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Versions: (draft-roca-tsvwg-rlc-fec-scheme) 00 01 02 03 04 05 06 07 08 09

TSVWG                                                            V. Roca
Internet-Draft                                                  B. Teibi
Intended status: Standards Track                                   INRIA
Expires: March 23, 2019                               September 19, 2018


Sliding Window Random Linear Code (RLC) Forward Erasure Correction (FEC)
                          Schemes for FECFRAME
                   draft-ietf-tsvwg-rlc-fec-scheme-09

Abstract

   This document describes two fully-specified Forward Erasure
   Correction (FEC) Schemes for Sliding Window Random Linear Codes
   (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
   with the possibility of controlling the code density.  They can
   protect arbitrary media streams along the lines defined by FECFRAME
   extended to sliding window FEC codes, as defined in [fecframe-ext].
   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 packet 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
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   This Internet-Draft will expire on March 23, 2019.

Copyright Notice

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




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   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
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   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 . . . . . . . . . . . . . . . . . .   6
   2.  Definitions and Abbreviations . . . . . . . . . . . . . . . .   6
   3.  Procedures  . . . . . . . . . . . . . . . . . . . . . . . . .   7
     3.1.  Possible Parameter Derivations  . . . . . . . . . . . . .   7
       3.1.1.  Case of a CBR Real-Time Flow  . . . . . . . . . . . .   8
       3.1.2.  Other Types of Real-Time Flow . . . . . . . . . . . .  10
       3.1.3.  Case of a Non Real-Time Flow  . . . . . . . . . . . .  11
     3.2.  ADU, ADUI and Source Symbols Mappings . . . . . . . . . .  11
     3.3.  Encoding Window Management  . . . . . . . . . . . . . . .  13
     3.4.  Pseudo-Random Number Generator (PRNG) . . . . . . . . . .  13
     3.5.  Coding Coefficients Generation Function . . . . . . . . .  15
     3.6.  Finite Fields Operations  . . . . . . . . . . . . . . . .  17
       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
       Packet Flows  . . . . . . . . . . . . . . . . . . . . . . . .  18
     4.1.  Formats and Codes . . . . . . . . . . . . . . . . . . . .  18
       4.1.1.  FEC Framework Configuration Information . . . . . . .  18
       4.1.2.  Explicit Source FEC Payload ID  . . . . . . . . . . .  19
       4.1.3.  Repair FEC Payload ID . . . . . . . . . . . . . . . .  20
       4.1.4.  Additional Procedures . . . . . . . . . . . . . . . .  21
   5.  Sliding Window RLC FEC Scheme over GF(2) for Arbitrary Packet
       Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21
     5.1.  Formats and Codes . . . . . . . . . . . . . . . . . . . .  21
       5.1.1.  FEC Framework Configuration Information . . . . . . .  22
       5.1.2.  Explicit Source FEC Payload ID  . . . . . . . . . . .  22
       5.1.3.  Repair FEC Payload ID . . . . . . . . . . . . . . . .  22
       5.1.4.  Additional Procedures . . . . . . . . . . . . . . . .  22
   6.  FEC Code Specification  . . . . . . . . . . . . . . . . . . .  22
     6.1.  Encoding Side . . . . . . . . . . . . . . . . . . . . . .  22



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     6.2.  Decoding Side . . . . . . . . . . . . . . . . . . . . . .  23
   7.  Implementation Status . . . . . . . . . . . . . . . . . . . .  24
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  24
     8.1.  Attacks Against the Data Flow . . . . . . . . . . . . . .  24
       8.1.1.  Access to Confidential Content  . . . . . . . . . . .  24
       8.1.2.  Content Corruption  . . . . . . . . . . . . . . . . .  25
     8.2.  Attacks Against the FEC Parameters  . . . . . . . . . . .  25
     8.3.  When Several Source Flows are to be Protected Together  .  26
     8.4.  Baseline Secure FEC Framework Operation . . . . . . . . .  26
     8.5.  Additional Security Considerations for Numerical
           Computations  . . . . . . . . . . . . . . . . . . . . . .  27
   9.  Operations and Management Considerations  . . . . . . . . . .  27
     9.1.  Operational Recommendations: Finite Field GF(2) Versus
           GF(2^^8)  . . . . . . . . . . . . . . . . . . . . . . . .  27
     9.2.  Operational Recommendations: Coding Coefficients Density
           Threshold . . . . . . . . . . . . . . . . . . . . . . . .  28
   10. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  28
   11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  28
   12. References  . . . . . . . . . . . . . . . . . . . . . . . . .  28
     12.1.  Normative References . . . . . . . . . . . . . . . . . .  28
     12.2.  Informative References . . . . . . . . . . . . . . . . .  29
   Appendix A.  TinyMT32 Pseudo-Random Number Generator  . . . . . .  31
   Appendix B.  Decoding Beyond Maximum Latency Optimization . . . .  35
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  36

