TSVWG                                                            V. Roca
Internet-Draft                                                  B. Teibi
Intended status: Standards Track                                   INRIA
Expires: April 29, September 5, 2018                                 March 4, 2018                                 October 26, 2017

Sliding Window Random Linear Code (RLC) Forward Erasure Correction (FEC)
                          Schemes for FECFRAME
                   draft-ietf-tsvwg-rlc-fec-scheme-01
                   draft-ietf-tsvwg-rlc-fec-scheme-02

Abstract

   This document describes two fully-specified FEC Schemes for Sliding
   Window Random Linear Codes (RLC), one for RLC over GF(2) (binary
   case), a second one for RLC over GF(2^^8), both of them with the
   possibility of controlling the code density.  They are meant to
   protect arbitrary media streams along the lines defined by FECFRAME
   extended to sliding window FEC codes.  These sliding window FEC codes
   rely on an encoding window that slides over the source symbols,
   generating new repair symbols whenever needed.  Compared to block FEC
   codes, these sliding window FEC codes offer key advantages with real-
   time flows in terms of reduced FEC-related latency while often
   providing improved erasure recovery capabilities.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on April 29, September 5, 2018.

Copyright Notice

   Copyright (c) 2017 2018 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Limits of Block Codes with Real-Time Flows  . . . . . . .   3
     1.2.  Lower Latency and Better Protection of Real-Time Flows
           with the Sliding Window RLC Codes . . . . . . . . . . . .   4
     1.3.  Small Transmission Overheads with the Sliding Window RLC
           FEC Scheme  . . . . . . . . . . . . . . . . . . . . . . .   5
     1.4.  Document Organization . . . . . . . . . . . . . . . . . .   5
   2.  Definitions and Abbreviations . . . . . . . . . . . . . . . .   6
   3.  Procedures  . . . . . . . . . . . . . . . . . . . . . . . . .   6
     3.1.  Parameters Derivation . . . . . . . . . . . . . . . . . .   6   7
     3.2.  ADU, ADUI and Source Symbols Mappings . . . . . . . . . .   8   9
     3.3.  Encoding Window Management  . . . . . . . . . . . . . . .   9  10
     3.4.  Pseudo-Random Number Generator  . . . . . . . . . . . . .  10  11
     3.5.  Coding Coefficients Generation Function . . . . . . . . .  11  12
   4.  Sliding Window RLC FEC Scheme over GF(2) GF(2^^8) for Arbitrary ADU
       Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13  14
     4.1.  Formats and Codes . . . . . . . . . . . . . . . . . . . .  13  14
       4.1.1.  FEC Framework Configuration Information . . . . . . .  13  14
       4.1.2.  Explicit Source FEC Payload ID  . . . . . . . . . . .  13  15
       4.1.3.  Repair FEC Payload ID . . . . . . . . . . . . . . . .  14  16
       4.1.4.  Additional Procedures . . . . . . . . . . . . . . . .  14  17
   5.  Sliding Window RLC FEC Scheme over GF(2^^8) GF(2) for Arbitrary ADU
       Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14  18
     5.1.  Formats and Codes . . . . . . . . . . . . . . . . . . . .  14  18
       5.1.1.  FEC Framework Configuration Information . . . . . . .  14  18
       5.1.2.  Explicit Source FEC Payload ID  . . . . . . . . . . .  15  18
       5.1.3.  Repair FEC Payload ID . . . . . . . . . . . . . . . .  16  18
       5.1.4.  Additional Procedures . . . . . . . . . . . . . . . .  17  18
   6.  FEC Code Specification  . . . . . . . . . . . . . . . . . . .  17  18
     6.1.  Encoding Side . . . . . . . . . . . . . . . . . . . . . .  17  18
     6.2.  Decoding Side . . . . . . . . . . . . . . . . . . . . . .  18  19
   7.  Implementation Status . . . . . . . . . . . . . . . . . . . .  18  20
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  19  20
     8.1.  Attacks Against the Data Flow . . . . . . . . . . . . . .  19  20
       8.1.1.  Access to Confidential Content  . . . . . . . . . . .  19  20
       8.1.2.  Content Corruption  . . . . . . . . . . . . . . . . .  19  21
     8.2.  Attacks Against the FEC Parameters  . . . . . . . . . . .  19  21
     8.3.  When Several Source Flows are to be Protected Together  .  20  21
     8.4.  Baseline Secure FEC Framework Operation . . . . . . . . .  20  21
   9.  Operations and Management Considerations  . . . . . . . . . .  20  22
     9.1.  Operational Recommendations: Finite Field GF(2) Versus
           GF(2^^8)  . . . . . . . . . . . . . . . . . . . . . . . .  21  22
     9.2.  Operational Recommendations: Coding Coefficients Density
           Threshold . . . . . . . . . . . . . . . . . . . . . . . .  21  22
   10. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  21  23
   11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  22  23
   12. References  . . . . . . . . . . . . . . . . . . . . . . . . .  22  23
     12.1.  Normative References . . . . . . . . . . . . . . . . . .  22  23
     12.2.  Informative References . . . . . . . . . . . . . . . . .  22  24
   Appendix A.  Decoding Beyond Maximum Latency Optimization . . . .  24  26
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  24  26

1.  Introduction

   Application-Level Forward Erasure Correction (AL-FEC) codes codes, or
   simply FEC codes, are a key element of communication systems.  They
   are used to recover from packet losses (or erasures) during content
   delivery sessions to a large number of receivers (multicast/broadcast
   transmissions).  This is the case with the FLUTE/ALC protocol
   [RFC6726] in case of reliable file transfers over lossy networks, and
   the FECFRAME protocol for reliable continuous media transfers over
   lossy networks.

   The present document only focusses on the FECFRAME protocol, used in
   multicast/broadcast delivery mode, with contents that feature
   stringent real-time constraints: each source packet has a maximum
   validity period after which it will not be considered by the
   destination application.

1.1.  Limits of Block Codes with Real-Time Flows

   With FECFRAME, there is a single FEC encoding point (either a end-
   host/server (source) or a middlebox) and a single FEC decoding point
   (either a end-host (receiver) or middlebox).  In this context,
   currently standardized AL-FEC codes for FECFRAME like Reed-Solomon
   [RFC6865], LDPC-Staircase [RFC6816], or Raptor/RaptorQ, are all
   linear block codes: they require the data flow to be segmented into
   blocks of a predefined maximum size.  The

   Defining this block size is a requires to find an appropriate balance
   between robustness (in particular and decoding latency: the larger the block size,
   the higher the robustness (e.g., in front of long packet erasure bursts for
   which there is an incentive to increase
   bursts), but also the higher the block size) and maximum decoding latency (for which there is (i.e., the
   maximum time required to recover an incentive lost (erased) packet thanks to decrease the
   block size).
   FEC protection).  Therefore, with a multicast/broadcast session, session where
   different receivers experience different packet loss rates, the block code is dimensioned
   size should be chosen by considering the worst communication
   channel
   conditions one wants to support, and this but without exceeding the desired
   maximum decoding latency.  This choice impacts will impact all receivers,
   no matter their individual channel quality. receivers.

