FEC Repair Packet can then carried in the Repair FEC Payload ID. The FEC Repair Packet can then
be passed to the transport layer for transmission. The source versus be passed to the transport layer for transmission. The source versus
repair FEC packet transmission order is out of scope of this document repair FEC packet transmission order is out of scope of this document
and several approaches exist that are implementation specific. and several approaches exist that are implementation-specific.
Other solutions are possible to select a repair key value when a new Other solutions are possible to select a repair key value when a new
FEC Repair Packet is needed, for instance by choosing a random FEC Repair Packet is needed, for instance, by choosing a random
integer between 0 and 65535. However, selecting the same repair key integer between 0 and 65535. However, selecting the same repair key
as before (which may happen in case of a random process) is only as before (which may happen in case of a random process) is only
meaningful if the encoding window has changed, otherwise the same FEC meaningful if the encoding window has changed, otherwise the same FEC
Repair Packet will be generated. Repair Packet will be generated.
6.2. Decoding Side 6.2. Decoding Side
This section provides a high level description of a Sliding Window This section provides a high level description of a Sliding Window
RLC decoder. RLC decoder.
A FECFRAME receiver needs to maintain a linear system whose variables A FECFRAME receiver needs to maintain a linear system whose variables
are the received and lost source symbols. Upon receiving a FEC are the received and lost source symbols. Upon receiving a FEC
Repair Packet, a receiver first extracts all the repair symbols it Repair Packet, a receiver first extracts all the repair symbols it
contains (in case several repair symbols are packed together). For contains (in case several repair symbols are packed together). For
each repair symbol, when at least one of the corresponding source each repair symbol, when at least one of the corresponding source
symbols it protects has been lost, the receiver adds an equation to symbols it protects has been lost, the receiver adds an equation to
the linear system (or no equation if this repair packet does not the linear system (or no equation if this repair packet does not
change the linear system rank). This equation of course re-uses the change the linear system rank). This equation of course re-uses the
ew_size coding coefficients that are computed by the same coefficient ew_size coding coefficients that are computed by the same coefficient
generation function (Section Section 3.5), using the repair key and generation function (Section Section 3.6), using the repair key and
encoding window descriptions carried in the Repair FEC Payload ID. encoding window descriptions carried in the Repair FEC Payload ID.
Whenever possible (i.e., when a sub-system covering one or more lost Whenever possible (i.e., when a sub-system covering one or more lost
source symbols is of full rank), decoding is performed in order to source symbols is of full rank), decoding is performed in order to
recover lost source symbols. Each time an ADUI can be totally recover lost source symbols. Gaussian elimination is one possible
recovered, padding is removed (thanks to the Length field, L, of the algorithm to solve this linear system. Each time an ADUI can be
ADUI) and the ADU is assigned to the corresponding application flow totally recovered, padding is removed (thanks to the Length field, L,
(thanks to the Flow ID field, F, of the ADUI). This ADU is finally of the ADUI) and the ADU is assigned to the corresponding application
passed to the corresponding upper application. Received FEC Source flow (thanks to the Flow ID field, F, of the ADUI). This ADU is
Packets, containing an ADU, MAY be passed to the application either finally passed to the corresponding upper application. Received FEC
immediately or after some time to guaranty an ordered delivery to the Source Packets, containing an ADU, MAY be passed to the application
application. This document does not mandate any approach as this is either immediately or after some time to guaranty an ordered delivery
an operational and management decision. to the application. This document does not mandate any approach as
this is an operational and management decision.
With real-time flows, a lost ADU that is decoded after the maximum With real-time flows, a lost ADU that is decoded after the maximum
latency or an ADU received after this delay has no value to the latency or an ADU received after this delay has no value to the
application. This raises the question of deciding whether or not an application. This raises the question of deciding whether or not an
ADU is late. This decision MAY be taken within the FECFRAME receiver ADU is late. This decision MAY be taken within the FECFRAME receiver
(e.g., using the decoding window, see Section 3.1) or within the (e.g., using the decoding window, see Section 3.1) or within the
application (e.g., using RTP timestamps within the ADU). Deciding application (e.g., using RTP timestamps within the ADU). Deciding
which option to follow and whether or not to pass all ADUs, including which option to follow and whether or not to pass all ADUs, including
those assumed late, to the application are operational decisions that those assumed late, to the application are operational decisions that
depend on the application and are therefore out of scope of this depend on the application and are therefore out of scope of this
document. Additionally, Appendix B discusses a backward compatible document. Additionally, Appendix D discusses a backward compatible
optimization whereby late source symbols MAY still be used within the optimization whereby late source symbols MAY still be used within the
FECFRAME receiver in order to improve transmission robustness. FECFRAME receiver in order to improve transmission robustness.
7. Implementation Status 7. Implementation Status
Editor's notes: RFC Editor, please remove this section motivated by Editor's notes: RFC Editor, please remove this section motivated by
RFC 6982 before publishing the RFC. Thanks. RFC 6982 before publishing the RFC. Thanks.
An implementation of the Sliding Window RLC FEC Scheme for FECFRAME An implementation of the Sliding Window RLC FEC Scheme for FECFRAME
exists: exists:
skipping to change at page 24, line 27 skipping to change at page 27, line 4
RFC 6982 before publishing the RFC. Thanks. RFC 6982 before publishing the RFC. Thanks.
An implementation of the Sliding Window RLC FEC Scheme for FECFRAME An implementation of the Sliding Window RLC FEC Scheme for FECFRAME
exists: exists:
o Organisation: Inria o Organisation: Inria
o Description: This is an implementation of the Sliding Window RLC o Description: This is an implementation of the Sliding Window RLC
FEC Scheme limited to GF(2^^8). It relies on a modified version FEC Scheme limited to GF(2^^8). It relies on a modified version
of our OpenFEC (http://openfec.org) FEC code library. It is of our OpenFEC (http://openfec.org) FEC code library. It is
integrated in our FECFRAME software (see [fecframe-ext]). integrated in our FECFRAME software (see [fecframe-ext]).
o Maturity: prototype. o Maturity: prototype.
o Coverage: this software complies with the Sliding Window RLC FEC o Coverage: this software complies with the Sliding Window RLC FEC
Scheme. Scheme.
o Licensing: proprietary. o Licensing: proprietary.
o Contact: vincent.roca@inria.fr o Contact: vincent.roca@inria.fr
8. Security Considerations 8. Security Considerations
The FEC Framework document [RFC6363] provides a comprehensive The FEC Framework document [RFC6363] provides a fairly comprehensive
analysis of security considerations applicable to FEC Schemes. analysis of security considerations applicable to FEC Schemes.
