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NWCRG                                                        J. Detchart
Internet-Draft                                                 E. Lochin
Intended status: Experimental                                   J. Lacan
Expires: January 9, 2017                                            ISAE
                                                                 V. Roca
                                                                   INRIA
                                                            July 8, 2016


             Tetrys, an On-the-Fly Network Coding protocol
                     draft-detchart-nwcrg-tetrys-03

Abstract

   This document describes Tetrys, an On-The-Fly Network Coding (NC)
   protocol that can be used to transport delay and loss sensitive data
   over a lossy network.  Tetrys can recover from erasures within a RTT-
   independent delay, thanks to the transmission of coded packets.  It
   can be used for both unicast, multicast and anycast communications.

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 http://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 January 9, 2017.

Copyright Notice

   Copyright (c) 2016 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
   (http://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



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   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  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Notation . . . . . . . . . . . . . . . . . .   3
   2.  Definitions, Notations and Abbreviations  . . . . . . . . . .   3
   3.  Architecture  . . . . . . . . . . . . . . . . . . . . . . . .   4
     3.1.  Use Cases . . . . . . . . . . . . . . . . . . . . . . . .   4
     3.2.  Overview  . . . . . . . . . . . . . . . . . . . . . . . .   5
   4.  Packet Format . . . . . . . . . . . . . . . . . . . . . . . .   6
     4.1.  Common Header Format  . . . . . . . . . . . . . . . . . .   6
       4.1.1.  Header Extensions . . . . . . . . . . . . . . . . . .   8
     4.2.  Source Packet Format  . . . . . . . . . . . . . . . . . .   9
     4.3.  Coded Packet Format . . . . . . . . . . . . . . . . . . .  10
     4.4.  Acknowledgement Packet Format . . . . . . . . . . . . . .  11
   5.  The Coding Coefficient Generator Identifiers  . . . . . . . .  12
     5.1.  Definition  . . . . . . . . . . . . . . . . . . . . . . .  13
     5.2.  Table of Identifiers  . . . . . . . . . . . . . . . . . .  13
   6.  Tetrys Basic Functions  . . . . . . . . . . . . . . . . . . .  13
     6.1.  Encoding  . . . . . . . . . . . . . . . . . . . . . . . .  13
       6.1.1.  Encoding Vector Formats . . . . . . . . . . . . . . .  14
     6.2.  The Elastic Encoding Window . . . . . . . . . . . . . . .  17
     6.3.  Recoding  . . . . . . . . . . . . . . . . . . . . . . . .  18
       6.3.1.  Principle . . . . . . . . . . . . . . . . . . . . . .  18
       6.3.2.  Generating a coded symbol at an intermediate node . .  18
     6.4.  Decoding  . . . . . . . . . . . . . . . . . . . . . . . .  18
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  18
   8.  Privacy Considerations  . . . . . . . . . . . . . . . . . . .  18
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  19
   10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  19
   11. References  . . . . . . . . . . . . . . . . . . . . . . . . .  19
     11.1.  Normative References . . . . . . . . . . . . . . . . . .  19
     11.2.  Informative References . . . . . . . . . . . . . . . . .  19
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  19

1.  Introduction

   This document describes Tetrys, a novel network coding protocol.
   Network codes were introduced in the early 2000s [AHL-00] to address
   the limitations of transmission over the Internet (delay, capacity
   and packet loss).  While the use of network codes is fairly recent in
   the Internet community, the use of application layer erasure codes in
   the IETF has already been standardized in the RMT [RMT] and the
   FECFRAME [FECFRAME] working groups.  The protocol presented here can
   be seen as a network coding extension to standards solutions.  The



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   current proposal can be considered as a combination of network
   erasure coding and feedback mechanisms [Tetrys].

   The main innovation of the Tetrys protocol is in the generation of
   coded packets from an elastic encoding window periodically updated
   with the receiver's feedbacks.  This update is done in such a way
   that any source packets coming from an input flow is included in the
   encoding window as long as it is not acknowledged or the encoding
   window did not reach a size limit.  This mechanism allows for losses
   on both the forward and return paths and in particular is resilient
   to acknowledgement losses.

   With Tetrys, a coded packet is a linear combination over a finite
   field of the data source packets belonging to the coding window.  The
   choice of the finite field of the coefficients is a trade-off between
   the best performance (with non-binary coefficients) and the system
   constraints (binary codes in an energy constrained environment) and
   is driven by the application.

