NWCRG J. Heide
Internet-Draft Steinwurf Aps
Intended status: Experimental S. Shi
Expires: March 12, 2020 K. Fouli
M. Medard
Code On Network Coding LLC
V. Chook
Inmarsat PLC
September 09, 2019
Random Linear Network Coding (RLNC)-Based Symbol Representation
draft-heide-nwcrg-rlnc-03
Abstract
This document describes a symbol representation for Random Linear
Network Coding (RLNC) schemes used for reliable data transfer.
Specifically, the following features are discussed and incorporated:
both block RLNC and a sliding window RLNC, varying data frame sizes,
and one or multiple symbols associated with a single symbol
representation header.
Requirements Language
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 RFC 2119 [RFC2119].
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on March 12, 2020.
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Copyright Notice
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Symbol Representation . . . . . . . . . . . . . . . . . . . . 3
2.1. Representation Setup . . . . . . . . . . . . . . . . . . 4
2.2. Field Types and Formats . . . . . . . . . . . . . . . . . 5
2.3. Externally Specified Parameters Required . . . . . . . . 7
2.4. Small Encoding Window . . . . . . . . . . . . . . . . . . 7
2.4.1. Examples . . . . . . . . . . . . . . . . . . . . . . 9
2.5. Large Encoding Window . . . . . . . . . . . . . . . . . . 10
3. Security Considerations . . . . . . . . . . . . . . . . . . . 11
4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 11
5. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.1. Normative References . . . . . . . . . . . . . . . . . . 11
5.2. Informative References . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 12
1. Introduction
Symbol representation specifies the format of the symbol-carrying
data unit that is to be used in network coding operations, including
header format and symbol concatenation. This document describes a
symbol representation format intended to be used for Network Coding
in general, and for Random Linear Network Coding (RLNC) in particular
[HK03].
Owing to its dynamic structure, network coding has requirements that
are distinct from conventional point-to-point codes, leading to a
highly reconfigurable symbol set. Consequently, the design choices
related to symbol representation are particularly important in
network coding as they have a direct impact on the viability of
network protocols, topologies, and architecture [RLNC-Background].
For example, recoding [RLNC-Background] requires the coefficients to
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be accessible at the recoding nodes. Hence, architectures and
protocols requiring recoding must specify coefficient location in
their symbol representation.
In addition to providing background on RLNC, [RLNC-Background] argues
that careful design and specification of a symbol representation is a
requirement for any viable network coding protocol, architecture, or
topology.
2. Symbol Representation
This section provides a symbol representation design for implementing
RLNC-based erasure correction schemes. In the decribed symbol
representation design, multiple symbols are concatenated and
associated with a single symbol representation header.
The symbol representation design is provided for constructing a data
payload portion of a data packet for a protocol that utilizes a
generation-based or sliding-window RLNC, where recoding can be used
at intermediate nodes. A data packet data payload comprises one or
more symbol representations. Each symbol representation in turn
comprises one or more symbols that can be systematic, coded or
recoded. The use of this symbol representation design is not limited
by transmission schemes. It can be applied to unicast, multiple-
unicast, multicast, multi-path, and multi-source settings and the
like.
Coding coefficient vectors must be implicitly or explicitly
transmitted from the sender to the receiver, generally along with the
coded data for successful decoding of the original data. One option
is to attach each coding coefficient vector to the corresponding
coded symbol as a header, thus also enabling recoding at intermediate
nodes. Another option is to attach the current state of a pseudo-
random generator for generating the coding coefficient vector, to
reduce the size of the header. Adding a header to each symbol may
result in a high overhead when the symbol size is small or when
generation or sliding window size is large. Adding a joint header to
the beginning of each generation may also cause synchronization to be
re-initiated only at the beginning of each generation instead of
every symbol. In what follows, a symbol representation is provided
that allow for both of these options such that both a general
representation with coding coefficients and a compact representation
with a seed for generating the coding coefficients can be used, in
order to reduce the header overhead.