Therefore, the present section follows the security considerations Therefore, the present section follows the security considerations
section of [RFC6363] and only discusses specific topics. section of [RFC6363] and only discusses specific topics.
8.1. Attacks Against the Data Flow 8.1. Attacks Against the Data Flow
8.1.1. Access to Confidential Content 8.1.1. Access to Confidential Content
The Sliding Window RLC FEC Scheme specified in this document does not The Sliding Window RLC FEC Scheme specified in this document does not
change the recommendations of [RFC6363]. To summarize, if change the recommendations of [RFC6363]. To summarize, if
skipping to change at page 25, line 31 skipping to change at page 28, line 7
o FEC Encoding ID: changing this parameter leads a receiver to o FEC Encoding ID: changing this parameter leads a receiver to
consider a different FEC Scheme. The consequences are severe, the consider a different FEC Scheme. The consequences are severe, the
format of the Explicit Source FEC Payload ID and Repair FEC format of the Explicit Source FEC Payload ID and Repair FEC
Payload ID of received packets will probably differ, leading to Payload ID of received packets will probably differ, leading to
various malfunctions. Even if the original and modified FEC various malfunctions. Even if the original and modified FEC
Schemes share the same format, FEC decoding will either fail or Schemes share the same format, FEC decoding will either fail or
lead to corrupted decoded symbols. This will happen if an lead to corrupted decoded symbols. This will happen if an
attacker turns value YYYY (i.e., RLC over GF(2)) to value XXXX attacker turns value YYYY (i.e., RLC over GF(2)) to value XXXX
(RLC over GF(2^^8)), an additional consequence being a higher (RLC over GF(2^^8)), an additional consequence being a higher
processing overhead at the receiver. In any case, the attack processing overhead at the receiver. In any case, the attack
results in a form of Denial of Service (DoS); results in a form of Denial of Service (DoS) or corrupted content.
o Encoding symbol length (E): setting this E parameter to a o Encoding symbol length (E): setting this E parameter to a
different value will confuse a receiver. If the size of a different value will confuse a receiver. If the size of a
received FEC Repair Packet is no longer multiple of the modified E received FEC Repair Packet is no longer multiple of the modified E
value, a receiver quickly detects a problem and SHOULD reject the value, a receiver quickly detects a problem and SHOULD reject the
packet. If the new E value is a sub-multiple of the original E packet. If the new E value is a sub-multiple of the original E
value (e.g., half the original value), then receivers may not value (e.g., half the original value), then receivers may not
detect the problem immediately. For instance a receiver may think detect the problem immediately. For instance, a receiver may
that a received FEC Repair Packet contains more repair symbols think that a received FEC Repair Packet contains more repair
(e.g., twice as many if E is reduced by half), leading to symbols (e.g., twice as many if E is reduced by half), leading to
malfunctions whose nature depends on implementation details. Here malfunctions whose nature depends on implementation details. Here
also, the attack always results in a form of DoS; also, the attack always results in a form of DoS or corrupted
content.
It is therefore RECOMMENDED that security measures be taken to It is therefore RECOMMENDED that security measures be taken to
guarantee the FFCI integrity, as specified in [RFC6363]. How to guarantee the FFCI integrity, as specified in [RFC6363]. How to
achieve this depends on the way the FFCI is communicated from the achieve this depends on the way the FFCI is communicated from the
sender to the receiver, which is not specified in this document. sender to the receiver, which is not specified in this document.
Similarly, attacks are possible against the Explicit Source FEC Similarly, attacks are possible against the Explicit Source FEC
Payload ID and Repair FEC Payload ID. More specifically, in case of Payload ID and Repair FEC Payload ID. More specifically, in case of
a FEC Source Packet, the following value can be modified by an a FEC Source Packet, the following value can be modified by an
attacker who targets receivers: attacker who targets receivers:
skipping to change at page 27, line 9 skipping to change at page 29, line 32
change the recommendations of [RFC6363] concerning the use of the change the recommendations of [RFC6363] concerning the use of the
IPsec/ESP security protocol as a mandatory to implement (but not IPsec/ESP security protocol as a mandatory to implement (but not
mandatory to use) security scheme. This is well suited to situations mandatory to use) security scheme. This is well suited to situations
where the only insecure domain is the one over which the FEC where the only insecure domain is the one over which the FEC
Framework operates. Framework operates.
8.5. Additional Security Considerations for Numerical Computations 8.5. Additional Security Considerations for Numerical Computations
In addition to the above security considerations, inherited from In addition to the above security considerations, inherited from
[RFC6363], the present document introduces several formulae, in [RFC6363], the present document introduces several formulae, in
particular in Section 3.1.1. It is RECOMMENDED to check that the particular in Appendix C.1. It is RECOMMENDED to check that the
computed values stay within reasonnable bounds since numerical computed values stay within reasonable bounds since numerical
overflows, caused by an erroneous implementation or an erroneous overflows, caused by an erroneous implementation or an erroneous
input value, may lead to hazardous behaviours. However what input value, may lead to hazardous behaviours. However, what
"reasonnable bounds" means is use-case and implementation dependent "reasonable bounds" means is use-case and implementation dependent
and is not detailed in this document. and is not detailed in this document.
Section 3.1.2 also mentions the possibility of "using the timestamp Appendix C.2 also mentions the possibility of "using the timestamp
field of an RTP packet header" when applicable. A malicious attacker field of an RTP packet header" when applicable. A malicious attacker
may deliberately corrupt this header field in order to trigger may deliberately corrupt this header field in order to trigger
hazardous behaviours at a FECFRAME receiver. Protection against this hazardous behaviours at a FECFRAME receiver. Protection against this
type of content corruption can be addressed with the above type of content corruption can be addressed with the above
recommendations on a baseline secure operation. In addition, it is recommendations on a baseline secure operation. In addition, it is
also RECOMMENDED to check that the timestamp value be within also RECOMMENDED to check that the timestamp value be within
reasonnable bounds. reasonable bounds.
