NWCRG                                                         B. Adamson
Internet-Draft                                                       NRL
Intended status: Informational                                  C. Adjih
Expires: January 18, 2018                                          INRIA
                                                               J. Bilbao
                                                               V. Firoiu
                                                             BAE Systems
                                                               F. Fitzek
                                                              TU Dresden
                                                               S. Ghanem
                                                               E. Lochin
                                                          ISAE - Supaero
                                                              A. Masucci
                                                          M-J. Montpetit
                                                             M. Pedersen
                                                      Aalborg University
                                                              G. Peralta
                                                            V. Roca, Ed.
                                                               P. Saxena
                                                      AnsuR Technologies
                                                            S. Sivakumar
                                                           July 17, 2017

                        Network Coding Taxonomy


   This document is the product of the Network Coding Research Group
   (NWCRG).  It summarizes a recommended terminology for Network Coding
   concepts and constructs.  It provides a comprehensive set of terms in
   order to avoid ambiguities in future Network Coding IRTF and IETF
   documents.  This document is intended to be in-line with the
   terminology used by the RFCs produced by the Reliable Multicast
   Transport (RMT) and FEC Framework (FECFRAME) IETF working groups.

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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 18, 2018.

Copyright Notice

   Copyright (c) 2017 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
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   4
   2.  General definitions and concepts  . . . . . . . . . . . . . .   4
   3.  Taxonomy of Code Uses . . . . . . . . . . . . . . . . . . . .   6
   4.  Coding Details  . . . . . . . . . . . . . . . . . . . . . . .   8
     4.1.  Coding Types  . . . . . . . . . . . . . . . . . . . . . .   8
     4.2.  Coding Basics . . . . . . . . . . . . . . . . . . . . . .   9
     4.3.  Coding In Practice  . . . . . . . . . . . . . . . . . . .  11
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  12
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  12
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  12
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  13
   Appendix A.  Additional references  . . . . . . . . . . . . . . .  13

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   Appendix B.  Authors and Contributors . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  13

1.  Introduction

   This document is not an IETF product and is not a standard.  This
   document is the product and represents the consensus of the Network
   Coding Research Group (NWCRG).  In 2017, it has been discussed during
   three well-attended audio conferences, each of them gathering 6 to 8
   participants, it has been openly co-edited, and finally subject to a
   RG Last Call.  The general feeling was that the document was ready
   for next step and only a few minor suggestions for improvement have
   been made during the Last Call.

   The literature on Network Coding research and system design, IETF
   included, led to a rich set of concepts and constructs.  This
   document collects terminology used in the domain, both outside and
   inside IETF, provides concise definitions, and introduces a high
   level taxonomy.  Its primary goal is to be useful to IETF and IRTF
   activities.  It is also intended to be in-line with the terminology
   already used by the RFCs produced by the Reliable Multicast Transport
   (RMT) and FEC Framework (FECFRAME) IETF working groups, in particular
   [RFC5052] [RFC6726] [RFC5775] [RFC5740] [RFC6363].

   This document only focuses on packet transmissions and packet losses,
   for instance because of congested routers, routing issues,
   intermittent connectivity (e.g., a mobile terminal can suddenly go
   behind an obstacle) and wireless communication issues.
   Communications may happen in various types of networks, physical
   links, UDP services, overlay networks or even virtual networks.  The
   notion of packet itself is multiform, depending on the target use-
   case and the notion of network (e.g., in which layer of the protocol
   stack).  For instance, a packet may be a UDP datagram because coding
   happens within a dedicated transport protocol on top of UDP.

   This document does not try to be exhaustive: it is voluntarily kept
   as simple as possible.

   This document does not consider physical layer transmission issues,
   nor physical layer codes, nor error detection: if low layer error
   codes detect but fail to correct bit errors, or if an upper layer
   checksum (e.g., within IP or UDP) identifies a corrupted packet, then
   this packet is supposed to be dropped.

   This document IS NOT restricted to constructs that perform re-coding
   within intermediate forwarding nodes.  While this document considers
   Network Coding (i.e., re-coding within the network), it also
   considers End-to-End Coding.

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   In the following definitions, the "(IETF)" tag indicates that the
   associated term is already used in IETF documents.

1.1.  Requirements Language

   The keywords "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in RFC 2119 [RFC2119].

2.  General definitions and concepts

   This section gathers general definitions and concepts that are used
   throughout this document.