1.  Introduction

   Application-Level Forward Erasure Correction (AL-FEC) 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 potentially large number of receivers
   (multicast/broadcast transmissions).  This is the case with the
   FLUTE/ALC protocol [RFC6726] when used for reliable file transfers
   over lossy networks, and the FECFRAME protocol when used for reliable
   continuous media transfers over lossy networks.

   The present document only focuses on the FECFRAME protocol, used in
   multicast/broadcast delivery mode, in particular for 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



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   [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.

   To define this block size, it is required to find an appropriate
   balance between robustness and decoding latency: the larger the block
   size, the higher the robustness (e.g., in front of long packet
   erasure bursts), but also the higher the maximum decoding latency
   (i.e., the maximum time required to recover a lost (erased) packet
   thanks to FEC protection).  Therefore, with a multicast/broadcast
   session where different receivers experience different packet loss
   rates, the block size should be chosen by considering the worst
   communication conditions one wants to support, but without exceeding
   the desired maximum decoding latency.  This choice then impacts the
   FEC-related latency of all receivers, even those experiencing a good
   communication quality, since no FEC encoding can happen until all the
   source data of the block is available at the sender, which directly
   depends on the block size.

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 Galois Fields (A.K.A.  Finite Fields) GF(2) (the
   "binary case") or GF(2^^8), each time with the possibility of
   controlling the code density.  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, and
   more generally Sliding Window FEC codes, are recommended for instance
   with media that feature real-time constraints sent within a
   multicast/broadcast session [Roca17].

   The RLC codes belong to the broad class of sliding window AL-FEC
   codes (A.K.A. convolutional codes) [RFC8406].  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), this
   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
   random linear combination of the source symbols present in the
   current encoding window, and passed to the transport layer.

   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 carried
   by each repair symbol received) are added upon receiving new packets.
   Variables and the equations they are involved in are removed when
   they are too old with respect to their validity period (real-time



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   constraints) .  Lost source symbols are then recovered thanks to this
   linear system whenever its rank permits to solve it (at least
   partially).

   The protection of any multicast/broadcast session needs to be
   dimensioned by considering the worst communication conditions one
   wants to support.  This is also true with RLC (more generally any
   sliding window) code.  However the receivers experiencing a good to
   medium communication quality will observe a reduced FEC-related
   latency compared to block codes [Roca17] since an isolated lost
   source packet is quickly recovered with the following repair packet.
   On the opposite, with a block code, recovering an isolated lost
   source packet always requires waiting for the first repair packet to
   arrive after the end of the block.  Additionally, under certain
   situations (e.g., with a limited FEC-related latency budget and with
   constant bitrate transmissions after FECFRAME encoding), sliding
   window codes can more efficiently achieve 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 to limit the packet
   header overhead.  The main requirement is that each repair packet
   header must enable a receiver to reconstruct the set of source
   symbols plus the associated 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 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 reconstruct the set
      of source symbols considered during encoding, the only constraint
      being that there cannot be any gap;
   o  the seed and density threshold parameters used by a coding
      coefficients generation function (Section 3.5).  These two pieces
      of information enable 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 features a fixed 64-bit long
   header, called Repair FEC Payload ID (Figure 7).  Similarly, each FEC



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   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 (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", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

   This document uses the following definitions and abbreviations:

   a^^b  a to the power of b
   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 (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:  RLC coding rate, ratio between the total number of source
      symbols and the total number of source plus repair symbols



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   ew_size:  encoding window current 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)
   ls_max_size:  linear system maximum size (or width) at a receiver (in
      symbols)
   PRNG:  pseudo-random number generator
   tinymt32_rand(maxv):  PRNG defined in Section 3.4 and used in this
      specification, that returns a new random integer in [0; maxv-1]
   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 these FEC
   Schemes.