1.2.  Lower Latency and Better Protection of Real-Time Flows with the
      Sliding Window RLC Codes

   This document introduces two fully-specified FEC Schemes that follow
   a totally different approach: the Sliding Window Random Linear Codes
   (RLC) over either Finite Field GF(2) or GF(8).  These FEC Schemes are
   used to protect arbitrary media streams along the lines defined by
   FECFRAME extended to sliding window FEC codes [fecframe-ext].  These
   FEC Schemes are extremely efficient for instance with media that
   feature real-time constraints sent within a multicast/broadcast
   session.

   The RLC codes belong to the broad class of sliding window AL-FEC
   codes (A.K.A. convolutional codes).  The encoding process 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), and which is
   either of fixed or variable size (elastic window).  Repair packets
   (symbols) are generated and sent on-the-fly, after computing a random
   linear combination of the source symbols present in the current
   encoding window.

   At the receiver, a linear system is managed from the set of received
   source and repair packets.  New variables (representing source
   symbols) and equations (representing the linear combination of each
   repair symbol received) are added upon receiving new packets.
   Variables are removed when they are too old with respect to their
   validity period (real-time constraints), as well as the associated
   equations they are involved in (Appendix A introduces an optimisation optimization
   that extends the time a variable is considered in the system).
   Erased  Lost
   source symbols are then recovered thanks to this linear system
   whenever its rank permits it.

   With RLC codes (more generally with sliding window codes), the
   protection of a multicast/broadcast session also needs to be
   dimensioned by considering the worst communication channel conditions one
   wants to support.  However the receivers experiencing a good to
   medium
   channel communication quality will observe a FEC-related latency close
   to zero [Roca17] since an isolated erased lost source packet is quickly
   recovered by with the following repair packet.  On the opposite, with a
   block code, recovering an isolated erased lost source packet always requires
   waiting the end of the block for the first repair packet to arrive.
   Additionally, under certain situations (e.g., with a limited FEC-
   related latency budget and with constant bit rate transmissions after
   FECFRAME encoding), sliding window codes achieve more easily a target
   transmission quality (e.g., measured by the residual loss after FEC
   decoding) by sending fewer repair packets (i.e., higher code rate)
   than block codes.

1.3.  Small Transmission Overheads with the Sliding Window RLC FEC
      Scheme

   The Sliding Window RLC FEC Scheme is designed so as to reduce the
   transmission overhead.  The main requirement is that each repair
   packet header must enable a receiver to reconstruct the list set of source
   symbols and plus the associated random coefficients used during the encoding
   process.  In order to minimize packet overhead, the set of source
   symbols in the encoding window as well as the set of coefficients
   over GF(2^^m) (where m is 1 or 8, depending on the FEC Scheme) used
   in the linear combination are not individually listed in the repair
   packet header.  Instead, each FEC repair packet Repair Packet header contains:

   o  the Encoding Symbol Identifier (ESI) of the first source symbol in
      the encoding window as well as the number of symbols (since this
      number may vary with a variable size, elastic window).  These two
      pieces of information enable each receiver to easily reconstruct
      the set of source symbols considered during encoding, the only
      constraint being that there cannot be any gap;
   o  the seed used by a coding coefficients generation function
      (Section 3.5).  This information enables each receiver to generate
      the same set of coding coefficients over GF(2^^m) as the sender;

   Therefore, no matter the number of source symbols present in the
   encoding window, each FEC repair packet Repair Packet features a fixed 64-bit long
   header, called Repair FEC Payload ID (Figure 7).  Similarly, each FEC
   source packet
   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 symbol (see the ADUI and source symbol mapping, Section 3.2).

1.4.  Document Organization

   This fully-specified FEC Scheme follows the structure required by
   [RFC6363], section 5.6.  "FEC Scheme Requirements", namely:

   3.  Procedures:  This section describes procedures specific to this
      FEC Scheme, namely: RLC parameters derivation, ADUI and source
      symbols mapping, pseudo-random number generator, and coding
      coefficients generation function;
   4.  Formats and Codes:  This section defines the Source FEC Payload
      ID and Repair FEC Payload ID formats, carrying the signalling
      information associated to each source or repair symbol.  It also
      defines the FEC Framework Configuration Information (FFCI)
      carrying signalling information for the session;

   5.  FEC Code Specification:  Finally this section provides the code
      specification.

2.  Definitions and Abbreviations

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

   This document uses the following definitions and abbreviations:

   GF(q)  denotes a finite field (also known as the Galois Field) with q
      elements.  We assume that q = 2^^m in this document
   m  defines the length of the elements in the finite field, in bits.
      In this document, m is equal to 1 or 8
   ADU:  Application Data Unit
   ADUI:  Application Data Unit Information (includes the F, L and
      padding fields in addition to the ADU)
   E: size of an encoding symbol size (i.e., source or repair symbol),
      assumed fixed (in bytes)
   br_in:  transmission bitrate at the input of the FECFRAME sender,
      assumed fixed (in bits/s)
   br_out:  transmission bitrate at the output of the FECFRAME sender,
      assumed fixed (in bits/s)
   max_lat:  maximum FEC-related latency within FECFRAME (in seconds)
   cr:  AL-FEC  RLC coding rate rate, ratio between the total number of source
      symbols and the total number of source plus repair symbols
   plr:  packet loss rate on the packet erasure channel
   ew_size:  encoding window current size at a sender (in symbols)
   ew_max_size:  encoding window maximum size at a sender (in symbols)
   dw_size:  decoding window current 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
      symbols)
   ls_size:  linear system current size (or width) at a receiver (in
      symbols)
   PRNG:  pseudo-random number generator
   pmms_rand(maxv):  PRNG defined in Section 3.4 and used in this
      specification, that returns a new random integer in [0; maxv-1]

3.  Procedures

   This section introduces the
   DT:  coding coefficients density threshold, an integer between 0 and
      15 (inclusive) the controls the fraction of coefficients that are
      non zero

3.  Procedures

   This section introduces the procedures that are used by this FEC
   Scheme.