   Packet Erasure Channel:  A communication path where packets are
           either dropped or received without any error.  This type of
           packet drop is referred to as an "erasure" or "loss".  The
           term "channel" must be understood as a generic term for any
           type of communication facility.  The "Erasure" channels are
           opposed to "Error" channels that are out of scope.

   Erasure Correcting Code (ECC), or (IETF) Forward Erasure Code (FEC):

                A code for the Packet Erasure Channel (only).  These
                codes are also called "Application-Level FEC" to
                highlight that they have been designed to be used within
                the higher layers of the protocol stack, to protect
                against packet losses.  These codes are opposed to
                "Error" correction codes that address errors and are out
                of scope.

        Original Payload, or Uncoded Payload, or Systematic Symbol, or
        (IETF) Source Symbol:
                A unit of data originating from the source that is used
                as input to encoding operations.  When there is a single
                Source Symbol per Source Packet, an Original Payload
                corresponds to a Source Packet.

        Coded Payload, Coded Symbol, or (IETF) Repair Symbol:  A unit of
                data that is the result of a coding operation, applied
                either to Source Symbols or (in case of recoding) Source
                and/or Repair Symbols.  When there is a single Repair
                Symbol per Repair Packet, a Coded Payload corresponds to
                a Repair Packet.

        Input Symbol and Output Symbol:  A unit of data that is used as
                input to an encoding operation or that is generated as
                output of an encoding operation.  At a re-coding node,

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                Repair Symbols are also part of the Input Symbols.  With
                Systematic Coding, Source Symbols are also part of the
                Output Symbols.

        (IETF) Encoding Symbol:  A Source or a Repair Symbol.

        (IETF) Source Packet:  A packet originating from the source
                which contributes to one or more Source Symbols.  For
                instance, an RTP packet as a whole can constitute a
                Source Symbol.  In other situations (e.g, to address
                variable size packets) a single RTP packet may
                contribute to various Source Symbols.

        (IETF) Repair Packet:  A packet containing one or more Repair

   Figure 1 illustrates the relationships between packets (what is sent
   in the Packet Erasure Channel) and symbols (what is manipulated
   during encoding and decoding operations) in case of FEC encoding, at
   a Coding Node.  A similar figure could be done for FEC decoding.

           source packet
                 | source packet to source symbols transform
                 | (one or more symbols per packet)
           source symbols
                 v input symbols
      |     FEC encoding     |
         | output symbols |
         v                v
   source symbols   repair symbols
         |                |
         |                | symbol to packet transform
         |                | (one or more symbols per packet)
         v                v
   source packet    repair packet

        Figure 1: Packet and symbol relationships at a Coding Node.

   Source Node:  A node that generates one or more Source Flows.

   Coding Node:  A node that performs FEC encoding operations.  It may
           be an end-host, a middlebox, or a forwarding node.

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   (IETF) Flow:  A stream of packets logically grouped.

   (IETF) Source Flow:  A flow of Source Packets coming from an
           application on a given host, and to which FEC encoding is to
           be applied, potentially along with other Source Flows.
           Depending on the use case, Source Flows may come from the
           same application, from different applications on the same
           host, or from different applications on different hosts.

   (IETF) Repair flow:  A flow containing Repair Packets, after FEC

3.  Taxonomy of Code Uses

   This section discusses the various ways of using coding, without
   going into coding details.

   Source Coding versus Channel Coding:  (see Fig. Figure 2) When both
           terms are opposed, "Source Coding" usually refers to
           compression techniques (e.g., audio and video compression)
           within the upper application that generates the source flow.
           On the opposite, "Channel Coding" refers to FEC encoding in
           order to improve transmission robustness, initially within
           the lower physical layer, potentially also encompassing the
           upper layers.  These terms should not be confused with
           respectively "FEC coding within the Source Node" and "FEC re-
           coding within an intermediate Coding Node".

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   raw data flow from camera      ^                video flow display
               |                  |                        ^
               v                  | upper                  |
   +-----------------------+      |            +-----------------------+
   |     source coding     |      | applica-   |  source (de)coding    |
   |(e.g. mpeg compression)|      | tion       |(eg. mpg decompression)|
   +-----------------------+      v            +-----------------------+
               |                                           ^
               v                                           |
   +-----------------------+      ^            +-----------------------+
   | network/AL-FEC coding |      | middle-    | network/AL-FEC coding |
   |  (e.g. RLC encoding)  |      | ware       |  (e.g. RLC decoding)  |
   +-----------------------+      v            +-----------------------+
               |                                           ^
               v                                           |
   +-----------------------+      ^            +-----------------------+
   |     packetization     |      |            |    depacketization    |
   |     (e.g. UDP/IP)     |      | communi-   |     (e.g. UDP/IP)     |
   +-----------------------+      | cation     +-----------------------+
               |                  |                        ^
               v                  | layers                 |
   +-----------------------+      |            +-----------------------+
   |       PHY layer       |      |            |       PHY layer       |
   |    (channel coding)   |      |            |   (channel decoding)  |
   +-----------------------+      v            +-----------------------+
               |                                           ^
               |          source + repair traffic          |