3.1.  Possible Parameter Derivations

   The Sliding Window RLC FEC Scheme relies on several parameters:

   Maximum FEC-related latency budget, max_lat (in seconds) with real-
   time flows:
      a source ADU flow can have real-time constraints, and therefore
      any FECFRAME related operation should take place within the
      validity period of each ADU (Appendix B describes an exception to
      this rule).  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).  The maximum FEC-related latency
      budget, max_lat, accounts for all sources of latency added by FEC
      encoding (at a sender) and FEC decoding (at a receiver).  Other
      sources of latency (e.g., added by network communications) are out
      of scope and must be considered separately (said differently, they
      have already been deducted from max_lat).  max_lat can be regarded
      as the latency budget permitted for all FEC-related operations.
      This is an input parameter that enables a FECFRAME sender to
      derive other internal parameters as explained below;
   Encoding window current (resp. maximum) size, ew_size (resp.
   ew_max_size) (in symbols):
      at a FECFRAME sender, during FEC encoding, a repair symbol is
      computed as a linear combination of the ew_size source symbols
      present in the encoding window.  The ew_max_size is the maximum
      size of this window, while ew_size is the current size.  For
      instance, at session start, upon receiving new source ADUs, the
      ew_size progressively increases until it reaches its maximum
      value, ew_max_size.  We have:




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         0 < ew_size <= ew_max_size
   Decoding window maximum size, dw_max_size (in symbols):  at a
      FECFRAME receiver, dw_max_size is the maximum number of received
      or lost source symbols that are still within their latency budget;
   Linear system maximum size, ls_max_size (in symbols):  at a FECFRAME
      receiver, the linear system maximum size, ls_max_size, is the
      maximum number of received or lost source symbols in the linear
      system (i.e., the variables).  It SHOULD NOT be smaller than
      dw_max_size since it would mean that, even after receiving a
      sufficient number of FEC Repair Packets, a lost ADU may not be
      recovered just because the associated source symbols have been
      prematurely removed from the linear system, which is usually
      counter-productive.  On the opposite, the linear system MAY grow
      beyond the dw_max_size (Appendix B);
   Symbol size, E (in bytes):  the E parameter determines the source and
      repair symbol sizes (necessarily equal).  This is an input
      parameter that enables a FECFRAME sender to derive other internal
      parameters, as explained below.  An implementation at a sender
      SHOULD fix the E parameter and communicate it as part of the FEC
      Scheme-Specific Information (Section 4.1.1.2).
   Code rate, cr:  The code rate parameter determines the amount of
      redundancy added to the flow.  More precisely the cr is the ratio
      between the total number of source symbols and the total number of
      source plus repair symbols and by definition: 0 < cr <= 1.  This
      is an input parameter that enables a FECFRAME sender to derive
      other internal parameters, as explained below.  However there is
      no need to communicate the cr parameter per see (it's not required
      to process a repair symbol at a receiver).  This code rate
      parameter can be static.  However, in specific use-cases (e.g.,
      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.

   The FEC Schemes can be used in various manners.  They can be used to
   protect a source ADU flow having real-time constraints, or a non-
   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




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   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





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   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).




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   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

   At a sender, an ADU coming from the application cannot directly be
   mapped to source symbols.  When multiple source flows (e.g., media
   streams) are mapped onto the same FECFRAME instance, each flow is
   assigned its own Flow ID value (see below).  At a sender, this
   identifier is prepended to each ADU before FEC encoding.  This way,
   FEC decoding at a receiver also recovers this Flow ID and a recovered



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   ADU can be assigned to the right source flow (note that transport
   port numbers and IP addresses cannot be used to that purpose as they
   are not recovered during FEC decoding).

   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 MUST created as follows.  First of
   all, 3 bytes are 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 session 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).

   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
   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, and a receiver who lost a certain FEC Source Packet (e.g.,
   the UDP datagram containing this FEC Source Packet when UDP is used



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   as the transport protocol) 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 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_size
   value, in addition to the maximum FEC-related latency budget
   (Section 3.1).

3.4.  Pseudo-Random Number Generator (PRNG)

   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).

   o  Official web site: <http://www.math.sci.hiroshima-u.ac.jp/~m-
      mat/MT/TINYMT/>
   o  Official github site and reference implementation:
      <https://github.com/MersenneTwister-Lab/TinyMT>

   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



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   requires a parameter set that needs to be pre-calculated.  For the
   RLC FEC Schemes defined in this document, the following parameter set
   MUST be used:

   o  mat1 = 0x8f7011ee = 2406486510;
   o  mat2 = 0xfc78ff1f = 4235788063;
   o  tmat = 0x3793fdff = 932445695.