3.1.  Parameters Derivation

   The Sliding Window RLC FEC Scheme relies on several key internal parameters:

   Maximum FEC-related latency budget, max_lat (in seconds)  A source
      ADU flow can have real-time constraints, and therefore any
      FECFRAME related operation must take place within the validity
      period of each ADU.  When there are multiple flows with different
      real-time constraints, we consider the most stringent constraints
      (see [RFC6363], Section 10.2, item 6, for recommendations when
      several flows are globally protected).  This  The maximum FEC-related
      latency budget, max_lat, accounts for all sources of latency added
      by FEC encoding
      (sender) (at a sender) and FEC decoding (receiver). (at a receiver).
      Other sources of latency (e.g., added by network communications)
      are out of scope and must be considered separately (e.g., (said
      differently, they have already been deducted).
      It deducted from max_lat).
      max_lat can be regarded as the latency budget permitted for all FEC-
      related
      FEC-related operations.  This is also an input parameter that enables
      to derive other internal parameters; parameters as explained below;
   Encoding window current (resp. maximum) size, ew_size (resp.
   ew_max_size) (in symbols):
      these parameters are used by a sender during FEC encoding.  More
      precisely, each repair symbol is a linear combination of the
      ew_size source symbols present in the encoding window when RLC
      encoding took place.  In all situations, we MUST have have:

         ew_size <=
      ew_max_size; ew_max_size
   Decoding window current (resp. maximum) maximum size, dw_size (resp.
   dw_max_size) dw_max_size (in symbols):
      these parameters are used by  at a receiver when managing the linear
      system used for decoding.  dw_size is
      receiver, this parameter determines the current maximum size of the
      decoding window, i.e., window.  Said differently, this is the set maximum number of
      received or erased lost source symbols that are currently part of in the linear system.  In all
      situations, we MUST have dw_size <= dw_max_size;

   In order to comply with system (i.e., the maximum FEC-related
      variables) that are still within their latency budget,
   assuming budget.  In
      situations where packets are sent with a constant transmission bitrate at the output of fixed period, the
   FECFRAME sender (br_out), encoding symbol size (E), and code rate
   (cr), we have:

      dw_max_size = (max_lat * br_out * cr) / (8 * E)

   This
      dw_max_size defines parameter directly determines the maximum delay after which an old source
   symbol may be recovered: after this delay, this old source symbol
   symbol will be removed from the decoding window.

   It is often good practice
      latency experienced by the receiver, which necessarily needs to choose:

      ew_max_size = dw_max_size / 2

   However any value ew_max_size < dw_max_size can be used without
   impact on
      in line with the maximum FEC-related latency budget.  Finding the optimal value
   can depend on the erasure channel one wants to support and should be
   determined after simulations or field trials.  Note also
      that the decoding beyond maximum latency optimisation
   (Appendix A) enables an old source symbol to be kept optimization detailed in Appendix A can extend the linear
      system with additional old source symbols (that timed-out) beyond the FEC-related latency budget, but not delivered to
      dw_max_size;
   Symbol size, E (in bytes) and RLC code rate (cr):  the E parameter
      determines the (source or repair) symbol sizes.  The cr parameter
      determines the code rate, i.e., the amount of redundancy added to
      the flow (it is the ratio between the total number of source
      symbols and the total number of source plus repair symbols).
      These two parameters are input parameters that enable to derive
      other internal parameters as explained below.  In practice they
      will usually be fixed, especially with multicast/broadcast
      transmissions.  In specific use-cases, in particular with unicast
      transmissions in presence of a feedback mechanism that estimates
      the communication quality (out-of-scope of FECFRAME), the code
      rate may be adjusted dynamically.

   Let us assume that the encoding symbol size (E, in bytes) and code
   rate (cr) are constant.  Let us also assume a constant transmission
   bitrate (br_out, in bits/s) at the output of the FECFRAME sender (as
   in [Roca17]).  It means that the source flow bitrate needs to be
   adjusted according to the added repair flow overhead in order to keep
   the total transmission bitrate fixed and equal to br_out.  In order
   to comply with the maximum FEC-related latency budget we need:

      dw_max_size = (max_lat * br_out * cr) / (8 * E)

   Sometimes the opposite can happen: the source flow bitrate at the
   input of the FECFRAME sender is fixed (br_in, in bits/s).  It means
   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 need:

      dw_max_size = (max_lat * br_in) / (8 * E)

   Finally, there are situations where no such assumption can be made
   (e.g., with a variable bit rate input flow).  In that case the
   encoding and decoding window maximum sizes may be initialized, based
   on the input flow features (e.g., the peak bitrate if it is known)
   and great care must be taken on timing aspects at a sender (see
   Section 3.3) and receiver.  The details of how to manage these
   situations are use-case dependent and out of scope of this document.

   Then, once the dw_max_size has been determined, the ew_max_size can
   be defined.  For decoding to be possible, it is required that the
   encoding window maximum size be at most equal to the decoding window
   maximum size.  It is often good practice to choose [Roca17]:

      ew_max_size = dw_max_size * 0.75

   However any value ew_max_size < dw_max_size can be used without
   impact on the FEC-related latency budget.  Finding the optimal value
   will depend on the use-case details and should be determined after
   simulations or field trials.  This is of course out of scope of this
   document.

   Note that the decoding beyond maximum latency optimization
   (Appendix A) enables an old source symbol to be kept in the linear
   system beyond the FEC-related latency budget, but not delivered to
   the receiving application.  Here we have: ls_size  In any case, the linear system maximum
   size is greater than (with the decoding optimization) or equal to
   (without) the decoding window maximum size:

      ls_max_size >= dw_max_size

3.2.  ADU, ADUI and Source Symbols Mappings

   An ADU, coming from the application, cannot be mapped to source
   symbols directly.  Indeed, an erased a lost ADU recovered at a receiver must
   contain enough information to be assigned to the right application
   flow (UDP port numbers and IP addresses cannot be used to that
   purpose as they are not protected by FEC encoding).  This requires
   adding the flow identifier to each ADU before doing FEC encoding.

   Additionally, since ADUs are of variable size, padding is needed so
   that each ADU (with its flow identifier) contribute to an integral
   number of source symbols.  This requires adding the original ADU
   length to each ADU before doing FEC encoding.  Because of these
   requirements, an intermediate format, the ADUI, or ADU Information,
   is considered [RFC6363].

   For each incoming ADU, an ADUI is created as follows.  First of all,
   3 bytes are prepended: prepended (Figure 1):

   Flow ID (F) (8-bit field):  this unsigned byte contains the integer
      identifier associated to the source ADU flow to which this ADU
      belongs.  It is assumed that a single byte is sufficient, which
      implies that no more than 256 flows will be protected by a single
      FECFRAME instance.
   Length (L) (16-bit field):  this unsigned integer contains the length
      of this ADU, in network byte order (i.e., big endian).  This
      length is for the ADU itself and does not include the F, L, or Pad
      fields.

   Then, zero padding is added to the ADU if needed:

   Padding (Pad) (variable size field):  this field contains zero
      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).

   Each ADUI contributes to an integral number of source symbols.

   The data unit resulting from the ADU and the F, L, and Pad fields is
   called ADU Information (or ADUI). ADUI.  Since ADUs can be of have different
   size, sizes, this is also the
   case for ADUIs.  However an ADUI always contributes to an integral
   number of source symbols.

      symbol length, E              E                     E
   < ------------------ >< ------------------ >< ------------------ >
   +-+--+---------------------------------------------+-------------+
   |F| L|                     ADU                     |     Pad     |
   +-+--+---------------------------------------------+-------------+

    Figure 1: ADUI Creation example (here 3 source symbols are created
                              for this ADUI).