   Thanks to the elastic encoding window, the coded packets are built
   on-the-fly, by using an algorithm or a function to choose the
   coefficients.  The redundancy ratio can be dynamically adjusted, and
   the coefficients can be generated in different ways along a
   transmission.  Compared to FEC block codes, this allows to reduce the
   bandwidth use and the decoding delay.

1.1.  Requirements Notation

   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].

2.  Definitions, Notations and Abbreviations

   The terminology used in this document is presented below.  It is
   aligned with the FECFRAME terminology as well as with recent
   activities in the Network Coding Research Group.

      Source symbol: a symbol that has to be transmitted between the
      ingress and egress of the network.

      Coded symbol: a linear combination over a finite field of a set of
      source symbols.

      Source symbol ID: a sequence number to identify the source
      symbols.

      Coded symbol ID: a sequence number to identify the coded symbols.



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      Encoding coefficients: elements of the finite field characterizing
      the linear combination used to generate a coded symbols.

      Encoding vector: set of the encoding coefficients and input source
      symbol IDs.

      Source packet: a source packet contains a source symbol with its
      associated IDs.

      Coded packet: a coded packet contains a coded symbol, the coded
      symbol's ID and encoding vector.

      Input symbol: a symbol at the input of the Tetrys Encoding
      Building Block.

      Output symbol: a symbol generated by the Tetrys Encoding Building
      Block.  For a non systematic mode, all output symbols are coded
      symbols.  For a systematic mode, output symbols can be the input
      symbols and a number of coded symbols that are linear combinations
      of the input symbols + the encoding vectors.

      Feedback packet: a feedback packet is a packet containing
      information about the decoded or received source symbols.  It can
      also bring additional information about the Packet Error Rate or
      the number of various packets in the receiver decoding window

      Elastic Encoding Window: an encoder-side buffer that stores all
      the non-acknowledged source packets of the input flow that are
      involved in the coding process.

      Coding Coefficient Generator Identifier: a unique identifier that
      define a function or an algorithm allowing to generate the
      encoding vector.

      Code rate: Define the rate between the number of input symbols and
      the number of output symbols.

3.  Architecture

      -- Editor's note: The architecture used in this document should be
      aligned with the future NC Architecture document [NWCRG-ARCH]. --

3.1.  Use Cases

   Tetrys is well suited, but not limited to the use case where there is
   a single flow originated by a single source, with intra stream coding
   that takes place at a single encoding node.  Note that the input
   stream can be a multiplex of several upper layer streams.



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   Transmission can be over a single path or multiple paths.  In
   addition, the flow can be sent in unicast, multicast, or anycast
   mode.  This is the simplest use-case, that is very much inline with
   currently proposed scenarios for end-to-end streaming.

3.2.  Overview

   +----------+                                            +----------+
   |          |                                            |          |
   |    App   |                                            |    App   |
   |          |                                            |          |
   +----------+                                            +----------+
        |                                                       ^
        |  source                                       source  |
        |  symbols                                      symbols |
        |                                                       |
        v                                                       |
   +----------+                +----------+                +----------+
   |          | output packets |          | output packets |          |
   |  Tetrys  |--------------->|  Tetrys  |--------------->|  Tetrys  |
   |  Encoder |feedback packets|  Recoder |feedback packets|  Decoder |
   |          |<---------------|          |<---------------|          |
   +----------+                +----------+                +----------+

                       Figure 1: Tetrys Architecture

   The Tetrys protocol features several key functionalities:

   o  On-the-fly encoding;

   o  Recoding;

   o  Decoding;

   o  Signaling, to carry in particular the symbol identifiers in the
      encoding window and the associated coding coefficients when
      meaningful, in a manner that was previously used in FEC;

   o  Feedback management;

   o  Elastic window management;

   o  Channel estimation;

   o  Dynamic adjustment of the code rate and flow control;

   o  Congestion control management (if appropriate);




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         -- Editor's note: must be discussed --

   o  Tetrys packet header creation and processing;

   o  -- Editor's note: something else? --

   These functionalities are provided by several building blocks:

   o  The Tetrys Building Block: this BB is used during encoding,
      recoding and decoding processes.  It must be noted that Tetrys
      does not mandate a specific building block.  Instead any building
      block compatible with the elastic encoding window feature of
      Tetrys can be used.

   o  The Window Management Building Block: this building block is in
      charge of managing the encoding encoding window at a Tetrys
      sender.