9. Operations and Management Considerations 9. Operations and Management Considerations
The FEC Framework document [RFC6363] provides a comprehensive The FEC Framework document [RFC6363] provides a fairly comprehensive
analysis of operations and management considerations applicable to analysis of operations and management considerations applicable to
FEC Schemes. Therefore, the present section only discusses specific FEC Schemes. Therefore, the present section only discusses specific
topics. topics.
9.1. Operational Recommendations: Finite Field GF(2) Versus GF(2^^8) 9.1. Operational Recommendations: Finite Field GF(2) Versus GF(2^^8)
The present document specifies two FEC Schemes that differ on the The present document specifies two FEC Schemes that differ on the
Finite Field used for the coding coefficients. It is expected that Finite Field used for the coding coefficients. It is expected that
the RLC over GF(2^^8) FEC Scheme will be mostly used since it the RLC over GF(2^^8) FEC Scheme will be mostly used since it
warrants a higher packet loss protection. In case of small encoding warrants a higher packet loss protection. In case of small encoding
windows, the associated processing overhead is not an issue (e.g., we windows, the associated processing overhead is not an issue (e.g., we
measured decoding speeds between 745 Mbps and 2.8 Gbps on an ARM measured decoding speeds between 745 Mbps and 2.8 Gbps on an ARM
Cortex-A15 embedded board in [Roca17]). Of course the CPU overhead Cortex-A15 embedded board in [Roca17] for an encoding window of size
will increase with the encoding window size, because more operations 18 or 23 symbols). Of course the CPU overhead will increase with the
in the GF(2^^8) finite field will be needed. encoding window size, because more operations in the GF(2^^8) finite
field will be needed.
The RLC over GF(2) FEC Scheme offers an alternative. In that case The RLC over GF(2) FEC Scheme offers an alternative. In that case
operations symbols can be directly XOR-ed together which warrants operations symbols can be directly XOR-ed together which warrants
high bitrate encoding and decoding operations, and can be an high bitrate encoding and decoding operations, and can be an
advantage with large encoding windows. However packet loss advantage with large encoding windows. However, packet loss
protection is significantly reduced by using this FEC Scheme. protection is significantly reduced by using this FEC Scheme.
9.2. Operational Recommendations: Coding Coefficients Density Threshold 9.2. Operational Recommendations: Coding Coefficients Density Threshold
In addition to the choice of the Finite Field, the two FEC Schemes In addition to the choice of the Finite Field, the two FEC Schemes
define a coding coefficient density threshold (DT) parameter. This define a coding coefficient density threshold (DT) parameter. This
parameter enables a sender to control the code density, i.e., the parameter enables a sender to control the code density, i.e., the
proportion of coefficients that are non zero on average. With RLC proportion of coefficients that are non zero on average. With RLC
over GF(2^^8), it is usually appropriate that small encoding windows over GF(2^^8), it is usually appropriate that small encoding windows
be associated to a density threshold equal to 15, the maximum value, be associated to a density threshold equal to 15, the maximum value,
in order to warrant a high loss protection. in order to warrant a high loss protection.
On the opposite, with larger encoding windows, it is usually On the opposite, with larger encoding windows, it is usually
appropriate that the density threshold be reduced. With large appropriate that the density threshold be reduced. With large
encoding windows, an alternative can be to use RLC over GF(2) and a encoding windows, an alternative can be to use RLC over GF(2) and a
density threshold equal to 7 (i.e., an average density equal to 1/2) density threshold equal to 7 (i.e., an average density equal to 1/2)
or smaller. or smaller.
Note that using a density threshold equal to 15 with RLC over GF(2) Note that using a density threshold equal to 15 with RLC over GF(2)
is equivalent to using an XOR code that compute the XOR sum of all is equivalent to using an XOR code that computes the XOR sum of all
the source symbols in the encoding window. In that case: (1) a the source symbols in the encoding window. In that case: (1) only a
single repair symbol can be produced for any encoding window, and (2) single repair symbol can be produced for any encoding window, and (2)
the repair_key parameter becomes useless (the coding coefficients the repair_key parameter becomes useless (the coding coefficients
generation function does not rely on the PRNG). generation function does not rely on the PRNG).
10. IANA Considerations 10. IANA Considerations
This document registers two values in the "FEC Framework (FECFRAME) This document registers two values in the "FEC Framework (FECFRAME)
FEC Encoding IDs" registry [RFC6363] as follows: FEC Encoding IDs" registry [RFC6363] as follows:
o YYYY refers to the Sliding Window Random Linear Codes (RLC) over o YYYY refers to the Sliding Window Random Linear Codes (RLC) over
GF(2) FEC Scheme for Arbitrary Packet Flows, as defined in GF(2) FEC Scheme for Arbitrary Packet Flows, as defined in
Section 5 of this document. Section 5 of this document.
o XXXX refers to the Sliding Window Random Linear Codes (RLC) over o XXXX refers to the Sliding Window Random Linear Codes (RLC) over
GF(2^^8) FEC Scheme for Arbitrary Packet Flows, as defined in GF(2^^8) FEC Scheme for Arbitrary Packet Flows, as defined in
Section 4 of this document. Section 4 of this document.
11. Acknowledgments 11. Acknowledgments
The authors would like to thank Russ Housley, Alan DeKok, Spencer The authors would like to thank the three TSVWG chairs, Wesley Eddy,
Dawkins, Gorry Fairhurst, Jonathan Detchart, Emmanuel Lochin, and our shepherd, David Black and Gorry Fairhurst, as well as Spencer
Marie-Jose Montpetit for their valuable feedbacks on this document. Dawkins, our responsible AD, and all those who provided comments,
namely (alphabetical order) Alan DeKok, Jonathan Detchart, Russ
Housley, Emmanuel Lochin, and Marie-Jose Montpetit. Last but not
least, the authors are really grateful to the IESG members, in
particular Benjamin Kaduk, Mirja Kuhlewind, Eric Rescorla, and Adam
Roach for their highly valuable feedbacks that greatly contributed to
improve this specification.