   Note that neither the initial 3 bytes nor the optional padding are
   sent over the network.  However, they are considered during FEC
   encoding.  It means that
   encoding, and a receiver who lost a certain FEC source
   packet Source Packet (e.g.,
   the UDP datagram containing this FEC source packet) Source Packet) will be able to
   recover the ADUI if FEC decoding succeeds.  Thanks to the initial 3
   bytes, this receiver will get rid of the padding (if any) and
   identify the corresponding ADU flow.

3.3.  Encoding Window Management

   Source symbols and the corresponding ADUs are removed from the
   encoding window:

   o  when the sliding encoding window has reached its maximum size,
      ew_max_size.  In that case the oldest symbol MUST be removed
      before adding a new symbol, so that the current encoding window
      size always remains inferior or equal to the maximum size: ew_size
      <= ew_max_size;
   o  when an ADU has reached its maximum validity duration in case of a
      real-time flow.  When this happens, all source symbols
      corresponding to the ADUI that expired SHOULD be removed from the
      encoding window;

   Source symbols are added to the sliding encoding window each time a
   new ADU arrives, once the ADU to ADUI and then to source symbols mapping has been
   performed (Section 3.2).  The current size of the encoding window,
   ew_size, is updated after adding new source symbols.  This process
   may require to remove old source symbols so that: ew_size <=
   ew_max_size.

   Note that a FEC codec may feature practical limits in the number of
   source symbols in the encoding window (e.g., for computational
   complexity reasons).  This factor may further limit the ew_max_lat ew_max_size
   value, in addition to the maximum FEC-related latency budget
   (Section 3.1).

3.4.  Pseudo-Random Number Generator

   The RLC codes rely on the following Pseudo-Random Number Generator
   (PRNG), identical to the PRNG used with LDPC-Staircase codes
   ([RFC5170], section 5.7).

   The Park-Miler "minimal standard" PRNG [PM88] MUST be used.  It
   defines a simple multiplicative congruential algorithm: Ij+1 = A * Ij
   (modulo M), with the following choices: A = 7^^5 = 16807 and M =
   2^^31 - 1 = 2147483647.  A validation criteria of such a PRNG is the
   following: if seed = 1, then the 10,000th value returned MUST be
   equal to 1043618065.

   Several implementations of this PRNG are known and discussed in the
   literature.  An optimized implementation of this algorithm, using
   only 32-bit mathematics, and which does not require any division, can
   be found in [rand31pmc].  It uses the Park and Miller algorithm
   [PM88] with the optimization suggested by D.  Carta in [CA90].  The
   history behind this algorithm is detailed in [WI08].  Yet, any other
   implementation of the PRNG algorithm that matches the above
   validation criteria, like the ones detailed in [PM88], is
   appropriate.

   This PRNG produces, natively, a 31-bit value between 1 and 0x7FFFFFFE
   (2^^31-2) inclusive.  Since it is desired to scale the pseudo-random
   number between 0 and maxv-1 inclusive, one must keep the most
   significant bits of the value returned by the PRNG (the least
   significant bits are known to be less random, and modulo-based
   solutions should be avoided [PTVF92]).  The following algorithm MUST
   be used:

   Input:

      raw_value: random integer generated by the inner PRNG algorithm,
      between 1 and 0x7FFFFFFE (2^^31-2) inclusive.
      maxv: upper bound used during the scaling operation.

   Output:

      scaled_value: random integer between 0 and maxv-1 inclusive.

   Algorithm:

      scaled_value = (unsigned long) ((double)maxv * (double)raw_value /
      (double)0x7FFFFFFF);
      (NB: the above C type casting to unsigned long is equivalent to
      using floor() with positive floating point values.)

   In this document, pmms_rand(maxv) denotes the PRNG function that
   implements the Park-Miller "minimal standard" algorithm, defined
   above, and that scales the raw value between 0 and maxv-1 inclusive,
   using the above scaling algorithm.

   Additionally, the pmms_srand(seed) function must be provided to
   enable the initialization of the PRNG with a seed before calling
   pmms_rand(maxv) the first time.  The seed is a 31-bit integer between
   1 and 0x7FFFFFFE inclusive.  In this specification, the seed is
   restricted to a value between 1 and 0xFFFF inclusive, as this is the
   Repair_Key 16-bit field value of the Repair FEC Payload ID
   (Section 5.1.3). 4.1.3).

3.5.  Coding Coefficients Generation Function

   The coding coefficients, used during the encoding process, are
   generated at the RLC encoder by the generate_coding_coefficients()
   function each time a new repair symbol needs to be produced.  Note
   that the  The
   fraction of coefficients that are non zero (density) (i.e., the density) is
   controlled by a dedicated parameter, the DT (Density Threshold). Threshold) parameter.  When
   this parameter DT equals
   15, the maximum value, the function guaranties that all coefficients
   are non zero (i.e., maximum density).  When the
   parameter DT is between 0 (minimum
   value) and strictly inferior to 15, the average probability of having
   a non zero coefficients coefficient equals (DT +1) / 16.  The density is reduced in a controlled manner.

   These considerations apply both the RLC over GF(2) and RLC over
   GF(2^^8), the only difference being the value of the m parameter.
   With the RLC over GF(2) FEC Scheme (Section 4), 5), m MUST be equal to 1.
   With RLC over GF(2^^8) FEC Scheme (Section 5), 4), m MUST be equal to 8.

   <CODE BEGINS>
   /*
    * Fills in the table of coding coefficients (of the right size)
    * provided with the appropriate number of coding coefficients to
    * use for the repair symbol key provided.
    *
    * (in) repair_key    key associated to this repair symbol symbol. This
    *                    parameter is ignored (useless) if m=2 and dt=15
    * (in) cc_tab[]      pointer to a table of the right size to store
    *                    coding coefficients. All coefficients are
    *                    stored as bytes, regardless of the m parameter,
    *                    upon return of this function.
    * (in) cc_nb[] cc_nb         number of entries in the table. This value is
    *                    equal to the current encoding window size.
    * (in) density_threshold value dt            integer between 0 and 15 (inclusive) that
    *                    controls the density. With value 15, all
    *                    coefficients are guaranteed to be non zero
    *                    (i.e. equal to 1 with GF(2) and equal to a
    *                    value in {1,... 255} with GF(2^^8)), otherwise
    *                    a fraction of them will be 0.
    * (in) m             Finite Field GF(2^^m) parameter. In this
    *                    version                    document only values 1 and 8 are considered.
    * (out)              returns an error code
    */
   int generate_coding_coefficients (UINT16    repair_key,
                                     UINT8     cc_tab[],
                                     UINT16    cc_nb,
                                     UINT8     density_threshold,     dt,
                                     UINT8     m)
   {
       UINT32    i;