   This parameter set is the first entry of the precalculated parameter
   sets in file tinymt32dc.0.1048576.txt, by Kenji Rikitake, and
   available at:

   o  <https://github.com/jj1bdx/tinymtdc-
      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,
   used as a seed.  The following function is used to this purpose:

      void tinymt32_init (tinymt32_t * s, uint32_t seed);

   With the FEC Schemes defined in this document, the seed is in
   practice restricted to a value between 0 and 0xFFFF inclusive (note
   that this PRNG accepts a seed equal to 0), since this is the
   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
   parameter a pointer to an instance of a tinymt32_t structure that is
   used to keep the internal state of the PRNG.

   Then, each time a new pseudo-random integer between 0 and maxv-1
   inclusive is needed, the following function is used:

      uint32_t tinymt32_rand (tinymt32_t * s, uint32_t maxv);

   This function takes as parameter both a pointer to the same
   tinymt32_t structure (that needs to be left unchanged between
   successive calls to the function) and the maxv value.








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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.  The
   fraction of coefficients that are non zero (i.e., the density) is
   controlled by the DT (Density Threshold) parameter.  When DT equals
   15, the maximum value, the function guaranties that all coefficients
   are non zero (i.e., maximum density).  When DT is between 0 (minimum
   value) and strictly inferior to 15, the average probability of having
   a non zero coefficient equals (DT +1) / 16.

   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 5), m MUST be equal to 1.
   With RLC over GF(2^^8) FEC Scheme (Section 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. 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         number of entries in the table. This value is
    *                    equal to the current encoding window size.
    * (in) 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
    *                    document only values 1 and 8 are considered.
    * (out)              returns an error code
    */
   int generate_coding_coefficients (uint16_t  repair_key,
                                     uint8_t   cc_tab[],
                                     uint16_t  cc_nb,
                                     uint8_t   dt,
                                     uint8_t   m)
   {
       uint32_t      i;



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       tinymt32_t    s;    /* PRNG internal state */

       if (dt > 15) {
           return SOMETHING_WENT_WRONG; /* bad dt parameter */
       }
       switch (m) {
       case 1:
           if (dt == 15) {
               /* all coefficients are 1 */
               memset(cc_tab, 1, cc_nb);
           } else {
               /* here coefficients are either 0 or 1 */
               tinymt32_init(&s, repair_key);
               for (i = 0 ; i < cc_nb ; i++) {
                   if (tinymt32_rand(&s, 16) <= dt) {
                       cc_tab[i] = (uint8_t) 1;
                   } else {
                       cc_tab[i] = (uint8_t) 0;
                   }
               }
           }
           break;

       case 8:
           tinymt32_init(&s, repair_key);
           if (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_t) tinymt32_rand(&s, 256);
                   } while (cc_tab[i] == 0);
               }
           } else {
               /* here a certain fraction of coefficients should be 0 */
               for (i = 0 ; i < cc_nb ; i++) {
                   if (tinymt32_rand(&s, 16) <= dt) {
                       do {
                           cc_tab[i] = (uint8_t) tinymt32_rand(&s, 256);
                       } while (cc_tab[i] == 0);
                   } else {
                       cc_tab[i] = 0;
                   }
               }
           }
           break;

       default:



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

       Figure 2: Coding Coefficients Generation Function pseudo-code

3.6.  Finite Fields Operations

3.6.1.  Finite Field Definitions

   The two RLC FEC Schemes specified in this document reuse the Finite
   Fields defined in [RFC5510], section 8.1.  More specifically, the
   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
   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
   operation on the binary representation of these elements.

   With GF(2^^8), multiplication between two elements is the
   multiplication modulo a given irreducible polynomial of degree 8.
   The following irreducible polynomial MUST be used for GF(2^^8):

      x^^8 + x^^4 + x^^3 + x^^2 + 1

   With GF(2), multiplication corresponds to a logical AND operation.

3.6.2.  Linear Combination of Source Symbols Computation

   The two RLC FEC Schemes require the computation of a linear
   combination of source symbols, using the coding coefficients produced
   by the generate_coding_coefficients() function and stored in the
   cc_tab[] array.