12. References 12. References
12.1. Normative References 12.1. Normative References
[fecframe-ext] [fecframe-ext]
Roca, V. and A. Begen, "Forward Error Correction (FEC) Roca, V. and A. Begen, "Forward Error Correction (FEC)
Framework Extension to Sliding Window Codes", Transport Framework Extension to Sliding Window Codes", Transport
Area Working Group (TSVWG) draft-ietf-tsvwg-fecframe-ext Area Working Group (TSVWG) draft-ietf-tsvwg-fecframe-ext
(Work in Progress), September 2018, (Work in Progress), January 2019,
<https://tools.ietf.org/html/ <https://tools.ietf.org/html/
draft-ietf-tsvwg-fecframe-ext>. draft-ietf-tsvwg-fecframe-ext>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997, DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>. <https://www.rfc-editor.org/info/rfc2119>.
[RFC6363] Watson, M., Begen, A., and V. Roca, "Forward Error [RFC6363] Watson, M., Begen, A., and V. Roca, "Forward Error
Correction (FEC) Framework", RFC 6363, Correction (FEC) Framework", RFC 6363,
skipping to change at page 29, line 34 skipping to change at page 32, line 16
Forward Error Correction (FEC) Framework", RFC 6364, Forward Error Correction (FEC) Framework", RFC 6364,
DOI 10.17487/RFC6364, October 2011, DOI 10.17487/RFC6364, October 2011,
<https://www.rfc-editor.org/info/rfc6364>. <https://www.rfc-editor.org/info/rfc6364>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>. May 2017, <https://www.rfc-editor.org/info/rfc8174>.
12.2. Informative References 12.2. Informative References
[Baccelli18]
Baccelli, E., Gundogan, C., Hahm, O., Kietzmann, P.,
Lenders, M., Petersen, H., Schleiser, K., Schmidt, T., and
M. Wahlisch, "RIOT: An Open Source Operating System for
Low-End Embedded Devices in the IoT", IEEE Internet of
Things Journal (Volume 5, Issue 6), DOI:
10.1109/JIOT.2018.2815038, December 2018.
[KR12] Rikitake, K., "TinyMT Pseudo Random Number Generator for [KR12] Rikitake, K., "TinyMT Pseudo Random Number Generator for
Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12), Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
September 14, 2012, Copenhagen, Denmark, DOI: September 14, 2012, Copenhagen, Denmark, DOI:
http://dx.doi.org/10.1145/2364489.2364504, September 2012. http://dx.doi.org/10.1145/2364489.2364504, September 2012.
[PGM13] Plank, J., Greenan, K., and E. Miller, "A Complete [PGM13] Plank, J., Greenan, K., and E. Miller, "A Complete
Treatment of Software Implementations of Finite Field Treatment of Software Implementations of Finite Field
Arithmetic for Erasure Coding Applications", University of Arithmetic for Erasure Coding Applications", University of
Tennessee Technical Report UT-CS-13-717, Tennessee Technical Report UT-CS-13-717,
http://web.eecs.utk.edu/~plank/plank/papers/ http://web.eecs.utk.edu/~plank/plank/papers/
UT-CS-13-717.html, October 2013, UT-CS-13-717.html, October 2013,
<http://web.eecs.utk.edu/~plank/plank/papers/ <http://web.eecs.utk.edu/~plank/plank/papers/
UT-CS-13-717.html>. UT-CS-13-717.html>.
[RFC5170] Roca, V., Neumann, C., and D. Furodet, "Low Density Parity
Check (LDPC) Staircase and Triangle Forward Error
Correction (FEC) Schemes", RFC 5170, DOI 10.17487/RFC5170,
June 2008, <https://www.rfc-editor.org/info/rfc5170>.
[RFC5510] Lacan, J., Roca, V., Peltotalo, J., and S. Peltotalo, [RFC5510] Lacan, J., Roca, V., Peltotalo, J., and S. Peltotalo,
"Reed-Solomon Forward Error Correction (FEC) Schemes", "Reed-Solomon Forward Error Correction (FEC) Schemes",
RFC 5510, DOI 10.17487/RFC5510, April 2009, RFC 5510, DOI 10.17487/RFC5510, April 2009,
<https://www.rfc-editor.org/info/rfc5510>. <https://www.rfc-editor.org/info/rfc5510>.
[RFC6726] Paila, T., Walsh, R., Luby, M., Roca, V., and R. Lehtonen, [RFC6726] Paila, T., Walsh, R., Luby, M., Roca, V., and R. Lehtonen,
"FLUTE - File Delivery over Unidirectional Transport", "FLUTE - File Delivery over Unidirectional Transport",
RFC 6726, DOI 10.17487/RFC6726, November 2012, RFC 6726, DOI 10.17487/RFC6726, November 2012,
<https://www.rfc-editor.org/info/rfc6726>. <https://www.rfc-editor.org/info/rfc6726>.
skipping to change at page 31, line 5 skipping to change at page 34, line 5
[Roca17] Roca, V., Teibi, B., Burdinat, C., Tran, T., and C. [Roca17] Roca, V., Teibi, B., Burdinat, C., Tran, T., and C.
Thienot, "Less Latency and Better Protection with AL-FEC Thienot, "Less Latency and Better Protection with AL-FEC
Sliding Window Codes: a Robust Multimedia CBR Broadcast Sliding Window Codes: a Robust Multimedia CBR Broadcast
Case Study", 13th IEEE International Conference on Case Study", 13th IEEE International Conference on
Wireless and Mobile Computing, Networking and Wireless and Mobile Computing, Networking and
Communications (WiMob17), October Communications (WiMob17), October
2017 https://hal.inria.fr/hal-01571609v1/en/, October 2017 https://hal.inria.fr/hal-01571609v1/en/, October
2017, <https://hal.inria.fr/hal-01571609v1/en/>. 2017, <https://hal.inria.fr/hal-01571609v1/en/>.
Appendix A. TinyMT32 Pseudo-Random Number Generator Appendix A. TinyMT32 Validation Criteria (Normative)
The TinyMT32 PRNG reference implementation is distributed under a BSD PRNG determinism, for a given seed, is a requirement. Consequently,
license by the authors and excerpts of it are reproduced in Figure 8. in order to validate an implementation of the TinyMT32 PRNG, the
The differences with respect to the original source code are: following criterias MUST be met.
o the unused parts of the original source code have been removed; The first criteria focusses on the core TinyMT32 PRNG, that produces
o the appropriate parameter set has been added to the initialization 32-bit pseudo-random numbers. Using a seed value of 1, the first 50
function; values returned by: tinymt32_generate_uint32(s) as 32-bit unsigned
o the tinymt32_rand() function has been added; integers MUST be equal to values provided in Figure 9. Note that
o the function order has been changed; these values come from the tinymt/check32.out.txt file provided by
o certain internal variables have been renamed for compactness the authors to validate implementations of TinyMT32, as part of the
purposes. MersenneTwister-Lab/TinyMT Github repository.