       if (repair_key == 0 || density_threshold (dt > 15) {
           return SOMETHING_WENT_WRONG; /* bad parameters dt parameter */
       }
       if (repair_key == 0 && dt != 15 && m != 2) {
           return SOMETHING_WENT_WRONG; /* bad repair_key parameter */
       }
       pmms_srand(repair_key);
       switch (m) {
       case 1:
           if (density_threshold (dt == 15) {
               /* all coefficients are 1 */
               memset(cc_tab, 1, cc_nb);
           } else {
               /* here coefficients are either 0 or 1 */
               pmms_srand(repair_key);
               for (i = 0 ; i < cc_nb ; i++) {
                   if (pmms_rand(16) <= density_threshold) dt) {
                       cc_tab[i] = (UINT8) 1;
                   } else {
                       cc_tab[i] = (UINT8) 0;
                   }
               }
           }
           break;

       case 8:
           pmms_srand(repair_key);
           if (density_threshold (dt == 15) {
               /* coefficient 0 is avoided here in order to include
                * all the source symbols */
               for (i = 0 ; i < cc_nb ; i++) {
                   do {
                       cc_tab[i] = (UINT8) pmms_rand(256);
                   } while (cc_tab[i] == 0);
               }
           } else {
               /* here a certain fraction of coefficients should be 0 */
               for (i = 0 ; i < cc_nb ; i++) {
                   if (pmms_rand(16) <= density_threshold) {
                       do {
                           cc_tab[i] = (UINT8) pmms_rand(256);
                       } while (cc_tab[i] == 0);
                   } else {
                       cc_tab[i] = 0;
                   }
               }
           }
           break;

       default:
           /* bad parameter m */
           return SOMETHING_WENT_WRONG;
       }
       return EVERYTHING_IS_OKAY;
   }
   <CODE ENDS>

       Figure 2: Coding Coefficients Generation Function pseudo-code

4.  Sliding Window RLC FEC Scheme over GF(2) for Arbitrary ADU Flows

   This fully-specified FEC Scheme defines the Sliding Window Random
   Linear Codes (RLC) over GF(2) (binary case).

4.1.  Formats and Codes

4.1.1.  FEC Framework Configuration Information

4.1.1.1.  Mandatory Information

   o  FEC Encoding ID: the value assigned to this fully specified FEC
      Scheme MUST be YYYY, as assigned by IANA (Section 10).

   When SDP is used to communicate the FFCI, this FEC Encoding ID is
   carried in the 'encoding-id' parameter.

4.1.1.2.  FEC Scheme-Specific Information

   All the considerations of Section 5.1.1.2 apply equally here.

4.1.2.  Explicit Source FEC Payload ID

   All the considerations of Section 5.1.1.2 apply equally here.

4.1.3.  Repair FEC Payload ID

   All the considerations of Section 5.1.1.2 apply equally here.

4.1.4.  Additional Procedures

   All is avoided here in order to include
                * all the considerations source symbols */
               for (i = 0 ; i < cc_nb ; i++) {
                   do {
                       cc_tab[i] = (UINT8) pmms_rand(256);
                   } while (cc_tab[i] == 0);
               }

           } else {
               /* here a certain fraction of Section 5.1.1.2 apply equally here.

5. coefficients should be 0 */
               for (i = 0 ; i < cc_nb ; i++) {
                   if (pmms_rand(16) <= dt) {
                       do {
                           cc_tab[i] = (UINT8) pmms_rand(256);
                       } while (cc_tab[i] == 0);
                   } else {
                       cc_tab[i] = 0;
                   }
               }
           }
           break;

       default:
           /* bad parameter m */
           return SOMETHING_WENT_WRONG;
       }
       return EVERYTHING_IS_OKAY;
   }
   <CODE ENDS>

       Figure 2: Coding Coefficients Generation Function pseudo-code

4.  Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary ADU Flows

   This fully-specified FEC Scheme defines the Sliding Window Random
   Linear Codes (RLC) over GF(2^^8).

5.1.

4.1.  Formats and Codes

5.1.1.

4.1.1.  FEC Framework Configuration Information

   The FEC Framework Configuration Information (or FFCI) includes
   information that MUST be communicated between the sender and
   receiver(s).  More specifically, it enables the synchronization of
   the FECFRAME sender and receiver instances.  It includes both
   mandatory elements and scheme-specific elements, as detailed below.

5.1.1.1.

4.1.1.1.  Mandatory Information

   o  FEC Encoding ID: the value assigned to this fully specified FEC
      Scheme MUST be XXXX, as assigned by IANA (Section 10).

   When SDP is used to communicate the FFCI, this FEC Encoding ID is
   carried in the 'encoding-id' parameter.

5.1.1.2.

4.1.1.2.  FEC Scheme-Specific Information

   The FEC Scheme-Specific Information (FSSI) includes elements that are
   specific to the present FEC Scheme.  More precisely:

   Encoding symbol size (E):  a non-negative integer that indicates the
      size of each encoding symbol in bytes;

   This element is required both by the sender (RLC encoder) and the
   receiver(s) (RLC decoder).

   When SDP is used to communicate the FFCI, this FEC Scheme-specific
   information is carried in the 'fssi' parameter in textual
   representation as specified in [RFC6364].  For instance:

   fssi=E:1400

   If another mechanism requires the FSSI to be carried as an opaque
   octet string (for instance, after a Base64 encoding), the encoding
   format consists of the following 2 octets:

      Encoding symbol length (E): 16-bit field.

    0                   1
    0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   Encoding Symbol Length (E)  |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      Figure 3: FSSI Encoding Format

5.1.2.

4.1.2.  Explicit Source FEC Payload ID

   A FEC source packet Source Packet MUST contain an Explicit Source FEC Payload ID
   that is appended to the end of the packet as illustrated in Figure 4.

   +--------------------------------+
   |           IP Header            |
   +--------------------------------+
   |        Transport Header        |
   +--------------------------------+
   |              ADU               |
   +--------------------------------+
   | Explicit Source FEC Payload ID |
   +--------------------------------+

   Figure 4: Structure of an FEC Source Packet with the Explicit Source
                              FEC Payload ID

   More precisely, the Explicit Source FEC Payload ID is composed of the
   following field (Figure 5):

   Encoding Symbol ID (ESI) (32-bit field):  this unsigned integer
      identifies the first source symbol of the ADUI corresponding to
      this FEC source packet. Source Packet.  The ESI is incremented for each new
      source symbol, and after reaching the maximum value (2^32-1),
      wrapping to zero occurs.

    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                   Encoding Symbol ID (ESI)                    |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

              Figure 5: Source FEC Payload ID Encoding Format

5.1.3.

