1. RFC 8406
Internet Research Task Force (IRTF)                           B. Adamson
Request for Comments: 8406                                           NRL
Category: Informational                                         C. Adjih
ISSN: 2070-1721                                                    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
                                                               June 2018

   Taxonomy of Coding Techniques for Efficient Network Communications


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

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Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Research Task Force
   (IRTF).  The IRTF publishes the results of Internet-related research
   and development activities.  These results might not be suitable for
   deployment.  This RFC represents the consensus of the Coding for
   Efficient Network Communications Research Group of the Internet
   Research Task Force (IRTF).  Documents approved for publication by
   the IRSG are not candidates for any level of Internet Standard; see
   Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at

Copyright Notice

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

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (https://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  General Definitions and Concepts  . . . . . . . . . . . . . .   4
   3.  Taxonomy of Code Uses . . . . . . . . . . . . . . . . . . . .   7
   4.  Coding Details  . . . . . . . . . . . . . . . . . . . . . . .   8
     4.1.  Coding Types  . . . . . . . . . . . . . . . . . . . . . .   8
     4.2.  Coding Basics . . . . . . . . . . . . . . . . . . . . . .   9
     4.3.  Coding in Practice  . . . . . . . . . . . . . . . . . . .  12
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  13
   7.  Informative References  . . . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  14

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1.  Introduction

   This document is the product of and represents the collaborative work
   and consensus of the Coding for Efficient Network Communications
   Research Group (NWCRG); it is not an IETF product and is not a
   standard.  In 2017, the document was discussed during three audio
   conferences, each of them gathering 6 to 8 key experts; it was
   co-edited and subjected to an RG Last Call.  The general feeling was
   that the document was ready.  Additional information about Network
   Coding may be found on these NWCRG pages: <https://irtf.org/nwcrg>
   and <https://datatracker.ietf.org/rg/nwcrg/about/>.

   The literature on Network Coding research and system design,
   including IETF documentation, 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 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], [RFC5740], [RFC5775], [RFC6363], and [RFC6726].  This
   document is also related to IETF work being done in the PAYLOAD and
   TSVWG WGs (in particular, the extension of FECFRAME to support
   Sliding Window Codes and the Random Linear Coding (RLC) sliding
   window FEC scheme) and past work in the AVTCORE and MMUSIC WGs.  Note
   that in the definitions, the "(IETF)" tag indicates that the
   associated term is already used in IETF documents (Internet-Drafts
   and RFCs).

   This document focuses on packet transmissions and losses.  These
   losses will typically be triggered by various types of networking
   issues and/or impairments (e.g., congested routers or intermittent
   wireless connectivity).  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 does the coding middleware
   operate?).  For instance, a "packet" may be a data unit to be carried
   as a UDP payload because the coding middleware is located between the
   application and UDP.  In another configuration, coding may be applied
   within an overlay network and the notion of "packet" will be totally
   different.  In any case, the goals of Network Coding can be to
   improve the network throughput, efficiency, latency, and scalability,
   as well as to provide resilience to partition, attacks, and
   eavesdropping (NWCRG charter).  Both End-to-End Coding and systems
   that also perform recoding within intermediate forwarding nodes are
   considered in this document.

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   This document does not consider physical-layer transmission issues,
   physical-layer codes, or 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 the
   packet is supposed to be dropped.

2.  General Definitions and Concepts

   This section provides 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 technology (e.g., an
      Ethernet link, a WiFi network, or a full path between two nodes
      over the Internet).  As opposed to the "Erasure" channels, "Error"
      channels are where one or multiple bit errors may happen during a
      packet transmission.  These "Error" channels are out of scope.

   Erasure Correcting Code (ECC) or (IETF) Forward Erasure Correction
      A code for the Packet Erasure Channel (only).  These codes are
      also called "Application-Level FECs" to highlight that they have
      been designed for use within the higher layers of the protocol
      stack to protect against packet losses.  As opposed to ECCs/FECs,
      "Error" correction codes are capable of identifying the presence
      of bit errors and perhaps correcting them.  The "Error" correction
      codes are out of scope.

   End-to-End Coding:
      A system where coding is performed at the source or (coding)
      middlebox, and decoding is performed at the destination(s) or
      (decoding) middlebox.  There is no recoding 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 is regarded as a special case of Network Coding.
      Depending on the use case, additional assumptions can be made: for
      instance, the destination knowing the Coding Nodes' topology and
      coding operations can help during decoding operations.