<CODE BEGINS> 2545341989 981918433 3715302833 2387538352 3591001365
/** 3820442102 2114400566 2196103051 2783359912 764534509
* Tiny Mersenne Twister only 127 bit internal state 643179475 1822416315 881558334 4207026366 3690273640
* 3240535687 2921447122 3984931427 4092394160 44209675
* Authors : Mutsuo Saito (Hiroshima University) 2188315343 2908663843 1834519336 3774670961 3019990707
* Makoto Matsumoto (University of Tokyo) 4065554902 1239765502 4035716197 3412127188 552822483
* 161364450 353727785 140085994 149132008 2547770827
* Copyright (c) 2011, 2013 Mutsuo Saito, Makoto Matsumoto, 4064042525 4078297538 2057335507 622384752 2041665899
* Hiroshima University and The University of Tokyo. 2193913817 1080849512 33160901 662956935 642999063
* All rights reserved. 3384709977 1723175122 3866752252 521822317 2292524454
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials
* provided with the distribution.
* - Neither the name of the Hiroshima University nor the names of
* its contributors may be used to endorse or promote products
* derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
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#include <stdint.h> Figure 9: First 50 decimal values returned by
tinymt32_generate_uint32(s) as 32-bit unsigned integers, with a seed
value of 1.
/** The second criteria focusses on the tinymt32_rand256(), where the
* tinymt32 internal state vector and parameters 32-bit integer of the core TinyMT32 PRNG is scaled down to an 8-bit
*/ integer. Using a seed value of 1, the first 50 values returned by:
typedef struct { tinymt32_rand256() as 8-bit unsigned integers MUST be equal to values
uint32_t status[4]; provided in Figure 10.
uint32_t mat1;
uint32_t mat2;
uint32_t tmat;
} tinymt32_t;
static void tinymt32_next_state (tinymt32_t * s); 37 225 177 176 21
static uint32_t tinymt32_temper (tinymt32_t * s); 246 54 139 168 237
static double tinymt32_generate_32double (tinymt32_t * s); 211 187 62 190 104
135 210 99 176 11
207 35 40 113 179
214 254 101 212 211
226 41 234 232 203
29 194 211 112 107
217 104 197 135 23
89 210 252 109 166
/** Figure 10: First 50 decimal values returned by tinymt32_rand256() as
* Parameter set to use for the IETF RLC FEC Schemes specification. 8-bit unsigned integers, with a seed value of 1.
* Do not change.
* This parameter set is the first entry of the precalculated parameter
* sets in file tinymt32dc.0.1048576.txt, by Kenji Rikitake, available
* at: https://github.com/jj1bdx/tinymtdc-longbatch/blob/master/
* tinymt32dc/tinymt32dc.0.1048576.txt
* It is also the parameter set used:
* Rikitake, K., "TinyMT Pseudo Random Number Generator for
* Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
* September, 2012.
*/
#define TINYMT32_MAT1_PARAM 0x8f7011ee
#define TINYMT32_MAT2_PARAM 0xfc78ff1f
#define TINYMT32_TMAT_PARAM 0x3793fdff
/** The third criteria focusses on the tinymt32_rand16(), where the
* This function initializes the internal state array with a 32-bit 32-bit integer of the core TinyMT32 PRNG is scaled down to a 4-bit
* unsigned integer seed. integer. Using a seed value of 1, the first 50 values returned by:
* @param s pointer to tinymt internal state. tinymt32_rand16() as 4-bit unsigned integers MUST be equal to values
* @param seed a 32-bit unsigned integer used as a seed. provided in Figure 11.
*/
void tinymt32_init (tinymt32_t * s, uint32_t seed)
{
#define MIN_LOOP 8
#define PRE_LOOP 8
s->status[0] = seed;
s->status[1] = s->mat1 = TINYMT32_MAT1_PARAM;
s->status[2] = s->mat2 = TINYMT32_MAT2_PARAM;
s->status[3] = s->tmat = TINYMT32_TMAT_PARAM;
for (int i = 1; i < MIN_LOOP; i++) {
s->status[i & 3] ^= i + UINT32_C(1812433253)
* (s->status[(i - 1) & 3]
^ (s->status[(i - 1) & 3] >> 30));
}
for (int i = 0; i < PRE_LOOP; i++) {
tinymt32_next_state(s);
}
}
/** 5 1 1 0 5
* This function outputs an integer in the [0 .. maxv-1] range. 6 6 11 8 13
* @param s pointer to tinymt internal state. 3 11 14 14 8
* @return 32-bit unsigned integer between 0 and maxv-1 inclusive. 7 2 3 0 11
*/ 15 3 8 1 3
uint32_t tinymt32_rand (tinymt32_t * s, uint32_t maxv) 6 14 5 4 3
{ 2 9 10 8 11
return (uint32_t)(tinymt32_generate_32double(s) * (double)maxv); 13 2 3 0 11
} 9 8 5 7 7
9 2 12 13 6
/** Figure 11: First 50 decimal values returned by tinymt32_rand16() as
* Internal tinymt32 constants and functions. 4-bit unsigned integers, with a seed value of 1.
* Users should not call these functions directly.