4.1.3.  Repair FEC Payload ID

   A FEC repair packet MUST contain a Repair FEC Payload ID that is
   prepended to the repair symbol as illustrated in Figure 6.  There Packet can
   be contain one or more repair symbols per FEC repair packet. symbols.  When this is
   there are several repair symbols, all of them MUST have been
   generated from the case, same encoding window, using Repair_Key values that
   are managed as explained below.  A receiver can easily deduce the
   number of repair symbols within this a FEC repair packet
   is easily deduced Repair Packet by comparing the known
   received FEC repair packet Repair Packet size (equal to the UDP payload size when
   UDP is the underlying transport protocol) and the symbol size, E,
   communicated in the FFCI.
   When this

   A FEC Repair Packet MUST contain a Repair FEC Payload ID that is the case, all
   prepended to the repair symbols MUST have been
   generated from the same encoding window. symbol as illustrated in Figure 6.

   +--------------------------------+
   |           IP Header            |
   +--------------------------------+
   |        Transport Header        |
   +--------------------------------+
   |     Repair FEC Payload ID      |
   +--------------------------------+
   |         Repair Symbol          |
   +--------------------------------+

      Figure 6: Structure of an FEC Repair Packet with the Repair FEC
                                Payload ID

   More precisely, the Repair FEC Payload ID is composed of the
   following fields (Figure 7):

   Repair_Key (16-bit field):  this unsigned integer is used as a seed
      by the coefficient generation function (Section 3.5) in order to
      generate the desired number of coding coefficients.  Value 0 MUST
      NOT be used.  When a FEC repair packet Repair Packet contains several repair
      symbols, this repair key value is that of the first repair symbol.
      The remaining repair keys can be deduced by incrementing by 1 this
      value, up to a maximum value of 65535 after which it loops back to
      1 (note that 0 is not a valid value).
   Coding coefficients
   Density Threshold, Threshold for the coding coefficients, DT (4-bit field):
      this unsigned integer carried the Density Threshold (DT) used by
      the coding coefficient generation function Section 3.5.  More
      precisely, it controls the probability of having a non zero coding
      coefficient, which equals (DT+1) / 16.  When a FEC repair packet Repair Packet
      contains several repair symbols, the DT value applies to all of
      them;
   Number of Source Symbols in the Encoding Window, encoding window, NSS (12-bit field):

      this unsigned integer indicates the number of source symbols in
      the encoding window when this repair symbol was generated.  When a
      FEC repair packet Repair Packet contains several repair symbols, this NSS value
      applies to all of them;
   ESI of first source symbol First Source Symbol in the encoding window, FSS_ESI (32-bit
   field):
      this unsigned integer indicates the ESI of the first source symbol
      in the encoding window when this repair symbol was generated.
      When a FEC repair packet Repair Packet contains several repair symbols, this
      FSS_ESI value applies to all of them;

    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |       Repair_Key              |  DT   |NSS (# src symb in ew) |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                            FSS_ESI                            |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

              Figure 7: Repair FEC Payload ID Encoding Format

5.1.4.

4.1.4.  Additional Procedures

   The following procedure applies:

   o  The ESI of source symbols MUST start with value 0 for the first
      source symbol and MUST be managed sequentially.  Wrapping to zero
      will happen
      happens after reaching the maximum 32-bit value.

5.  Sliding Window RLC FEC Scheme over GF(2) for Arbitrary ADU Flows

   This fully-specified FEC Scheme defines the Sliding Window Random
   Linear Codes (RLC) over GF(2) (binary case).

5.1.  Formats and Codes

5.1.1.  FEC Framework Configuration Information

5.1.1.1.  Mandatory Information

   o  FEC Encoding ID: the value assigned to this fully specified FEC
      Scheme MUST be YYYY, as assigned by IANA (Section 10).

   When SDP is used to communicate the FFCI, this FEC Encoding ID is
   carried in the 'encoding-id' parameter.

5.1.1.2.  FEC Scheme-Specific Information

   All the considerations of Section 4.1.1.2 apply here.

5.1.2.  Explicit Source FEC Payload ID

   All the considerations of Section 4.1.1.2 apply here.

5.1.3.  Repair FEC Payload ID

   All the considerations of Section 4.1.1.2 apply here, with the only
   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
   coefficient generation function does not use any PRNG).  When DT = 15
   it is RECOMMENDED that the sender use value 0 for the Repair_Key
   field, but a receiver SHALL ignore this field.

5.1.4.  Additional Procedures

   All the considerations of Section 4.1.1.2 apply here.

6.  FEC Code Specification

6.1.  Encoding Side

   This section provides a high level description of a Sliding Window
   RLC encoder.

   Whenever a new FEC repair packet Repair Packet is needed, the RLC encoder instance
   first gathers the ew_size source symbols currently in the sliding
   encoding window.  Then it chooses a repair key, which can be a non
   zero monotonically increasing integer value, incremented for each
   repair symbol up to a maximum value of 65535 (as it is carried within
   a 16-bit field) after which it loops back to 1 (indeed, being used as
   a PRNG seed, value 0 is prohibited).  This repair key is communicated
   to the coefficient generation function (Section Section 3.5) in order
   to generate ew_size coding coefficients.  Finally, the FECFRAME
   sender computes the repair symbol as a linear combination of the
   ew_size source symbols using the ew_size coding coefficients.  When E
   is small and when there is an incentive to pack several repair
   symbols within the same FEC Repair Packet, the appropriate number of
   repair symbols are computed.  The only constraint is to increment by
   1 the repair key for each of them, keeping the same ew_size source
   symbols, since only the first repair key will be carried in the
   Repair FEC Payload ID.  The FEC repair packet Repair Packet can then be sent.  The
   source versus repair FEC packet transmission order is out of scope of
   this document and several approaches exist that are implementation
   specific.

   Other solutions are possible to select a repair key value when a new
   FEC Repair Packet is needed, for instance by choosing a random
   integer between 1 and 65535.  However, selecting the same repair key
   as before (which may happen in case of a random process) is only
   meaningful if the encoding window has changed, otherwise the same FEC
   Repair Packet will be generated.

6.2.  Decoding Side

   This section provides a high level description of a Sliding Window
   RLC decoder.

   A FECFRAME receiver needs to maintain a linear system whose variables
   are the received and lost source symbols.  Upon receiving a FEC
   repair packet,
   Repair Packet, a receiver first extracts all the repair symbols it
   contains (in case several repair symbols are packed together).  For
   each repair symbol, when at least one of the corresponding source
   symbols it protects has been lost, the receiver adds an equation to
   the linear system (or no equation if this repair packet does not
   change the linear system rank).  This equation of course re-uses the
   ew_size coding coefficients that are computed by the same coefficient
   generation function (Section Section 3.5), using the repair key and
   encoding window descriptions carried in the Repair FEC Payload ID.
   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
   recover lost source symbols.  Each time an ADUI can be totally
   recovered, it padding is removed (thanks to the Length field, L, of the
   ADUI) and the ADU is assigned to the corresponding application flow
   (thanks to the Flow ID (F) field of the ADUI) and padding (if any)
   removed (thanks to the Length (L) field field, F, of the ADUI).  This ADU is finally
   passed to the corresponding upper application.  Received FEC
   source packets, Source
   Packets, containing an ADU, can be passed to the application either
   immediately or after some time to guaranty an ordered delivery to the application(s).
   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
   latency (or or an ADU received far too late) after this delay should not be considered by passed to
   the application.  Instead the associated source symbols should be
   removed from the linear system maintained by the receiver(s).
   Appendix A discusses a backward compatible optimization whereby those
   late source symbols may still be useful used in order to improve the global loss
   recovery performance.
   robustness.