   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
   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
   symbol, where i belongs to {0; E-1}, compute:

      repair[i] = cc_tab[0] * src_0[i] + cc_tab[1] * src_1[i] + ... +
      cc_tab[ew_size - 1] * src_ew_size_1[i]

   where * is the multiplication over GF(2^^8) and + is an XOR
   operation.  In practice various optimizations need to be used in
   order to make this computation efficient (see in particular [PGM13]).



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   With the RLC over GF(2) FEC Scheme (binary case), a linear
   combination is computed as follows.  The repair symbol is the XOR sum
   of all the source symbols corresponding to a coding coefficient
   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
   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,
   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
   extensions).

   With both FEC Schemes, the details of how to optimize the computation
   of these linear combinations are of high practical importance but out
   of scope of this document.

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

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

4.1.  Formats and Codes

4.1.1.  FEC Framework Configuration Information

   Following the guidelines of [RFC6363], section 5.6, this section
   provides the FEC Framework Configuration Information (or FFCI).  This
   FCCI needs to be shared (e.g., using SDP) between the FECFRAME sender
   and receiver instances in order to synchronize them.  It includes a
   FEC Encoding ID, mandatory for any FEC Scheme specification, plus
   scheme-specific elements.

4.1.1.1.  FEC Encoding ID

   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.

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;




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   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

4.1.2.  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.

   +--------------------------------+
   |           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.  The ESI is incremented for each new




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      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

4.1.3.  Repair FEC Payload ID

   A FEC Repair Packet MAY contain one or more repair symbols.  When
   there are several repair symbols, all of them MUST have been
   generated from the same encoding window, using Repair_Key values that
   are managed as explained below.  A receiver can easily deduce 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
   UDP is the underlying transport protocol) and the symbol size, E,
   communicated in the FFCI.

   A FEC Repair Packet MUST contain a Repair FEC Payload ID that is
   prepended to the repair 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.  When a FEC
      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 0.



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   Density Threshold for the coding coefficients, DT (4-bit field):
      this unsigned integer carries 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
      contains several repair symbols, the DT value applies to all of
      them;
   Number of Source Symbols in the 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 contains several repair symbols, this NSS value
      applies to all of them;
   ESI of 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 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

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
      happens after reaching the maximum 32-bit value.

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

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

5.1.  Formats and Codes







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5.1.1.  FEC Framework Configuration Information

5.1.1.1.  FEC Encoding ID

   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 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
   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 0.  This repair key is
   communicated to the coefficient generation function (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



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   (Section 3.6).  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.  In that case 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
   carried in the Repair FEC Payload ID.  The FEC Repair Packet can then
   be passed to the transport layer for transmission.  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 0 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, 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, 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 field, F, of the ADUI).  This ADU is finally
   passed to the corresponding upper application.  Received FEC Source
   Packets, containing an ADU, MAY be passed to the application either
   immediately or after some time to guaranty an ordered delivery 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
   latency or an ADU received after this delay has no value to the
   application.  This raises the question of deciding whether or not an



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   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
   application (e.g., using RTP timestamps within the ADU).  Deciding
   which option to follow and whether or not to pass all ADUs, including
   those assumed late, to the application are operational decisions that
   depend on the application and are therefore out of scope of this
   document.  Additionally, Appendix B discusses a backward compatible
   optimization whereby late source symbols MAY still be used within the
   FECFRAME receiver in order to improve transmission 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 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.
   o  Licensing: 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




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   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 targets receivers
   (Section 4.1.1.2):

   o  FEC Encoding ID: changing this parameter leads a receiver to
      consider a different FEC Scheme.  The consequences are severe, the
      format of the Explicit Source FEC Payload ID and Repair FEC
      Payload ID of received packets will probably differ, leading to
      various malfunctions.  Even if the original and modified FEC
      Schemes share the same format, FEC decoding will either fail or
      lead to corrupted decoded symbols.  This will happen if an
      attacker turns value YYYY (i.e., RLC over GF(2)) to value XXXX
      (RLC over GF(2^^8)), an additional consequence being a higher
      processing overhead at the receiver.  In any case, the attack
      results in a form of Denial of Service (DoS);
   o  Encoding symbol length (E): setting this E parameter to a
      different value will confuse a receiver.  If the size of a
      received FEC Repair Packet is no longer multiple of the modified E
      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
      value (e.g., half the original value), then receivers may not
      detect the problem immediately.  For instance a receiver may think
      that a received FEC Repair Packet contains more repair symbols
      (e.g., twice as many if E is reduced by half), leading to
      malfunctions whose nature depends on implementation details.  Here
      also, the attack always results in a form of DoS;