         -- Editor's note: Is it worth moving it in a dedicated BB?  To
         be discussed --

   o  Other ?

   In order to enable future components and services to be added
   dynamically, Tetrys adds a header extension mechanism, compatible
   with that of LCT, NORM, FECFRAME [REFS].

4.  Packet Format

4.1.  Common Header Format

   All types of Tetrys packets share the same common header format (see
   Figure 2).


















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    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   V   | C |S|     Reserved    |   HDR_LEN     |  Packet Type  |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   Congestion Control Information (CCI, length = 32*C bits)    |
   |                          ...                                  |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |    Transport Session Identifier (TSI, length = 32*S bits)     |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                Header Extensions (if applicable)              |
   |                          ...                                  |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      Figure 2: Common Header Format

      -- Editor's note: this format inherits from the LCT header format
      (RFC 5651) with slight modifications. --

   o  Tetrys version number (V): 4 bits.  Indicates the Tetrys version
      number.  The Tetrys version number for this specification is 1.

   o  Congestion control flag (C): 2 bits.  C=0 indicates the Congestion
      Control Information (CCI) field is 0 bits in length.  C=1
      indicates the CCI field is 32 bits in length.  C=2 indicates the
      CCI field is 64 bits in length.  C=3 indicates the CCI field is 96
      bits in length.

         -- Editor's note: version number and congestion control to be
         discussed --

   o  Transport Session Identifier flag (S): 1 bit.  This is the number
      of full 32-bit words in the TSI field.  The TSI field is 32*S bits
      in length, i.e., the length is either 0 bits or 32 bits.

   o  Reserved (Resv): 9 bits.  These bits are reserved.  In this
      version of the specification, they MUST be set to zero by senders
      and MUST be ignored by receivers.

   o  Header length (HDR_LEN): 8 bits.  Total length of the Tetrys
      header in units of 32-bit words.  The length of the Tetrys header
      MUST be a multiple of 32 bits.  This field can be used to directly
      access the portion of the packet beyond the Tetrys header, i.e.,
      to the first other header if it exists, or to the packet payload
      if it exists and there is no other header, or to the end of the
      packet if there are no other headers or packet payload.

   o  Packet Type: 8 bits.  Type of packet.



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   o  Congestion Control Information (CCI): 0, 32, 64, or 96 bits Used
      to carry congestion control information.  For example, the
      congestion control information could include layer numbers,
      logical channel numbers, and sequence numbers.  This field is
      opaque for the purpose of this specification.  This field MUST be
      0 bits (absent) if C=0.  This field MUST be 32 bits if C=1.  This
      field MUST be 64 bits if C=2.  This field MUST be 96 bits if C=3.

   o  Transport Session Identifier (TSI): 0 or 32 bits The TSI uniquely
      identifies a session among all sessions from a particular sender.
      The TSI is scoped by the IP address of the sender, and thus the IP
      address of the sender and the TSI together uniquely identify the
      session.  Although a TSI in conjunction with the IP address of the
      sender always uniquely identifies a session, whether or not the
      TSI is included in the Tetrys header depends on what is used as
      the TSI value.  If the underlying transport is UDP, then the
      16-bit UDP source port number MAY serve as the TSI for the
      session.  If there is no underlying TSI provided by the network,
      transport or any other layer, then the TSI MUST be included in the
      Tetrys header.

4.1.1.  Header Extensions

   Header Extensions are used in Tetrys to accommodate optional header
   fields that are not always used or have variable size.  The presence
   of Header Extensions can be inferred by the Tetrys header length
   (HDR_LEN).  If HDR_LEN is larger than the length of the standard
   header, then the remaining header space is taken by Header
   Extensions.

   If present, Header Extensions MUST be processed to ensure that they
   are recognized before performing any congestion control procedure or
   otherwise accepting a packet.  The default action for unrecognized
   Header Extensions is to ignore them.  This allows the future
   introduction of backward-compatible enhancements to Tetrys without
   changing the Tetrys version number.  Non-backward-compatible Header
   Extensions CANNOT be introduced without changing the Tetrys version
   number.