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   Packet versus Symbol:
      Generally speaking, a Packet is the unit of data that is sent in
      the Packet Erasure Channel, while a Symbol is the unit of data
      that is manipulated during the encoding and decoding operations.

   Original Payload, Uncoded Payload, Systematic Symbol, or (IETF)
      Source Symbol:
      A unit of data originating from the source that is used as input
      to encoding operations.

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

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

   (En)coding versus Recoding versus Decoding:
      (En)coding is an operation that takes Source Symbols as input and
      produces Encoding Symbols as output.  Recoding is an operation
      that takes Encoding Symbols as input and produces Encoding Symbols
      as output.  Decoding is an operation takes Encoding Symbols as
      input and produces Source Symbols as output.

   (IETF) Source Packet:
      A packet originating from the source that 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 Symbols.

   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 a Systematic

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   Coding at a Coding Node that performs Encoding (rather than
   Recoding).  FEC decoding procedures are similarly performed in the
   reverse order.

           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
                That Performs Encoding (Rather Than Recoding)

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

   Coding Node:
      A node that performs FEC Encoding or Recoding operations.  It may
      be an end host or a middlebox (Encoding case), or a forwarding
      node (Recoding case).

   (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 encoding.

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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 Figure 2) When both terms are used, "Source Coding" usually
      refers to compression techniques (e.g., audio and video
      compression) within the upper application that generates the
      Source Flow.  "Channel Coding" refers to FEC encoding in order to
      improve transmission robustness, for instance, within the lower
      physical layer (out of scope of this document) or as part of
      Network Coding.  These terms should not be confused with "FEC
      coding within the Source Node" and "FEC recoding within an
      intermediate Coding Node", respectively.

   raw data flow from camera     ^              video flow display
               |                 |                      ^
               v                 | upper                |
   +------------------------+    |           +-------------------------+
   |     source coding      |    | applica-  |  source (de)coding      |
   |(e.g., mpeg compression)|    | tion      |(e.g., 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

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      Figure 2 shows 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 to allow recoding within the network.

   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 flows.

   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 nodes.

   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 discussed in subsequent 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

   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.

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

   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, the size
      may depend on acknowledgments sent by the receiver(s) for a
      particular Source Symbol or Source Packet (received, decoded, or

   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.  Alternately, 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.

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

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

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

   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 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 time.

   Rank of a Payload Set or Rank of the Linear System:
      At a receiver, 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" where decoding is possible or
      "partial rank" where only partial decoding is possible.

   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

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

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   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
      typical 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 recoding in an
      intermediate node).

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

   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 density.

   Finite Field, Galois Field, or Coding Field:
      Finite Fields, used in Linear Codes, have the desired property of
      having all elements (except zero) invertible for the + and *
      operators, 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.  The 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 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, the list of available Source Packets received
      or decoded (acknowledgement), 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

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4.3.  Coding in Practice

   This section discusses practical aspects.  Indeed, a practical
   solution must specify the exact manner in which encoding and decoding
   are performed but also detail 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 a particular FEC code as well as the
      additional protocol aspects required to use this 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 decoders.

   Payload Index or (IETF) Encoding Symbol Identifier (ESI):
      An identifier of a Source or Repair Symbol.  With Block Coding,
      each symbol of a given block is identified by a unique ESI value.
      With Sliding Window Coding, a continuous Source Flow and a limited
      field size to hold the ESI, wrapping to zero is unavoidable and
      the same integer value will be reused 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 or may not
      be compressed), 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
      Pseudorandom 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 or may not be
      compressed) or the ESI of the first Source Symbol along with their
      number (assuming there is no gap).

5.  IANA Considerations

   This document has no IANA actions.

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6.  Security Considerations

   This document introduces a recommended terminology for Network Coding
   and therefore does not contain any security considerations.  This
   does not mean that Network Coding systems do not have any security

7.  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,

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Authors' Addresses

   Brian Adamson
   United States of America

   Email: brian.adamson@nrl.navy.mil

   Cedric Adjih

   Email: cedric.adjih@inria.fr

   Josu Bilbao

   Email: jbilbao@ikerlan.es

   Victor Firoiu
   BAE Systems
   United States of America

   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

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   Antonia Masucci

   Email: antoniamaria.masucci@orange.com

   Marie-Jose Montpetit
   United States of America

   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
   United States of America

   Email: ssenthil@cisco.com

Adamson, et al.               Informational                    [Page 15]
  1. RFC 8406