   It is therefore RECOMMENDED that security measures be 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.  More specifically, in case of




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   a FEC Source Packet, the following value can be modified by an
   attacker who targets receivers:

   o  Encoding Symbol ID (ESI): changing the ESI leads a receiver to
      consider a wrong ADU, resulting in severe consequences, including
      corrupted content passed to the receiving application;

   And in case of a FEC Repair Packet:

   o  Repair Key: changing this value leads a receiver to generate a
      wrong coding coefficient sequence, and therefore any source symbol
      decoded using the repair symbols contained in this packet will be
      corrupted;
   o  DT: changing this value also leads a receiver to generate a wrong
      coding coefficient sequence, and therefore any source symbol
      decoded using the repair symbols contained in this packet will be
      corrupted.  In addition, if the DT value is significantly
      increased, it will generate a higher processing overhead at a
      receiver.  In case of very large encoding windows, this may impact
      the terminal performance;
   o  NSS: changing this value leads a receiver to consider a different
      set of source symbols, and therefore any source symbol decoded
      using the repair symbols contained in this packet will be
      corrupted.  In addition, if the NSS value is significantly
      increased, it will generate a higher processing overhead at a
      receiver, which may impact the terminal performance;
   o  FSS_ESI: changing this value also leads a receiver to consider a
      different set of source symbols and therefore any source symbol
      decoded using the repair symbols contained in this packet will be
      corrupted.

   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.




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8.5.  Additional Security Considerations for Numerical Computations

   In addition to the above security considerations, inherited from
   [RFC6363], the present document introduces several formulae, in
   particular in Section 3.1.1.  It is RECOMMENDED to check that the
   computed values stay within reasonnable bounds since numerical
   overflows, caused by an erroneous implementation or an erroneous
   input value, may lead to hazardous behaviours.  However what
   "reasonnable bounds" means is use-case and implementation dependent
   and is not detailed in this document.

   Section 3.1.2 also mentions the possibility of "using the timestamp
   field of an RTP packet header" when applicable.  A malicious attacker
   may deliberately corrupt this header field in order to trigger
   hazardous behaviours at a FECFRAME receiver.  Protection against this
   type of content corruption can be addressed with the above
   recommendations on a baseline secure operation.  In addition, it is
   also RECOMMENDED to check that the timestamp value be within
   reasonnable bounds.

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
   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 higher packet loss protection.  In case of small encoding
   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
   Cortex-A15 embedded board in [Roca17]).  Of course the CPU overhead
   will increase with the 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
   operations symbols can be directly XOR-ed together which warrants
   high bitrate encoding and decoding operations, and can be an
   advantage with large encoding windows.  However packet loss
   protection is significantly reduced by using this FEC Scheme.







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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 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 larger encoding windows, it 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 7 (i.e., an average density equal to 1/2)
   or smaller.

   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
   the source symbols in the encoding window.  In that case: (1) a
   single repair symbol can be produced for any encoding window, and (2)
   the repair_key parameter 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 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 4 of this document.

11.  Acknowledgments

   The authors would like to thank Russ Housley, Alan DeKok, Spencer
   Dawkins, Gorry Fairhurst, Jonathan Detchart, Emmanuel Lochin, and
   Marie-Jose Montpetit for their valuable feedbacks on this document.

12.  References

12.1.  Normative References







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   [fecframe-ext]
              Roca, V. and A. Begen, "Forward Error Correction (FEC)
              Framework Extension to Sliding Window Codes", Transport
              Area Working Group (TSVWG) draft-ietf-tsvwg-fecframe-ext
              (Work in Progress), September 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>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

12.2.  Informative References

   [KR12]     Rikitake, K., "TinyMT Pseudo Random Number Generator for
              Erlang",  ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
              September 14, 2012, Copenhagen, Denmark, DOI:
              http://dx.doi.org/10.1145/2364489.2364504, September 2012.

   [PGM13]    Plank, J., Greenan, K., and E. Miller, "A Complete
              Treatment of Software Implementations of Finite Field
              Arithmetic for Erasure Coding Applications", University of
              Tennessee Technical Report UT-CS-13-717,
              http://web.eecs.utk.edu/~plank/plank/papers/
              UT-CS-13-717.html, October 2013,
              <http://web.eecs.utk.edu/~plank/plank/papers/
              UT-CS-13-717.html>.