   There are two formats for Header Extensions, as depicted in Figure 3.
   The first format is used for variable-length extensions, with Header
   Extension Type (HET) values between 0 and 127.  The second format is
   used for fixed-length (one 32-bit word) extensions, using HET values
   from 128 to 255.







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    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |  HET (<=127)  |       HEL     |                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               +
   .                                                               .
   .              Header Extension Content (HEC)                   .
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |  HET (>=128)  |       Header Extension Content (HEC)          |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                     Figure 3: Header Extension Format

   o  Header Extension Type (HET): 8 bits The type of the Header
      Extension.  This document defines a number of possible types.
      Additional types may be defined in future versions of this
      specification.  HET values from 0 to 127 are used for variable-
      length Header Extensions.  HET values from 128 to 255 are used for
      fixed-length 32-bit Header Extensions.

   o  Header Extension Length (HEL): 8 bits The length of the whole
      Header Extension field, expressed in multiples of 32-bit words.
      This field MUST be present for variable-length extensions (HETs
      between 0 and 127) and MUST NOT be present for fixed-length
      extensions (HETs between 128 and 255).

   o  Header Extension Content (HEC): variable length The content of the
      Header Extension.  The format of this sub-field depends on the
      Header Extension Type.  For fixed-length Header Extensions, the
      HEC is 24 bits.  For variable-length Header Extensions, the HEC
      field has variable size, as specified by the HEL field.  Note that
      the length of each Header Extension MUST be a multiple of 32 bits.
      Also note that the total size of the Tetrys header, including all
      Header Extensions and all optional header fields, cannot exceed
      255 32-bit words.

4.2.  Source Packet Format

   A source packet is the encapsulation of a Common Packet Header, a
   Source Symbol ID and a source symbol (payload).  The source symbols
   can have variable sizes.






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    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   /                      Common Packet Header                     /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                         Source Symbol ID                      |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   /                            Payload                            /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      Figure 4: Source Packet Format

   Common Packet Header: a common packet header where Packet Type=0.

   Source Symbol ID: the sequence number to identify a source symbol.

   Payload: the payload (source symbol)

4.3.  Coded Packet Format

   A coded packet is the encapsulation of a Common Packet Header, a
   Coded Symbol ID, the associated Encoding Vector and a coded symbol
   (payload).  As the source symbols CAN have variable sizes, each
   source symbol size need to be encoded, and the result must be stored
   in the coded packet as the Encoded Payload Size (16 bits): as it is
   an optional field, the encoding vector MUST signal the use of
   variable source symbol sizes with the field V (see Section 6.1.1.2).




















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    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   /                      Common Packet Header                     /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                          Coded Symbol ID                      |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   /                         Encoding Vector                       /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |     Encoded Payload Size      |                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               +
   |                                                               |
   /                            Payload                            /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                       Figure 5: Coded Packet Format

   Common Packet Header: a common packet header where Packet Type=1.

   Coded Symbol ID: the sequence number to identify a coded symbol.

   Encoding Vector: an encoding vector to define the linear combination
   used (coefficients, and source symbols).

   Encoded Payload Size: the coded payload size used if the source
   symbols have variable size (optional, Section 6.1.1.2)).

   Payload: the coded symbol.

4.4.  Acknowledgement Packet Format

   A Tetrys Decoding Building Block or Tetrys Recoding Building Block
   MAY send back to another building block some Acknowledgement packets.
   They contain information about what it has received and/or decoded,
   and other information such as a packet loss rate or the size of the
   decoding buffers.  The acknowledgement packets are OPTIONAL hence
   they could be omitted or lost in transmission without impacting the
   protocol behavior.








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    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   /                      Common Packet Header                     /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                  Nb of missing source symbols                 |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |              Nb of not already used coded symbols             |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                    First Source Symbol ID                     |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   SACK size   |                                               |
   +-+-+-+-+-+-+-+-+                                               +
   |                                                               |
   /                          SACK Vector                          /
   |                                                               |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                  Figure 6: Acknowledgement Packet Format

   Common Packet Header: a common packet header where Packet Type=2.

   Nb missing source symbols: the number of missing source symbols in
   the receiver since the beginning of the session.

   Nb of not already used coded symbols: the number coded symbols at the
   receiver that have not already been used for decoding (e.g., the
   linear combinations contains at least 2 unknown source symbols).