   Figure 2: Example of end-to-end flow manipulation with Network Coding
      between the application and UDP layers (as with RMT or FECFRAME
   architectures).  Other architectures are possible, for instance with
   network coding below the transport layer in order to allow re-coding
                            within the network.

   End-to-End Coding:  A system where coding is performed at the source
           or (coding) middlebox, and decoding at the destination(s) or
           (decoding) middlebox.  There is no re-coding operation at
           intermediate nodes.  This is the approach followed in the
           FLUTE/ALC [RFC6726][RFC5775], NORM [RFC5740] and FECFRAME
           [RFC6363] protocols.

   Network Coding:  A system where coding can be performed at the source
           as well as at intermediate forwarding nodes (all or a subset
           of them).  End-to-End Coding can be regarded as a special
           case of Network Coding.  Depending on the use case,
           additional assumptions can be made: for instance the

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           knowledge by the destination of the coding node topology and
           coding operations can help during decoding operations.

   Intra-Flow Coding, or Single Source Network Coding:  Process where
           incoming packets to the Coding Node belong to the same flow.

   Inter-Flow Coding, or Multi-Source Network Coding:  Process where
           incoming packets to the Coding Node belong to different

   Single-Path Coding:  Network Coding over a route that has a single
           path from the source to each destination(s).  In case of
           multicast or broadcast traffic, this route is a tree.  Coding
           may be done end-to-end and/or at intermediate forwarding

   Multi-Path Coding:  Network Coding over a route that has multiple (at
           least partially) disjoint paths from the source to each given
           destination.  Coding may be done end-to-end and/or at
           intermediate forwarding nodes.

4.  Coding Details

4.1.  Coding Types

   This section provides a high level taxonomy of coding techniques.
   Technical details are left for the following sections.

   Linear Coding:  Linear combination of a set of input symbols (i.e.,
           Source and/or Repair Symbols) using a given set of
           coefficients and resulting in a Repair Symbol.  Many linear
           codes exist that differ from the way coding coefficients are
           drawn from a Finite Field of a given size.

   Random Linear Coding (RLC):  Particular case of Linear Coding using a
           set of random coding coefficients.

   Adaptive Linear Coding:  Linear Coding that utilizes cross layer
           adaptation.  For instance, an adaptive coding scheme may
           adapt the generation and transmission of Repair Packets
           according to the channel variations over time, accounting for
           the predictive loss of degrees of freedom due to erasures.

   Block Coding:  Coding technique where the input Flow(s) must be first
           segmented into a sequence of blocks, FEC encoding and
           decoding being performed independently on a per-block basis.
           The term "Chunk Coding" is sometimes used, where a "Chunk"
           denotes a block.

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   Sliding Window Coding, or Convolutional Coding:  General class of
           coding techniques that rely on a sliding encoding window.
           This is an alternative solution to Block Coding.

   Fixed or Elastic Sliding Window Coding:  Coding technique that
           generates Repair Symbol(s) on-the-fly, from the set of Source
           Symbols present in the sliding encoding window at that time,
           usually by using Linear Coding.  The sliding window may be
           either of fixed size or of variable size over the time (also
           known as "elastic sliding window").  For instance this size
           may depend on acknowledgments sent by the receiver(s) for a
           particular Source Symbol or Source Packet (received, decoded,
           or decodable).

   Systematic Coding:  A coding technique where Source Symbols are part
           of the output Flow generated by a Coding Node.

   Rateless and Non-Rateless Coding:  Rateless Coding can generate an
           unlimited number of Repair Symbols (in practice this number
           can be limited by practical considerations or because of use-
           case requirements) from a given set of Source Symbols,
           meaning that the code rate is null.  RLC codes are an example
           of Rateless Codes.  On the opposite, Non-Rateless Coding
           usually has a predefined maximum number of Repair Symbols
           that can be generated from a given set of Source Symbols.

4.2.  Coding Basics

   This section discusses and defines low level coding aspects.

