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Internet Research Task Force (IRTF) B. Adamson
Request for Comments: 8406 NRL
Category: Informational C. Adjih
ISSN: 2070-1721 INRIA
J. Bilbao
Ikerlan
V. Firoiu
BAE Systems
F. Fitzek
TU Dresden
S. Ghanem
Independent
E. Lochin
ISAE - Supaero
A. Masucci
Orange
M-J. Montpetit
Independent
M. Pedersen
Aalborg University
G. Peralta
Ikerlan
V. Roca, Ed.
INRIA
P. Saxena
AnsuR Technologies
S. Sivakumar
Cisco
June 2018
Taxonomy of Coding Techniques for Efficient Network Communications
Abstract
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
groups.
Adamson, et al. Informational [Page 1]
RFC 8406 Taxonomy of Coding Techniques June 2018
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
https://www.rfc-editor.org/info/rfc8406.
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
Adamson, et al. Informational [Page 2]
RFC 8406 Taxonomy of Coding Techniques June 2018
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.
Adamson, et al. Informational [Page 3]
RFC 8406 Taxonomy of Coding Techniques June 2018
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
(FEC):
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.
Adamson, et al. Informational [Page 4]
RFC 8406 Taxonomy of Coding Techniques June 2018
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
Symbols.
(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
Adamson, et al. Informational [Page 5]
RFC 8406 Taxonomy of Coding Techniques June 2018
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)
v
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.
Adamson, et al. Informational [Page 6]
RFC 8406 Taxonomy of Coding Techniques June 2018
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
Adamson, et al. Informational [Page 7]
RFC 8406 Taxonomy of Coding Techniques June 2018
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
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.
Adamson, et al. Informational [Page 8]
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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
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. 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.
Adamson, et al. Informational [Page 9]
RFC 8406 Taxonomy of Coding Techniques June 2018
(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
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 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
"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, Code Dimension, or (IETF) Block Size:
With Block Codes, the number of Source Symbols, k, belonging to a
Block.
Adamson, et al. Informational [Page 10]
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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:
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
System.
Adamson, et al. Informational [Page 11]
RFC 8406 Taxonomy of Coding Techniques June 2018
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.
Adamson, et al. Informational [Page 12]
RFC 8406 Taxonomy of Coding Techniques June 2018
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
implication.
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,
<https://www.rfc-editor.org/info/rfc5052>.
[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,
<https://www.rfc-editor.org/info/rfc5740>.
[RFC5775] Luby, M., Watson, M., and L. Vicisano, "Asynchronous
Layered Coding (ALC) Protocol Instantiation", RFC 5775,
DOI 10.17487/RFC5775, April 2010,
<https://www.rfc-editor.org/info/rfc5775>.
[RFC6363] Watson, M., Begen, A., and V. Roca, "Forward Error
Correction (FEC) Framework", RFC 6363,
DOI 10.17487/RFC6363, October 2011,
<https://www.rfc-editor.org/info/rfc6363>.
[RFC6726] Paila, T., Walsh, R., Luby, M., Roca, V., and R. Lehtonen,
"FLUTE - File Delivery over Unidirectional Transport",
RFC 6726, DOI 10.17487/RFC6726, November 2012,
<https://www.rfc-editor.org/info/rfc6726>.
Adamson, et al. Informational [Page 13]
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Authors' Addresses
Brian Adamson
NRL
United States of America
Email: brian.adamson@nrl.navy.mil
Cedric Adjih
INRIA
France
Email: cedric.adjih@inria.fr
Josu Bilbao
Ikerlan
Spain
Email: jbilbao@ikerlan.es
Victor Firoiu
BAE Systems
United States of America
Email: victor.firoiu@baesystems.com
Frank Fitzek
TU Dresden
Germany
Email: frank.fitzek@tu-dresden.de
Samah A. M. Ghanem
Independent
Email: samah.ghanem@gmail.com
Emmanuel Lochin
ISAE - Supaero
France
Email: emmanuel.lochin@isae-supaero.fr
Adamson, et al. Informational [Page 14]
RFC 8406 Taxonomy of Coding Techniques June 2018
Antonia Masucci
Orange
France
Email: antoniamaria.masucci@orange.com
Marie-Jose Montpetit
Independent
United States of America
Email: marie@mjmontpetit.com
Morten V. Pedersen
Aalborg University
Denmark
Email: mvp@es.aau.dk
Goiuri Peralta
Ikerlan
Spain
Email: gperalta@ikerlan.es
Vincent Roca (editor)
INRIA
France
Email: vincent.roca@inria.fr
Paresh Saxena
AnsuR Technologies
Norway
Email: paresh.saxena@ansur.es
Senthil Sivakumar
Cisco
United States of America
Email: ssenthil@cisco.com
Adamson, et al. Informational [Page 15]