   First Source Symbol ID: ID of the first source symbol to consider for
   acknowledgement.

   SACK size: the size of the SACK vector in 32-bit words.  For
   instance, with value 2, the SACK vector is 64 bits long.

   SACK vector: bit vector indicating the acknowledged symbols from the
   first source symbol ID.  The "First Source Symbol" is included in
   this bit vector.  A bit equal to 1 at position i means that the
   source symbol of ID equal to "First Source Symbol ID" + i is
   acknowledged by this acknowledgment packet.

5.  The Coding Coefficient Generator Identifiers







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5.1.  Definition

   The Coding Coefficient Generator Identifiers define a function or an
   algorithm to build the coding coefficients used to generate the coded
   symbols.  They MUST be known by all the Tetrys encoders, recoders or
   decoders.

5.2.  Table of Identifiers

   0000: GF256 (or GF(2**8)) Vandermonde based coefficients.  Each
   coefficient is built as alpha^( (source_symbol_id*coded_symbol_id) %
   255).

   0001: GF16 (or GF(2**4)) Vandermonde based coefficients.  Each
   coefficient is built as alpha^( (source_symbol_id*coded-symbol_id) %
   15).

   0010: SRLC.

   Others: To be discussed.

6.  Tetrys Basic Functions

6.1.  Encoding

   At the beginning of a transmission, a Tetrys Encoding Building Block
   or MUST choose an initial code rate (added redundancy) as it doesn't
   know the packet loss rate of the channel.  In steady state, depending
   on the code-rate, the Tetrys Encoding Building Block CAN generate
   coded symbols when it receives a source symbol from the application
   or some feedback from the decoding or recoding blocks.

   When a Tetrys Encoding Building Block needs to generate a coded
   symbol, it considers the set of source symbols stored in the Elastic
   Encoding Window.  These source symbols are the set of source symbols
   which are not yet acknowledged by the receiver.

   A Tetrys Encoding Building Block SHOULD set a limit to the Elastic
   Encoding Window maximum size.  This allows to control the algorithmic
   complexity at the encoder and decoder by limiting the size of linear
   combinations.  It is also needed in situations where acknowledgment
   packets are all lost or absent.

   At the generation of a coded symbol, the Tetrys Encoding Building
   Block generates an encoding vector containing the IDs of the source
   symbols stored in the Elastic Encoding Window.  For each source
   symbol, a finite field coefficient is determined using a Coding
   Coefficient Generator.  This generator CAN take as input the source



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   symbol ID and the coded symbol ID and CAN determine a coefficient in
   a deterministic way.  A classical example of such deterministic
   function is a generator matrix where the rows are indexed by the
   source symbol IDs and the columns by the coded symbol IDs.  For
   example, the entries of this matrix can be built from a Vandermonde
   structure, like Reed-Solomon codes, or from a sparse binary matrix,
   like Low-Density Generator Matrix codes.  Finally, the coded symbol
   is the sum of the source symbols multiplied by their corresponding
   coefficients.

6.1.1.  Encoding Vector Formats

   Each coded packet contains an encoding vector.  The encoding vectors
   CAN contain the ID and/or coefficient of each source symbol contained
   in the coded symbol.

6.1.1.1.  Transmitting the source symbol IDs

   The source symbol IDs are organized as a sorted list of 32-bit
   unsigned integers.  Depending on the feedback, the source symbol IDs
   can be successive or not in the list.

   If they are successive, the boundaries are stored in the encoding
   vector: it just needs 2*32-bit of information.

   If not, the edge blocks CAN be stored directly, or a differential
   transform to reduce the number of bits needed to represent an ID CAN
   be used.

6.1.1.1.1.  Compressed list of Source symbol IDs

   Assume the symbol IDs used in the combination are:
   [1..3],[5..6],[8..10].

   1.  Keep the first element in the packet as the first_source_id: 1.

   2.  Apply a differential transform to the others elements
       ([3,5,6,8,10]) which removes the element i-1 to the element i,
       starting with the first_source_id as i0, and get the list L =>
       [2,2,1,2,2]

   3.  Compute b, the number of bits needed to store all the elements,
       which is ceil(log2(max(L))): here, 2 bits.

   4.  Write b in the corresponding field, and write all the b * [(2 *
       NB blocks) - 1] elements in a bit vector, here: 10 10 01 10 10.