*/
#define TINYMT32_MEXP 127
#define TINYMT32_SH0 1
#define TINYMT32_SH1 10
#define TINYMT32_SH8 8
#define TINYMT32_MASK UINT32_C(0x7fffffff)
#define TINYMT32_MUL (1.0f / 16777216.0f)
/** The deterministic behavior of the implementation of Figure 2 has been
* This function changes internal state of tinymt32. checked across several platforms: high-end laptops running 64-bits
* @param s pointer to tinymt internal state. Mac OSX and Linux/Ubuntu; a board featuring a 32-bits ARM Cortex-A15
*/ and running 32-bit Linux/Ubuntu; several embedded cards featuring
static void tinymt32_next_state (tinymt32_t * s) either an ARM Cortex-M0+, a Cortex-M3 or a Cortex-M4 32-bit
{ microcontroller, all of them running RIOT [Baccelli18]; two low-end
uint32_t x; embedded cards featuring either a 16-bit microcontroller (TI MSP430)
uint32_t y; or a 8-bit microcontroller (Arduino ATMEGA2560), both of them running
RIOT.
y = s->status[3]; Appendix B. Assessing the PRNG Adequacy (Informational)
x = (s->status[0] & TINYMT32_MASK)
^ s->status[1]
^ s->status[2];
x ^= (x << TINYMT32_SH0);
y ^= (y >> TINYMT32_SH0) ^ x;
s->status[0] = s->status[1];
s->status[1] = s->status[2];
s->status[2] = x ^ (y << TINYMT32_SH1);
s->status[3] = y;
s->status[1] ^= -((int32_t)(y & 1)) & s->mat1;
s->status[2] ^= -((int32_t)(y & 1)) & s->mat2;
}
/** This annex discusses the adequacy of the TinyMT32 PRNG and the
* This function outputs 32-bit unsigned integer from internal state. tinymt32_rand16() and tinymt32_rand256() functions, to the RLC FEC
* @param s pointer to tinymt internal state. Schemes. The goal is to assess the adequacy of these two functions
* @return 32-bit unsigned pseudos number in producing coding coefficients that are sufficiently different from
*/ one another, across various repair symbols with repair key values in
static uint32_t tinymt32_temper (tinymt32_t * s) sequence (we can expect this approach to be commonly used by
{ implementers Section 6.1). This section is purely informational and
uint32_t t0, t1; does not claim to be a solid evaluation.
t0 = s->status[3];
t1 = s->status[0] + (s->status[2] >> TINYMT32_SH8);
t0 ^= t1;
t0 ^= -((int32_t)(t1 & 1)) & s->tmat;
return t0;
}
/** The two RLC FEC Schemes use the PRNG to produce pseudo-random coding
* This function outputs double precision floating point number from coefficients (Section 3.6), each time a new repair symbol is needed.
* internal state. The returned value has 32-bit precision. A different repair key is used for each repair symbol, usually by
* In other words, this function makes one double precision floating incrementing the repair key value (Section 6.1). For each repair
* point number from one 32-bit unsigned integer. symbol, a limited number of pseudo-random numbers is needed,
* @param s pointer to tinymt internal state. depending on the DT and encoding window size (Section 3.6), using
* @return floating point number r (0.0 <= r < 1.0) either tinymt32_rand16() or tinymt32_rand256(). Therefore we are
*/ more interested in the randomness of small sequences of random
static double tinymt32_generate_32double (tinymt32_t * s) numbers mapped to 4-bit or 8-bit integers, than in the randomness of
{ a very large sequence of random nmbers which is not representative of
tinymt32_next_state(s); the usage of the PRNG.
return (double)tinymt32_temper(s) * (1.0 / 4294967296.0);
}
<CODE ENDS>
Figure 8: TinyMT32 pseudo-code Evaluation of tinymt32_rand16(): We first generate a huge number
(1,000,000,000) of small sequences (20 pseudo-random numbers per
sequence), and perform statistics on the number of occurrences of
each of the 16 possible values across all sequences.
Appendix B. Decoding Beyond Maximum Latency Optimization value occurrences percentage (%) (total of 20000000000)
0 1250036799 6.2502
1 1249995831 6.2500
2 1250038674 6.2502
3 1250000881 6.2500
4 1250023929 6.2501
5 1249986320 6.2499
6 1249995587 6.2500
7 1250020363 6.2501
8 1249995276 6.2500
9 1249982856 6.2499
10 1249984111 6.2499
11 1250009551 6.2500
12 1249955768 6.2498
13 1249994654 6.2500
14 1250000569 6.2500
15 1249978831 6.2499
Figure 12: tinymt32_rand16(): occurrence statistics across a huge
number (1,000,000,000) of small sequences (20 pseudo-random numbers
per sequence), with 0 as the first PRNG seed.
The results (Figure 12) show that all possible values are almost
equally represented, or said differently, that the tinymt32_rand16()
output converges to a uniform distribution where each of the 16
possible value would appear exactly 1 / 16 * 100 = 6.25% of times.
Other types of biases may exist that may be visible with smaller
tests (e.g., to evaluation the convergence speed to a uniform
distribution). We therefore perform 200 tests, each of them
consisting in producing 200 sequences, keeping ony the first value of
each sequence. We use non overlapping repair keys for each sequence,
starting with value 0 and increasing it after each use.
value min occurrences max occurrences average occurrences
0 4 21 6.3675
1 4 22 6.0200
2 4 20 6.3125
3 5 23 6.1775
4 5 24 6.1000
5 4 21 6.5925
6 5 30 6.3075
7 6 22 6.2225
8 5 26 6.1750
9 3 21 5.9425
10 5 24 6.3175
11 4 22 6.4300
12 5 21 6.1600
13 5 22 6.3100
14 4 26 6.3950
15 4 21 6.1700
Figure 13: tinymt32_rand16(): occurrence statistics across 200 tests,
each of them consisting in 200 sequences of 1 pseudo-random number
each, with non overlapping PRNG seeds in sequence starting from 0.
Figure 13 shows across all 200 tests, for each of the 16 possible
pseudo-random number values, the minimum (resp. maximum) number of
times it appeared in a tests, as well as the average number of
occurrences across the 200 tests. Although the distribution is not
perfect, there is no major bias. On the opposite, in the same
conditions, the Park Miller linear congruential PRNG of [RFC5170]
with a result scaled down to 4-bit values, using seeds in sequence
starting from 1, returns systematically 0 as the first value during
some time, then after a certain repair key value threshold, it
systematically returns 1, etc.
Evaluation of tinymt32_rand256(): The same approach is used here.
Results (not shown) are similar: occurrences vary between 7,810,3368
(i.e., 0.3905%) and 7,814,7952 (i.e., 0.3907%). Here also we see a
convergence to the theoretical uniform distribution where each of the
possible value would appear exactly 1 / 256 * 100 = 0.390625% of
times.