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2.1. Representation Setup
This section specifies a symbol representation that enables both a
general form with coding coefficient vectors attached, and a compact
form where a seed is attached which is used to generate one or
multiple coding coefficient vectors. Different maximum GENERATION
and WINDOW SIZE are supported for RLNC encoding, recoding, and
decoding.
To encode over a set of data symbols, a coding coefficient vector is
first generated, comprising a number of finite field elements as
specified by a GENERATION SIZE or WINDOW SIZE variable. For a
generation based code the GENERATION SIZE defines the number of
original symbols in each generation. For a window based code the
WINDOW SIZE specifies the maximal number of symbols in the window
over which coding can be performed. In the case of systematic codes,
systematic symbols correspond to unit coding coefficient vectors.
Figure 1 illustrates the general symbol representation design. Four
header fields precede the symbol data: TYPE flag (T), SYMBOLS,
ENCODER RANK, and SEED or CODING COEFFICIENTS. The TYPE Flag (T)
indicates if the symbol is systematic, coded, or recoded. SYMBOLS
indicates the number of symbols in the SYMBOLS(S) DATA field.
ENCODER RANK represents the current rank of the encoder, which is the
number of symbols being linearly combined. SEED is used to generate
the coding coefficient vector(s) using a pseudo-random number
generator, for a compact form of the symbol representation. The
CODING COEFFICIENTS field is a list of SYMBOLS number of coding
coefficient vectors used to generate the SYMBOL(S) DATA, and used in
the case where no random number generator is available or practical
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| T |SYMBOLS| ENCODER RANK | SEED or CODING COEFFICIENTS |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOL(S) DATA |
| ... |
| |
+---------------------------------------------------------------+
Figure 1: A general symbol representation design.
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2.2. Field Types and Formats
The TYPE Flag (T) indicates if the symbol is systematic, coded, or
recoded, and has the following properties:
o 2 bits long.
o If the TYPE flag is '1', all symbols included in this symbol
representation are systematic or uncoded, with symbol index
starting from ENCODER RANK. This option allows for efficient
representation of systematic symbols.
o If the TYPE is '2', all symbols included in this symbol
representation are coded, with coding coefficient vectors
generated using the included SEED and the ENCODER RANK.
Consequently, only the first ENCODER RANK elements in the coding
coefficient vector can be non-zero, whereas the remaing elements
(e.g. GENERATION SIZE - ENCODER RANK) in the coding coefficient
vector are zeros. This option allows for compact and efficient
representation of coded symbols, which may also subsequently be
recoded.
o If the TYPE is '3', all symbols included in this symbol
representation are either uncoded, coded or recoded. Each coding
vector included is composed of GENERATION SIZE or WINDOW SIZE
coefficients.
SYMBOLS indicates the number of symbols in the 'Symbol(s) Data'
field, and has the following properties:
o 4 bits long. A maximum number of 15 symbols are concatenated
within each symbol representation.
o The special case of SYMBOLS = 0 indicates that zero symbols are
included, and consequently the size of SYMBOLS(S) DATA is 0 bytes.
This can, for example, be used to implement a flush functionality
or ensure that protocol operations do not stop in certain case for
purely event-driven protocols.
ENCODER RANK represents the current rank of the encoder, that is, the
number of original symbols used to compute the coded symbols(s). It
has the following properties:
o MUST be no larger than GENERATION/WINDOW SIZE.
o If TYPE flag is '1', ENCODER RANK is the symbol index of the first
data symbol in this symbol representation.
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o If TYPE flag is '2' or '3', ENCODER RANK is the number of data
symbols over which coding was performed for all coded symbols in
this symbol representation.
SEED is used to generate the coding coefficient vector(s) using a
pseudo-random number generator, for a compact form of the symbol
representation, and has the following properties:
o The SEED field is only present when TYPE flag is '2'. If TYPE is
'1' or '3', this field is absent.
o The pseudo-random generator MUST be seeded with this value and all
coding coefficient vectors are produced by the same generator.