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6.1.1.1.2.  Decompressing the Source symbol IDs

   When a Tetrys Decoding Building Block wants to reverse the
   operations, this algorithm is used:

   1.  Rebuild the list of the transmitted elements by reading the bit
       vector and b: [10 10 01 10 10] => [2,2,1,2,2]

   2.  Apply the reverse transform by adding successively the elements,
       starting with first_source_id: [1,1+2,(1+2)+2,(1+2+2)+1,...] =>
       [1,3,5,6,8,10]

   3.  Rebuild the blocks using the list and first_source_id:
       [1..3],[5..6],[8..10].

6.1.1.2.  Encoding Vector Format

   The encoding vector CAN be used to store the source symbol IDs
   included in the associated coded symbol, the coefficients used in the
   combination, or both.  It CAN be used to send only the number of
   source symbols included in the coded symbol.

   If the source IDs are stored, the number of blocks MUST be different
   from 0.

   The encoding vector format uses a 4-bit Coding Coefficient Generator
   Identifier to identity the algorithm to generate the coefficients,
   and contains a set of blocks for the source symbol IDs used in the
   combination.  In this format, the number of blocks is stored as a
   8-bit unsigned integer.  To reduce the overhead, a compressed way to
   store the symbol IDs is used: the IDs are not stored as themselves,
   but stored as the difference between the previous.



















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    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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |     EV_LEN    |  CCGI | I |C|V|   NB_BLOCKS   |   NB_COEFS    |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                        FIRST_SOURCE_ID                        |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |     b_id      |                                               |
   +-+-+-+-+-+-+-+-+            id_bit_vector        +-+-+-+-+-+-+-+
   |                                                 |   Padding   |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |    b_coef     |                                               |
   +-+-+-+-+-+-+-+-+          coef_bit_vector        +-+-+-+-+-+-+-+
   |                                                 |   Padding   |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                     Figure 7: Encoding Vector Format

   o  Encoding Vector Length (EV_LEN) (8-bits): size in units of 32-bit
      words.

   o  Coding Coefficient Generator Identifier (CCGI): 4-bit ID to
      identify the algorithm or the function used to generate the
      coefficients (see Section 5).  As a CCGI is included in each
      encoded vector, it can dynamically change between the generation
      of 2 coded symbols.

   o  Store the Source symbol IDs (I) (2 bits):

      *  00 means there is no source symbol ID information.

      *  01 means the encoding vector contains the edge blocks of the
         source symbol IDs without compression.

      *  10 means the encoding vector contains the compressed list of
         the source symbol IDs.

   o  Store the coefficients (C): 1 bit to know if an encoding vector
      contains information about the coefficients used.

   o  Having source symbols with variable size (V): set V to 1 if the
      combination which refers the encoding vector is a combination of
      source symbols with variable sizes.  In this case, the coded
      packets MUST have the 'Encoded Payload Size' field.

   o  Number of blocks used to store the source symbol IDs (NB_BLOCKS):
      the number of blocks used to store all the source symbol IDs.




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   o  Number of coefficients (NB_COEFS): The number of the coefficients
      used to generate the associated coded symbol.

   o  The first source Identifier (FIRST_SOURCE_ID): the first source
      symbol ID used in the combination.

   o  Number of bits for each edge block (b_id): the number of bits
      needed to store the edge (see Section 6.1.1.1).

   o  Information about the source symbol IDs (id_bit_vector): if I=01,
      store the edge blocks as b_id * (NB_BLOCKS * 2 - 1).  If I=10,
      store in a compressed way the edge blocks.

   o  Number of bits needed to store each coefficient (b_coef): the
      number of bits used to store the coefficients.

   o  The coefficients (coef_bit_vector): The coefficients stored (as a
      vector of b_coef * NB_COEFS).

   o  Padding: padding to have an Encoding Vector size multiple of
      32-bit (for the id and coefficient part).

6.2.  The Elastic Encoding Window

   When an input source symbol is passed to a Tetrys Encoding Building
   Block, it is added to the Elastic Encoding Window.  This window MUST
   have a limit set by the encoding building Block (depending of the use
   case: unicast, multicast, file transfer, real-time transfer, ...).
   If the Elastic Encoding Window reached its limit, the window slides
   over the symbols: the first (oldest) symbols are removed.  Then, a
   packet containing this symbol can be sent onto the network.  As an
   element of the coding window, this symbol is included in the next
   linear combinations created to generate the coded symbols.