Appendix C. Possible Parameter Derivation (Informational)
Section 3.1 defines several parameters to control the encoder or
decoder. This annex proposes techniques to derive these parameters
according to the target use-case. This annex is informational, in
the sense that using a different derivation technique will not
prevent the encoder and decoder to interoperate: a decoder can still
recover an erased source symbol without any error. However, in case
of a real-time flow, an inappropriate parameter derivation may lead
to the decoding of erased source packets after their validity period,
making them useless to the target application. This annex proposes
an approach to reduce this risk, among other things.
The FEC Schemes defined in this document can be used in various
manners, depending on the target use-case:
o the source ADU flow they protect may or may not have real-time
constraints;
o the source ADU flow may be a Constant Bitrate (CBR) or Variable
BitRate (VBR) flow;
o with a VBR source ADU flow, the flow's minimum and maximum
bitrates may or may not be known;
o and the communication path between encoder and decoder may be a
CBR communication path (e.g., as with certain LTE-based broadcast
channels) or not (general case, e.g., with Internet).
The parameter derivation technique should be suited to the use-case,
as described in the following sections.
C.1. Case of a CBR Real-Time Flow
In the following, we consider a real-time flow with max_lat latency
budget. The encoding symbol size, E, is constant. The code rate,
cr, is also constant, its value depending on the expected
communication loss model (this choice is out of scope of this
document).
In a first configuration, the source ADU flow bitrate at the input of
the FECFRAME sender is fixed and equal to br_in (in bits/s), and this
value is known by the FECFRAME sender. It follows that the
transmission bitrate at the output of the FECFRAME sender will be
higher, depending on the added repair flow overhead. In order to
comply with the maximum FEC-related latency budget, we have:
dw_max_size = (max_lat * br_in) / (8 * E)
assuming that the encoding and decoding times are negligible with
respect to the target max_lat. This is a reasonable assumption in
many situations (e.g., see Section 9.1 in case of small window
sizes). Otherwise the max_lat parameter should be adjusted in order
to avoid the problem. In any case, interoperability will never be
compromized by choosing a too large value.
In a second configuration, the FECFRAME sender generates a fixed
bitrate flow, equal to the CBR communication path bitrate equal to
br_out (in bits/s), and this value is known by the FECFRAME sender,
as in [Roca17]. The maximum source flow bitrate needs to be such
that, with the added repair flow overhead, the total transmission
bitrate remains inferior or equal to br_out. We have:
dw_max_size = (max_lat * br_out * cr) / (8 * E)
assuming here also that the encoding and decoding times are
negligible with respect to the target max_lat.
For decoding to be possible within the latency budget, it is required
that the encoding window maximum size be smaller than or at most
equal to the decoding window maximum size. The ew_max_size is the
main parameter at a FECFRAME sender, but its exact value has no
impact on the the FEC-related latency budget. The ew_max_size
parameter is computed as follows:
ew_max_size = dw_max_size * WSR / 255
In line with [Roca17], WSR = 191 is considered as a reasonable value
(the resulting encoding to decoding window size ratio is then close
to 0.75), but other values between 1 and 255 inclusive are possible,
depending on the use-case.
The dw_max_size is computed by a FECFRAME sender but not explicitly
communicated to a FECFRAME receiver. However, a FECFRAME receiver
can easily evaluate the ew_max_size by observing the maximum Number
of Source Symbols (NSS) value contained in the Repair FEC Payload ID
of received FEC Repair Packets (Section 4.1.3). A receiver can then
easily compute dw_max_size:
dw_max_size = max_NSS_observed * 255 / WSR
A receiver can then chose an appropriate linear system maximum size:
ls_max_size >= dw_max_size
It is good practice to use a larger value for ls_max_size as
explained in Appendix D, which does not impact maximum latency nor
interoperability.
In any case, for a given use-case (i.e., for target encoding and
decoding devices and desired protection levels in front of
communication impairments) and for the computed ew_max_size,
dw_max_size and ls_max_size values, it is RECOMMENDED to check that
the maximum encoding time and maximum memory requirements at a
FECFRAME sender, and maximum decoding time and maximum memory
requirements at a FECFRAME receiver, stay within reasonable bounds.
When assuming that the encoding and decoding times are negligible
with respect to the target max_lat, this should be verified as well,
otherwise the max_lat SHOULD be adjusted accordingly.
The particular case of session start needs to be managed
appropriately since the ew_size, starting at zero, increases each
time a new source ADU is received by the FECFRAME sender, until it
reaches the ew_max_size value. Therefore a FECFRAME receiver SHOULD
continuously observe the received FEC Repair Packets, since the NSS
value carried in the Repair FEC Payload ID will increase too, and
adjust its ls_max_size accordingly if need be. With a CBR flow,
session start is expected to be the only moment when the encoding
window size will increase. Similarly, with a CBR real-time flow, the
session end is expected to be the only moment when the encoding
window size will progressively decrease. No adjustment of the
ls_max_size is required at the FECFRAME receiver in that case.
C.2. Other Types of Real-Time Flow
In the following, we consider a real-time source ADU flow with a
max_lat latency budget and a variable bitrate (VBR) measured at the
entry of the FECFRAME sender. A first approach consists in
considering the smallest instantaneous bitrate of the source ADU
flow, when this parameter is known, and to reuse the derivation of
Appendix C.1. Considering the smallest bitrate means that the
encoding and decoding window maximum size estimations are
pessimistic: these windows have the smallest size required to enable
on-time decoding at a FECFRAME receiver. If the instantaneous
bitrate is higher than this smallest bitrate, this approach leads to
an encoding window that is unnecessarily small, which reduces
robustness in front of long erasure bursts.
Another approach consists in using ADU timing information (e.g.,
using the timestamp field of an RTP packet header, or registering the
time upon receiving a new ADU). From the global FEC-related latency
budget, the FECFRAME sender can derive a practical maximum latency
budget for encoding operations, max_lat_for_encoding. For the FEC
Schemes specified in this document, this latency budget SHOULD be
computed with:
max_lat_for_encoding = max_lat * WSR / 255
It follows that any source symbols associated to an ADU that has
timed-out with respect to max_lat_for_encoding SHOULD be removed from
the encoding window. With this approach there is no pre-determined
ew_size value: this value fluctuates over the time according to the
instantaneous source ADU flow bitrate. For practical reasons, a
FECFRAME sender may still require that ew_size does not increase
beyond a maximum value (Appendix C.3).