7.  Implementation Status

   Editor's notes: RFC Editor, please remove this section motivated by
   RFC 6982 before publishing the RFC.  Thanks.

   An implementation of the Sliding Window RLC FEC Scheme for FECFRAME
   exists:

   o  Organisation: Inria
   o  Description: This is an implementation of the Sliding Window RLC
      FEC Scheme. Scheme limited to GF(2^^8).  It relies on a modified version
      of our OpenFEC (http://openfec.org) FEC code library.  It is
      integrated in our FECFRAME software (see [fecframe-ext]).
   o  Maturity: prototype.
   o  Coverage: this software complies with the Sliding Window RLC FEC
      Scheme (limited to m=8 as of June, 2017).
      Scheme.
   o  Lincensing: proprietary.
   o  Contact: vincent.roca@inria.fr

8.  Security Considerations

   The FEC Framework document [RFC6363] provides a comprehensive
   analysis of security considerations applicable to FEC Schemes.
   Therefore, the present section follows the security considerations
   section of [RFC6363] and only discusses specific topics.

8.1.  Attacks Against the Data Flow

8.1.1.  Access to Confidential Content

   The Sliding Window RLC FEC Scheme specified in this document does not
   change the recommendations of [RFC6363].  To summarize, if
   confidentiality is a concern, it is RECOMMENDED that one of the
   solutions mentioned in [RFC6363] is used with special considerations
   to the way this solution is applied (e.g., is encryption applied
   before or after FEC protection, within the end-system or in a
   middlebox) to the operational constraints (e.g., performing FEC
   decoding in a protected environment may be complicated or even
   impossible) and to the threat model.

8.1.2.  Content Corruption

   The Sliding Window RLC FEC Scheme specified in this document does not
   change the recommendations of [RFC6363].  To summarize, it is
   RECOMMENDED that one of the solutions mentioned in [RFC6363] is used
   on both the FEC Source and Repair Packets.

8.2.  Attacks Against the FEC Parameters

   The FEC Scheme specified in this document defines parameters that can
   be the basis of attacks.  More specifically, the following parameters
   of the FFCI may be modified by an attacker who only targets receivers
   (Section 5.1.1.2): 4.1.1.2):

   o  FEC Encoding ID: changing this parameter leads the receivers to
      consider a different FEC Scheme, which enables an attacker to
      create a Denial of Service (DoS);
   o  Encoding symbol length (E): setting this E parameter to a
      different value will confuse the receivers and create a DoS.  More
      precisely, the FEC Repair Packets received will probably no longer
      be multiple of E, leading receivers to reject them;

   An attacker who only targets a sender will achieve the same results.
   However if the attacker targets both sender and receivers at the same
   time (the same wrong piece of information is communicated to
   everybody), the results will be suboptimal but less severe.

   It is therefore RECOMMENDED that security measures are taken to
   guarantee the FFCI integrity, as specified in [RFC6363].  How to
   achieve this depends on the way the FFCI is communicated from the
   sender to the receiver, which is not specified in this document.

   Similarly, attacks are possible against the Explicit Source FEC
   Payload ID and Repair FEC Payload ID: by modifying the Encoding
   Symbol ID (ESI), or the repair key, NSS or FSS_ESI.  It is therefore
   RECOMMENDED that security measures are taken to guarantee the FEC
   Source and Repair Packets as stated in [RFC6363].

8.3.  When Several Source Flows are to be Protected Together

   The Sliding Window RLC FEC Scheme specified in this document does not
   change the recommendations of [RFC6363].

8.4.  Baseline Secure FEC Framework Operation

   The Sliding Window RLC FEC Scheme specified in this document does not
   change the recommendations of [RFC6363] concerning the use of the
   IPsec/ESP security protocol as a mandatory to implement (but not
   mandatory to use) security scheme.  This is well suited to situations
   where the only insecure domain is the one over which the FEC
   Framework operates.

9.  Operations and Management Considerations

   The FEC Framework document [RFC6363] provides a comprehensive
   analysis of operations and management considerations applicable to
   FEC Schemes.  Therefore, the present section only discusses specific
   topics.

9.1.  Operational Recommendations: Finite Field GF(2) Versus GF(2^^8)

   The present document specifies two FEC Schemes that differ on the
   associated
   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
   warrants a high higher packet loss protection.  Additionally, elements in
   the finite field are 8 bits long, which makes read/write memory
   operations aligned on bytes during  In case of small encoding
   windows, the associated processing overhead is not an issue (e.g., we
   measured decoding speeds between 745 Mbps and decoding.

   Finally, 2.8 Gbps on an ARM
   Cortex-A15 embedded board in particular when dealing [Roca17]).  Of course the CPU overhead
   will increase with large the encoding windows, an
   alternative is window size, because more operations
   in the GF(2^^8) finite field will be needed.

   The RLC over GF(2) FEC Scheme. Scheme offers an alternative.  In that case
   operations symbols can be directly XORed XOR-ed together which warrants
   high bitrate encoding and decoding operations. operations, and can be an
   advantage with large encoding windows.  However packet loss
   protection is significantly reduced by using this FEC Scheme.

9.2.  Operational Recommendations: Coding Coefficients Density Threshold

   In addition to the choice of the Finite Field, the two FEC Schemes
   define a coding coefficient density threshold (DT) parameter.  This
   parameter enables a sender to control the code density, i.e., the
   proportion of coefficients that are non zero on average.  With RLC
   over GF(2^^8), it is recommended usually appropriate that small encoding windows
   be associated to a density threshold equal to 15, the maximum value,
   in order to warrant a high loss protection.

   On the opposite, with large larger encoding windows, it it recommened is usually
   appropriate that the density threshold be reduced.  With large
   encoding windows, an alternative can be to use RLC over GF(2) and a
   density threshold equal to 8 7 (i.e., an average density equal to 1/2)
   or smaller.

   Note also that using a density threshold equal to 15 with RLC over GF(2)
   is equivalent to using an XOR code that XOR's compute the XOR sum of all
   the source symbols
   of in the encoding window.  In that case it follows that: case: (1) a
   single repair symbol can be produced for a given any encoding window, and (2)
   the repair_key parameter is becomes useless (the coding coefficients
   generation function does not rely on the PRNG).