   Code Rate:  In case of a Block Code, the Code Rate is the k/n ratio
           between the number of Source Symbols, k, and the number of
           Source plus Repair Symbols, n.  With a Sliding Window Code,
           the Code Rate is defined similarly over a certain time
           interval, since the Code Rate may change dynamically.  By
           definition, the Code Rate is such that: 0 < Code Rate <= 1.
           A Code Rate close to 1 indicates that a small number of
           Repair Symbols have been produced during the encoding process
           and vice-versa.

   (En)coding Window:  A set of Source (and Repair in the case of re-
           coding) Symbols used as input to the coding operations.  The
           set of symbols will typically change over the time, as the
           Coding Window slides over the input Flow(s).

   (En)coding Window Size:  The number of Source (and Repair in case of
           re-coding) Symbols in the current Encoding Window.  This size
           may change over the time.

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   Payload Set:  The set of Source and Repair Symbols available (i.e.,
           received or previously decoded) at the receiver and used
           during FEC decoding operations.

   Decoding window:  The set of Source Symbols (only) that are
           considered in the current linear system of a receiver,
           independently of the fact these Source Symbols have been
           received, decoded, or lost.  The Decoding Window will
           typically change over the time, as transmissions and decoding
           progress, and may be different for different receivers of a
           session where content is multicast or broadcast.

   Decoding Window Size:  The number of Source Symbols (only) in the
           current Decoding Window.  This size may change over the time.

   Rank of a Payload Set, or (IETF) Rank of the Linear System:  At a rec
           eiver, number of linearly independent members of a Payload
           Set, or equivalently the number of linearly independent
           equations of the linear system.  It is also known as "Degrees
           of Freedom".  The system may be of "full rank" and decoding
           is possible, or "partial rank", and only partial decoding is

   Seen Payload, or Seen Symbol:  A Source Symbol is Seen when the
           receiver can compute a linear combination with this symbol
           and Source Symbols that are strictly more recent (i.e., with
           logically higher Encoding Symbol Identifiers).  Otherwise the
           Source Symbol is considered as "unseen".

   Generation, or (IETF) Block:  With Block Codes, the set of Source
           Symbols of the input Flow(s) that are logically grouped into
           a Block, before doing encoding.

   Generation Size, or Code Dimension, or (IETF) Block Size:  With Block
           Codes, the number k of Source Symbols belonging to a Block.

   Coding Matrix, or Generator Matrix:  A matrix G that transforms the
           set of Input Symbols X into a set of Repair Symbols: Y = X *
           G.  Defining a Generator Matrix is usual with Block Codes.
           The set of Input Symbols X can consist only of Source Symbols
           (e.g., with End-to-End Coding) or can consist of Source and
           Repair Symbols (e.g., with re-coding in an intermediate

   Coding Coefficient:  With Linear Coding, this is a coefficient in a
           certain Finite Field.  This coefficient may be chosen in
           different ways: randomly, or in a pre-defined table, or using
           a pre-defined algorithm plus a seed.

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   Coding Vector:  A set of Coding Coefficients used to generate a
           certain Repair Symbol through Linear Coding.  The number of
           nonzero coefficients in the Coding Vector defines its

   Finite Field, or Galois Field, or Coding Field:  Finite fields, used
           in Linear Codes, have the desired property of having all
           elements (except zero) invertible for + and * and all
           operations over any elements do not result in an overflow or
           underflow.  Examples of Finite Fields are prime fields
           {0..p^m-1}, where p is prime.  Most used fields use p=2 and
           are called binary extension fields {0..2^m-1}, where m often
           equals 1, 4 or 8 for practical reasons.

   Finite Field size, or Coding Field size:  The number of elements in a
           finite field.  For example the binary extension field
           {0..2^m-1} has size q=2^m.

   Feedback:  Feedback information sent by a decoding node to a Coding
           Node (or from a receiver to a source in case of End-to-End
           Coding).  The nature of information contained in a feedback
           packet varies, depending on the use-case.  It can provide
           reception and/or FEC decoding statistics, or the list of
           available Source Packets received or decoded
           (acknowledgement), or the list of lost Source Packets that
           should be retransmitted (negative acknowledgement), or a
           number of additional Repair Symbols needed to have a Full
           Rank Linear System.

4.3.  Coding In Practice

   This section discusses practical aspects.  Indeed, a practical
   solution must specify the exact manner encoding and decoding is
   performed but also all the peripheral aspects, for instance how an
   encoder informs a decoder about the parameters used to generate a
   certain Repair Packet (signaling).