For example, if ENCODER RANK is 12, then the coding coefficient
vector for the first symbol in this symbol representation is
coefficients 0 through 11 generated by the pseudo-random generator
seeded by SEED, and coding coefficient vector for the second
symbol in this symbol representation is coefficients 12 through 23
generated by the pseudo-random generator seeded by SEED. If
GENERATION/WINDOW SIZE is larger than ENCODER RANK, the remaining
coefficients in the coding coefficient vector are zero.
o To ensure that SEED can be interpreted correctly at the receiver,
the same pseudo-random number generator MUST be used by the sender
and a recoding or receiving node. Otherwise, more than one SEED
field would need to be used.
o 8 bits long. Thus, 256 different seed values can be served. One
SEED is used per symbol representation, each of which can contain
up to 15 symbols, all derived using the same SEED. For distinct
ENCODER RANKs, different coding coefficient vectors would be
generated from the same SEED, since only an ENCODER RANK number of
coefficients from the random generator is grouped as a coding
coefficient vector, before progressing to the next coding
coefficient vector for the next symbol in the symbol
representation. Consequently, the maximal number of coded symbols
that can be generated for a generation is |SEED| * |SYMBOLS|
* |ENCODER RANK| which in the best case is (2^8)*(2^4-1)*(2^10) ~
2^22, which for all practical considerations can be considered as
an infinite number of coded symbols. If all coded symbols that
can be represented using a SEED is exhausted, symbols where the
coding coefficient vectors is included can be sent instead.
CODING COEFFICIENTS field is a list of SYMBOLS number of coding
vectors used to generate the ensuing SYMBOL(S) DATA, and has the
following properties:
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o The CODING COEFFICIENT field is only present when TYPE flag is
'3'. If TYPE is '1' or '2', this field is absent.
o Each coding coefficient vector includes ENCODER RANK number of
coding coefficients.
2.3. Externally Specified Parameters Required
This section specifies parameters that are REQUIRED for the use of
this symbol representation but which are not included in the symbol
representation and therefore MUST be communicated by means of some
outer mecanism. Typically these parameters will be static throughout
a protocol session. Consequently, there is little to gain by
incorporating these parameters into the representation but conversely
it would add additional overhead.
o Field polynomial, the underlying field over which coding is
performed.
o Pseudo Random Generator, used to generate coding coefficient
vectors.
o Symbol Size, used to divide the original data into symbols.
o GENERATION SIZE or WINDOW SIZE, for block and sliding window
codes, respectively.
o Small or large encoding window, this symbol representation
supports both a small and a large coding window, but the variant
used is not communicated.
2.4. Small Encoding Window
In a first small encoding window symbol representation, ENCODER RANK
is 10 bits long, and the maximum GENERATION/WINDOW SIZE is 2^10.
Figures 2 to 4 below illustrate systematic, coded, and recoded symbol
representations within an encoding window of size 2^10. Systematic
symbols are uncoded. Coded symbols are compact in form and comprise
a seed for coding coefficient generation. Recoded symbols are
general in form and comprise the coding coefficient vectors
explicitly.
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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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 1 |SYMBOLS| ENCODER RANK | SYMBOL(S) DATA |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOLS(S) DATA continued |
| ... |
| |
+---------------------------------------------------------------+
Figure 2: A systematic symbol representation.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 2 |SYMBOLS| ENCODER RANK | SEED |SYMBOL(S) DATA |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOL(S) DATA continued |
| ... |
| |
+---------------------------------------------------------------+
Figure 3: A compact, coded symbol representation.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 3 |SYMBOLS| ENCODER RANK | CODING COEFFICIENTS |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| CODING COEFFICIENTS continued |
| ... |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOL(S) DATA |
| ... |
| |
+---------------------------------------------------------------+
Figure 4: A recoded symbol representation.
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2.4.1. Examples
The following examples show different symbol representations for an
illustrative case where the symbol size is 2 bytes, GENERATION/WINDOW
SIZE is 8, and field size is 2^8.