With both approaches, and no matter the choice of the FECFRAME
sender, a FECFRAME receiver can still easily evaluate the ew_max_size
by observing the maximum Number of Source Symbols (NSS) value
contained in the Repair FEC Payload ID of received FEC Repair
Packets. A receiver can then compute dw_max_size and derive an
appropriate ls_max_size as explained in Appendix C.1.
When the observed NSS fluctuates significantly, a FECFRAME receiver
may want to adapt its ls_max_size accordingly. In particular when
the NSS is significantly reduced, a FECFRAME receiver may want to
reduce the ls_max_size too in order to limit computation complexity.
A balance must be found between using an ls_max_size "too large"
(which increases computation complexity and memory requirements) and
the opposite (which reduces recovery performance).
C.3. Case of a Non Real-Time Flow
Finally there are configurations where a source ADU flow has no real-
time constraints. FECFRAME and the FEC Schemes defined in this
document can still be used. The choice of appropriate parameter
values can be directed by practical considerations. For instance, it
can derive from an estimation of the maximum memory amount that could
be dedicated to the linear system at a FECFRAME receiver, or the
maximum computation complexity at a FECFRAME receiver, both of them
depending on the ls_max_size parameter. The same considerations also
apply to the FECFRAME sender, where the maximum memory amount and
computation complexity depend on the ew_max_size parameter.
Here also, the NSS value contained in FEC Repair Packets is used by a
FECFRAME receiver to determine the current coding window size and
ew_max_size by observing its maximum value over the time.
Appendix D. Decoding Beyond Maximum Latency Optimization
(Informational)
This annex introduces non normative considerations. It is provided This annex introduces non normative considerations. It is provided
as suggestions, without any impact on interoperability. For more as suggestions, without any impact on interoperability. For more
information see [Roca16]. information see [Roca16].
With a real-time source ADU flow, it is possible to improve the With a real-time source ADU flow, it is possible to improve the
decoding performance of sliding window codes without impacting decoding performance of sliding window codes without impacting
maximum latency, at the cost of extra memory and CPU overhead. The maximum latency, at the cost of extra memory and CPU overhead. The
optimization consists, for a FECFRAME receiver, to extend the linear optimization consists, for a FECFRAME receiver, to extend the linear
system beyond the decoding window maximum size, by keeping a certain system beyond the decoding window maximum size, by keeping a certain
skipping to change at page 35, line 32 skipping to change at page 42, line 17
ls_max_size = 2 * dw_max_size ls_max_size = 2 * dw_max_size
When the dw_max_size is very small, it may be preferable to keep a When the dw_max_size is very small, it may be preferable to keep a
minimum ls_max_size value (e.g., LS_MIN_SIZE_DEFAULT = 40 symbols). minimum ls_max_size value (e.g., LS_MIN_SIZE_DEFAULT = 40 symbols).
Going below this threshold will not save a significant amount of Going below this threshold will not save a significant amount of
memory nor CPU cycles. Therefore: memory nor CPU cycles. Therefore:
ls_max_size = max(2 * dw_max_size, LS_MIN_SIZE_DEFAULT) ls_max_size = max(2 * dw_max_size, LS_MIN_SIZE_DEFAULT)
Finally, it is worth noting that a good receiver, i.e., a receiver Finally, it is worth noting that a receiver that benefits from an FEC
that benefits from an FEC protection significantly higher than what protection significantly higher than what is required to recover from
is required to recover from packet losses, can choose to reduce the packet losses, can choose to reduce the ls_max_size. In that case
ls_max_size. In that case lost ADUs will be recovered without lost ADUs will be recovered without relying on this optimization.
relying on this optimization.
ls_max_size ls_max_size
/---------------------------------^-------------------------------\ /---------------------------------^-------------------------------\
late source symbols late source symbols
(pot. decoded but not delivered) dw_max_size (pot. decoded but not delivered) dw_max_size
/--------------^-----------------\ /--------------^---------------\ /--------------^-----------------\ /--------------^---------------\
src0 src1 src2 src3 src4 src5 src6 src7 src8 src9 src10 src11 src12 src0 src1 src2 src3 src4 src5 src6 src7 src8 src9 src10 src11 src12
Figure 9: Relationship between parameters to decode beyond maximum Figure 14: Relationship between parameters to decode beyond maximum
latency. latency.
It means that source symbols, and therefore ADUs, may be decoded even It means that source symbols, and therefore ADUs, may be decoded even
if the added latency exceeds the maximum value permitted by the if the added latency exceeds the maximum value permitted by the
application (the "late source symbols" of Figure 9). It follows that application (the "late source symbols" of Figure 14). It follows
the corresponding ADUs will not be useful to the application. that the corresponding ADUs will not be useful to the application.
However, decoding these "late symbols" significantly improves the However, decoding these "late symbols" significantly improves the
global robustness in bad reception conditions and is therefore global robustness in bad reception conditions and is therefore
recommended for receivers experiencing bad communication conditions recommended for receivers experiencing bad communication conditions
[Roca16]. In any case whether or not to use this optimization and [Roca16]. In any case whether or not to use this optimization and
what exact value to use for the ls_max_size parameter are local what exact value to use for the ls_max_size parameter are local
decisions made by each receiver independently, without any impact on decisions made by each receiver independently, without any impact on
the other receivers nor on the source. the other receivers nor on the source.
Authors' Addresses Authors' Addresses
skipping to change at page 36, line 21 skipping to change at page 43, line 4
the other receivers nor on the source. the other receivers nor on the source.
Authors' Addresses Authors' Addresses
Vincent Roca Vincent Roca
INRIA INRIA
Univ. Grenoble Alpes Univ. Grenoble Alpes
France France
EMail: vincent.roca@inria.fr EMail: vincent.roca@inria.fr
Belkacem Teibi Belkacem Teibi
INRIA INRIA
Univ. Grenoble Alpes Univ. Grenoble Alpes
France France
EMail: belkacem.teibi@inria.fr EMail: belkacem.teibi@gmail.com
Emmanuel Baccelli
INRIA
France
EMail: emmanuel.baccelli@inria.fr
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