10.  IANA Considerations

   This document registers two values in the "FEC Framework (FECFRAME)
   FEC Encoding IDs" registry [RFC6363] as follows:

   o  YYYY refers to the Sliding Window Random Linear Codes (RLC) over
      GF(2) FEC Scheme for Arbitrary Packet Flows, as defined in
      Section 4 5 of this document.
   o  XXXX refers to the Sliding Window Random Linear Codes (RLC) over
      GF(2^^8) FEC Scheme for Arbitrary Packet Flows, as defined in
      Section 5 4 of this document.

11.  Acknowledgments

   The authors would like to thank Marie-Jose Montpetit for her valuable
   feedbacks on this document.

12.  References

12.1.  Normative References

   [fecframe-ext]
              Roca, V. and A. Begen, "Forward Error Correction (FEC)
              Framework Extension to Sliding Window Codes", Transport
              Area Working Group (TSVWG) draft-roca-tsvwg-fecframev2 draft-ietf-tsvwg-fecframe-ext
              (Work in Progress), June 2017,
              <https://tools.ietf.org/html/draft-roca-tsvwg-fecframev2>. March 2018,
              <https://tools.ietf.org/html/
              draft-ietf-tsvwg-fecframe-ext>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC6363]  Watson, M., Begen, A., and V. Roca, "Forward Error
              Correction (FEC) Framework", RFC 6363,
              DOI 10.17487/RFC6363, October 2011,
              <https://www.rfc-editor.org/info/rfc6363>.

   [RFC6364]  Begen, A., "Session Description Protocol Elements for the
              Forward Error Correction (FEC) Framework", RFC 6364,
              DOI 10.17487/RFC6364, October 2011,
              <https://www.rfc-editor.org/info/rfc6364>.

12.2.  Informative References

   [CA90]     Carta, D., "Two Fast Implementations of the Minimal
              Standard Random Number Generator",  Communications of the
              ACM, Vol. 33, No. 1, pp.87-88, January 1990.

   [PM88]     Park, S. and K. Miller, "Random Number Generators: Good
              Ones are Hard to Find",  Communications of the ACM, Vol.
              31, No. 10, pp.1192-1201, 1988.

   [PTVF92]   Press, W., Teukolsky, S., Vetterling, W., and B. Flannery,
              "Numerical Recipies in C; Second Edition", Cambridge
              University Press, ISBN: 0-521-43108-5, 1992.

   [rand31pmc]
              Whittle, R., "31 bit pseudo-random number generator",
              September 2005, <http://www.firstpr.com.au/dsp/rand31/
              rand31-park-miller-carta.cc.txt>.

   [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>.

   [RFC6726]  Paila, T., Walsh, R., Luby, M., Roca, V., and R. Lehtonen,
              "FLUTE - File Delivery over Unidirectional Transport",
              RFC 6726, DOI 10.17487/RFC6726, November 2012,
              <https://www.rfc-editor.org/info/rfc6726>.

   [RFC6816]  Roca, V., Cunche, M., and J. Lacan, "Simple Low-Density
              Parity Check (LDPC) Staircase Forward Error Correction
              (FEC) Scheme for FECFRAME", RFC 6816,
              DOI 10.17487/RFC6816, December 2012,
              <https://www.rfc-editor.org/info/rfc6816>.

   [RFC6865]  Roca, V., Cunche, M., Lacan, J., Bouabdallah, A., and K.
              Matsuzono, "Simple Reed-Solomon Forward Error Correction
              (FEC) Scheme for FECFRAME", RFC 6865,
              DOI 10.17487/RFC6865, February 2013,
              <https://www.rfc-editor.org/info/rfc6865>.

   [Roca16]   Roca, V., Teibi, B., Burdinat, C., Tran, T., and C.
              Thienot, "Block or Convolutional AL-FEC Codes? A
              Performance Comparison for Robust Low-Latency
              Communications", HAL open-archive document,hal-01395937
              https://hal.inria.fr/hal-01395937/en/, November 2016, <
              https://hal.inria.fr/hal-01395937/en/>.
              <https://hal.inria.fr/hal-01395937/en/>.

   [Roca17]   Roca, V., Teibi, B., Burdinat, C., Tran, T., and C.
              Thienot, "Less Latency and Better Protection with AL-FEC
              Sliding Window Codes: a Robust Multimedia CBR Broadcast
              Case Study", 13th IEEE International Conference on
              Wireless and Mobile Computing, Networking and
              Communications (WiMob17), October
              2017 https://hal.inria.fr/hal-01571609v1/en/, October
              2017, < https://hal.inria.fr/hal-01395937/en/>. <https://hal.inria.fr/hal-01571609v1/en/>.

   [WI08]     Whittle, R., "Park-Miller-Carta Pseudo-Random Number
              Generator",  http://www.firstpr.com.au/dsp/rand31/,
              January 2008, <http://www.firstpr.com.au/dsp/rand31/>.

Appendix A.  Decoding Beyond Maximum Latency Optimization

   This annex introduces non normative considerations.  They are
   provided as suggestions, without any impact on interoperability.  For
   more information see [Roca16].

   It is possible to improve the decoding performance of sliding window
   codes without impacting maximum latency, at the cost of extra CPU
   overhead.  The optimization consists, for a receiver, to extend the
   linear system beyond the decoding window: window, by keeping a certain number
   of old source symbols:

      ls_max_size > dw_max_size

   Usually the following choice is a good trade-off between decoding
   performance and extra CPU overhead:

      ls_max_size = 2 * dw_max_size

                                ls_max_size
   /---------------------------------^-------------------------------\

           late source symbols
    (pot. decoded but not delivered)            dw_max_size
   /--------------^-----------------\ /--------------^---------------\
   src0 src1 src2 src3 src4 src5 src6 src7 src8 src9 src10 src11 src12

    Figure 8: Relationship between parameters to decode beyond maximum
                                 latency.

   It means that source symbols (and symbols, and therefore ADUs) ADUs, may be decoded even
   if their transport protocol the added latency exceeds the maximum value permitted by the
   application.  It follows that these source symbols the corresponding ADUs SHOULD NOT be
   delivered to the application and SHOULD be dropped once they are no
   longer needed.  However, decoding these late symbols "late symbols" significantly
   improves the global robustness in bad reception conditions and is
   therefore recommended for receivers experiencing bad channels[Roca16]. communication
   conditions [Roca16].  In any case whether or not to use this
   facility
   optimization and what exact value to use for the ls_max_size
   parameter are decisions made by each receiver independently, without
   any impact on others, neither the other receivers nor on the source.

Authors' Addresses
   Vincent Roca
   INRIA
   Grenoble
   France

   EMail: vincent.roca@inria.fr

   Belkacem Teibi
   INRIA
   Grenoble
   France

   EMail: belkacem.teibi@inria.fr