Example 1: Three systematic symbols with ID 0, 1 and 2. As the TYPE
flag is '1' , SEED/CODING COEFFICIENTS is absent, and ENCODER RANK is
the symbol index of the first data symbol with ID 0 in this compact
symbol representation.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 1 | 3 | 0 | Systematic Symbol 0 Data |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Systematic Symbol 1 Data | Systematic Symbol 2 Data |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: A symbol representation with 3 systematic, uncoded symbols.
Example 2: Two coded symbols using a compact representation. In this
example, TYPE is '2', the SEED to the pseudo-random number generator
shared by the sender and receiver is 4. The coding coefficient
vector for Symbol A is coefficients 0 to 7 generated by the pseudo-
random number generator, the coding coefficient vector for symbol B
is coefficients 8 to 15 generated by the pseudo-random number
generator.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 2 | 2 | 8 | 4 | Coded Symbol A
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Data | Coded Symbol B Data |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 6: A symbol representation with 2 coded symbols.
Example 3: Two recoded symbols. Coefficients A0 to A7 constitute the
coding coefficient vector for Symbol A, coefficients B0 to B7
constitute the coding coefficient vector for symbol B. In practical
implementations, symbol sizes are much larger than 2, leading to
amortization of the coding coefficient overheads.
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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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 3 | 2 | 8 | A0 | A1 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| A2 | A3 | A4 | A5 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| A6 | A7 | B0 | B1 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| B2 | B3 | B4 | B5 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| B6 | B7 | Coded Symbol A Data |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Coded Symbol B Data |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: A symbol representation with 2 recoded symbols having
coding coefficients attached.
2.5. Large Encoding Window
In a second large encoding window symbol representation, ENCODER RANK
is 18-bit long, and the maximum GENERATION/WINDOW SIZE is 2^18.
Figures 8 to 10 below illustrate systematic, coded, and recoded
symbol representations within an encoding window of size 2^18.
Systematic symbols are uncoded. Coded symbols are compact in form
and comprise a seed for coding coefficient generation. Recoded
symbols are general in form and comprise the coding coefficient
vectors explicitly (CODING COEFFICIENTS or CODING COEFFS).
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 1 |SYMBOLS| ENCODER RANK |SYMBOL(S) DATA |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOL(S) DATA continued |
| ... |
| |
+---------------------------------------------------------------+
Figure 8: A systematic symbol representation.
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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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 2 |SYMBOLS| ENCODER RANK | SEED |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOL(S) DATA |
| ... |
| |
+---------------------------------------------------------------+
Figure 9: A coded symbol representation.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 3 |SYMBOLS| ENCODER RANK | CODING COEFFS |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| CODING COEFFICIENTS continued |
| ... |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| SYMBOL(S) DATA |
| ... |
| |
+---------------------------------------------------------------+
Figure 10: A recoded symbol representation.
3. Security Considerations
This document does not present new security considerations.
4. IANA Considerations
This document has no actions for IANA.
5. References
5.1. 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,
<https://www.rfc-editor.org/info/rfc2119>.
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[RLNC-Background]
Heide, J., Shi, S., Fouli, K., Medard, M., and V. Chook,
"Random Linear Network Coding (RLNC): Background and
Practical Considerations", February 2018,
<https://datatracker.ietf.org/doc/
draft-heide-nwcrg-rlnc-background/>.
5.2. Informative References
[HK03] Ho, T., Koetter, R., Medard, M., Karger, D., and M.
Effros, "The Benefits of Coding over Routing in a
Randomized Setting", July 2003,
<http://ieeexplore.ieee.org/document/1228459/>.
Authors' Addresses
Janus Heide
Steinwurf Aps
Aalborg
Denmark
Email: janus@steinwurf.com
Shirley Shi
Code On Network Coding LLC
Cambridge
USA
Email: xshi@alum.mit.edu
Kerim Fouli
Code On Network Coding LLC
Cambridge
USA
Email: fouli@codeontechnologies.com
Muriel Medard
Code On Network Coding LLC
Cambridge
USA
Email: muriel.medard@codeontechnologies.com
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Vince Chook
Inmarsat PLC
London
United Kingdom
Email: Vince.Chook@inmarsat.com
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