   (IETF) FEC Scheme:  A specification that defines the additional
           protocol aspects required to use a particular FEC code.  In
           particular the FEC Scheme defines in band (e.g., information
           contained in Source and Repair Packet header or trailers) and
           out of band (e.g., information contained in an SDP
           description) signaling needed to synchronize encoders and

   Payload Indices, or (IETF) Encoding Symbol Identifiers (ESI):  An ide
           ntifier of a Source or Repair Symbol.  If conceptually, each
           symbol is identified by a unique ESI value, in practice, with

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           a continuous flow and a limited field size to hold the ESI,
           wrapping to zero in unavoidable and the same integer value
           will be re-used several times.

   (IETF) FEC Payload ID:  Information that identifies the contents of a
           packet with respect to the FEC Scheme.  The FEC Payload ID of
           a packet containing Source Symbol(s) is usually different
           from that of a packet containing Repair Symbol(s).  The FEC
           Payload ID typically contains at least an ESI.

   Coding Vector and Encoding Window Signaling:  With Sliding Window
           Codes, the FEC Payload ID of a Repair Packet contains
           information needed and sufficient to identify the Coding
           Vector and Coding Window.  Concerning the Coding Vector, this
           may consist of a full list of Coding Coefficients (that may
           be compressed or not), or a piece of information (e.g., a
           seed) that can be used to generate the list of Coding
           Coefficients thanks to a predefined algorithm known by
           encoders and decoders (e.g., a Pseudo Random Number
           Generator, or PRNG), or an ESI that points to a given entry
           in a Generator Matrix in case of a Block Code.  Concerning
           the Coding Window, this may consist of the full list of ESI
           of symbols in the Coding Window (that may be compressed or
           not), or the ESI of the first Source Symbol along with their
           number (assuming there is no gap).

5.  IANA Considerations

   This document is not subject to IANA registration.

6.  Security Considerations

   This document introduces a recommended terminology for network coding
   and therefore does not contain any security consideration.  This does
   not mean that network coding systems do not have any security

7.  References

7.1.  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,

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7.2.  Informative References

   [RFC5052]  Watson, M., Luby, M., and L. Vicisano, "Forward Error
              Correction (FEC) Building Block", RFC 5052,
              DOI 10.17487/RFC5052, August 2007,

   [RFC5740]  Adamson, B., Bormann, C., Handley, M., and J. Macker,
              "NACK-Oriented Reliable Multicast (NORM) Transport
              Protocol", RFC 5740, DOI 10.17487/RFC5740, November 2009,

   [RFC5775]  Luby, M., Watson, M., and L. Vicisano, "Asynchronous
              Layered Coding (ALC) Protocol Instantiation", RFC 5775,
              DOI 10.17487/RFC5775, April 2010,

   [RFC6363]  Watson, M., Begen, A., and V. Roca, "Forward Error
              Correction (FEC) Framework", RFC 6363,
              DOI 10.17487/RFC6363, October 2011,

   [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,

Appendix A.  Additional references

   Additional references on network coding are available in the NWCRG
   research web site: https://irtf.org/nwcrg

Appendix B.  Authors and Contributors

   This document is the result of a collaborative work that involved may
   authors and contributors from the NWCRG IRTF research group.  They
   are listed below in alphabetical order in this document.

Authors' Addresses

   Brian Adamson

   Email: brian.adamson@nrl.navy.mil

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   Cedric Adjih

   Email: cedric.adjih@inria.fr

   Josu Bilbao

   Email: jbilbao@ikerlan.es

   Victor Firoiu
   BAE Systems

   Email: victor.firoiu@baesystems.com

   Frank Fitzek
   TU Dresden

   Email: frank.fitzek@tu-dresden.de

   Samah A. M. Ghanem

   Email: samah.ghanem@gmail.com

   Emmanuel Lochin
   ISAE - Supaero

   Email: emmanuel.lochin@isae-supaero.fr

   Antonia Masucci

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   Marie-Jose Montpetit

   Email: marie@mjmontpetit.com

   Morten V. Pedersen
   Aalborg University

   Email: mvp@es.aau.dk

   Goiuri Peralta

   Email: gperalta@ikerlan.es

   Vincent Roca (editor)

   Email: vincent.roca@inria.fr

   Paresh Saxena
   AnsuR Technologies

   Email: paresh.saxena@ansur.es

   Senthil Sivakumar

   Email: ssenthil@cisco.com

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