   As explained below, the receiver or the recoder sends periodic
   feedback indicating the received or decoded source symbols.  In the
   case of a unicast transmission, when the sender receives the
   information that a source symbol was received and/or decoded by the
   receiver, it removes this symbol from the coding window.

   In a multicast transmission:

   o  If the acknowledgement packets are not enabled, the coding window
      grows up to a limit.  When the limit is reached, the oldest
      symbols are removed from the coding window.

   o  If the acknowledgement packets are enabled, a source symbol is
      removed from the coding window when all the receivers have



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      received or decoded it or when the coding window reaches its
      limit.

6.3.  Recoding

6.3.1.  Principle

   A Tetrys Recoding Block maintains a list of the ID of the source
   symbols included in the Elastic Coding Window of the sender.  It also
   stores a set of received source and coded symbols able to regenerate
   the set or a subset of the symbols of the Elastic Coding Window.  In
   other words, if R1, ..., Rt represent t received symbols and S1, ...,
   Sk represent the set or a subset of the source symbols of the Elastic
   Coding Window, there exists a t*k-matrix M such that (R1, ..., Rt).M
   = (S1, ..., Sk).

6.3.2.  Generating a coded symbol at an intermediate node

   At the generation of a coded symbol, the Tetrys Recoding Building
   Block generates an encoding vector containing the IDs of the source
   symbols stored in the Elastic Encoding Window or in the subset of the
   Elastic Encoding Window that it is able to regenerate.  The Tetrys
   Recoding Building Block then generates a new coded symbol ID
   different from the received coded symbol IDs.  From this coded symbol
   ID and the source symbol IDs of (S1, ..., Sk), a finite field
   coefficient is determined using a Coding Coefficient Generator.  Let
   (a1, ...,ak) denote the obtained coefficients.  To compute the linear
   combination (s1, ..., Sk).transpose(a1, ..., ak) the Tetrys Recoding
   Building block computes the vector v = (a1, ...,ak).transpose(M) and
   then computes the coded symbol R = (R1, ..., Rt).transpose(v).  It
   can be verified that the new coded symbol is obtained without any
   decoding operation.

6.4.  Decoding

   A classical matrix inversion is sufficient to recover the source
   symbols.

7.  Security Considerations

   N/A

8.  Privacy Considerations

   N/A






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9.  IANA Considerations

   N/A

10.  Acknowledgments

   N/A

11.  References

11.1.  Normative References

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

11.2.  Informative References

   [AHL-00]   Ahlswede, R., Ning Cai, , Li, S., and R. Yeung, "Network
              information flow", IEEE Transactions on Information
              Theory vol.46, no.4, pp.1204,1216, July 2000.

   [FECFRAME]
              Watson, M., Begen, A., and V. Roca, "Forward Error
              Correction (FEC) Framework", Request for Comments 6363,
              October 2011.

   [NWCRG-ARCH]
              NWCRG, , "Network Coding Architecture", TBD TBD.

   [RMT]      Vicisano, L., Gemmel, J., Rizzo, L., Handley, M., and J.
              Crowcroft, "Forward Error Correction (FEC) Building
              Block", Request for Comments 3452, December 2002.

   [Tetrys]   Lacan, J. and E. Lochin, "Rethinking reliability for long-
              delay networks", International Workshop on Satellite and
              Space Communications 2008 (IWSSC08), October 2008.

Authors' Addresses











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   Jonathan Detchart
   ISAE
   10, avenue Edouard-Belin
   BP 54032
   Toulouse CEDEX 4  31055
   France

   Email: jonathan.detchart@isae.fr


   Emmanuel Lochin
   ISAE
   10, avenue Edouard-Belin
   BP 54032
   Toulouse CEDEX 4  31055
   France

   Email: emmanuel.lochin@isae.fr


   Jerome Lacan
   ISAE
   10, avenue Edouard-Belin
   BP 54032
   Toulouse CEDEX 4  31055
   France

   Email: jerome.lacan@isae.fr


   Vincent Roca
   INRIA
   655, av. de l'Europe
   Inovallee; Montbonnot
   ST ISMIER cedex  38334
   France

   Email: vincent.roca@inria.fr













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