   [RFC5510]  Lacan, J., Roca, V., Peltotalo, J., and S. Peltotalo,
              "Reed-Solomon Forward Error Correction (FEC) Schemes",
              RFC 5510, DOI 10.17487/RFC5510, April 2009,
              <https://www.rfc-editor.org/info/rfc5510>.




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   [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>.

   [RFC8406]  Adamson, B., Adjih, C., Bilbao, J., Firoiu, V., Fitzek,
              F., Ghanem, S., Lochin, E., Masucci, A., Montpetit, M-J.,
              Pedersen, M., Peralta, G., Roca, V., Ed., Saxena, P., and
              S. Sivakumar, "Taxonomy of Coding Techniques for Efficient
              Network Communications", RFC 8406, DOI 10.17487/RFC8406,
              June 2018, <https://www.rfc-editor.org/info/rfc8406>.

   [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/>.

   [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-01571609v1/en/>.












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Appendix A.  TinyMT32 Pseudo-Random Number Generator

   The TinyMT32 PRNG reference implementation is distributed under a BSD
   license by the authors and excerpts of it are reproduced in Figure 8.
   The differences with respect to the original source code are:

   o  the unused parts of the original source code have been removed;
   o  the appropriate parameter set has been added to the initialization
      function;
   o  the tinymt32_rand() function has been added;
   o  the function order has been changed;
   o  certain internal variables have been renamed for compactness
      purposes.

 <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,



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  * 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.
  */

 #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 double tinymt32_generate_32double (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.
  */
 #define TINYMT32_MAT1_PARAM     0x8f7011ee
 #define TINYMT32_MAT2_PARAM     0xfc78ff1f
 #define TINYMT32_TMAT_PARAM     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)
 {



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 #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);
     }
 }

 /**
  * This function outputs an integer in the [0 .. maxv-1] range.
  * @param s     pointer to tinymt internal state.
  * @return      32-bit unsigned integer between 0 and maxv-1 inclusive.
  */
 uint32_t tinymt32_rand (tinymt32_t * s, uint32_t maxv)
 {
     return (uint32_t)(tinymt32_generate_32double(s) * (double)maxv);
 }


 /**
  * Internal tinymt32 constants and functions.
  * 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)

 /**
  * 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];



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     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 double precision floating point number from
  * internal state. The returned value has 32-bit precision.
  * In other words, this function makes one double precision floating
  * point number from one 32-bit unsigned integer.
  * @param s     pointer to tinymt internal state.
  * @return      floating point number r (0.0 <= r < 1.0)
  */
 static double tinymt32_generate_32double (tinymt32_t * s)
 {
     tinymt32_next_state(s);
     return (double)tinymt32_temper(s) * (1.0 / 4294967296.0);
 }
 <CODE ENDS>

                      Figure 8: TinyMT32 pseudo-code







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Appendix B.  Decoding Beyond Maximum Latency Optimization

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

   With a real-time source ADU flow, it is possible to improve the
   decoding performance of sliding window codes without impacting
   maximum latency, at the cost of extra memory and CPU overhead.  The
   optimization consists, for a FECFRAME receiver, to extend the linear
   system beyond the decoding window maximum size, by keeping a certain
   number of old source symbols whereas their associated ADUs timed-out:

      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

   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).
   Going below this threshold will not save a significant amount of
   memory nor CPU cycles.  Therefore:

      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
   that benefits from an FEC protection significantly higher than what
   is required to recover from packet losses, can choose to reduce the
   ls_max_size.  In that case lost ADUs will be recovered without
   relying on this optimization.

                                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 9: Relationship between parameters to decode beyond maximum
                                 latency.

   It means that source symbols, and therefore ADUs, may be decoded even
   if the added latency exceeds the maximum value permitted by the
   application (the "late source symbols" of Figure 9).  It follows that
   the corresponding ADUs will not be useful to the application.



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   However, decoding these "late symbols" significantly improves the
   global robustness in bad reception conditions and is therefore
   recommended for receivers experiencing bad communication conditions
   [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
   decisions made by each receiver independently, without any impact on
   the other receivers nor on the source.

Authors' Addresses

   Vincent Roca
   INRIA
   Univ. Grenoble Alpes
   France

   EMail: vincent.roca@inria.fr


   Belkacem Teibi
   INRIA
   Univ. Grenoble Alpes
   France

   EMail: belkacem.teibi@inria.fr



























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