draft-ietf-rmt-bb-fec-ldpc-06.txt   draft-ietf-rmt-bb-fec-ldpc-07.txt 
RMT V. Roca RMT V. Roca
Internet-Draft INRIA Internet-Draft INRIA
Intended status: Experimental C. Neumann Intended status: Standards Track C. Neumann
Expires: November 8, 2007 Thomson Research Expires: May 19, 2008 Thomson
D. Furodet D. Furodet
STMicroelectronics STMicroelectronics
May 7, 2007 November 16, 2007
Low Density Parity Check (LDPC) Staircase and Triangle Forward Error Low Density Parity Check (LDPC) Staircase and Triangle Forward Error
Correction (FEC) Schemes Correction (FEC) Schemes
draft-ietf-rmt-bb-fec-ldpc-06.txt draft-ietf-rmt-bb-fec-ldpc-07.txt
Status of this Memo Status of this Memo
By submitting this Internet-Draft, each author represents that any By submitting this Internet-Draft, each author represents that any
applicable patent or other IPR claims of which he or she is aware applicable patent or other IPR claims of which he or she is aware
have been or will be disclosed, and any of which he or she becomes have been or will be disclosed, and any of which he or she becomes
aware will be disclosed, in accordance with Section 6 of BCP 79. aware will be disclosed, in accordance with Section 6 of BCP 79.
Internet-Drafts are working documents of the Internet Engineering Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF), its areas, and its working groups. Note that Task Force (IETF), its areas, and its working groups. Note that
skipping to change at page 1, line 38 skipping to change at page 1, line 38
and may be updated, replaced, or obsoleted by other documents at any and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress." material or to cite them other than as "work in progress."
The list of current Internet-Drafts can be accessed at The list of current Internet-Drafts can be accessed at
http://www.ietf.org/ietf/1id-abstracts.txt. http://www.ietf.org/ietf/1id-abstracts.txt.
The list of Internet-Draft Shadow Directories can be accessed at The list of Internet-Draft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html. http://www.ietf.org/shadow.html.
This Internet-Draft will expire on November 8, 2007. This Internet-Draft will expire on May 19, 2008.
Copyright Notice Copyright Notice
Copyright (C) The IETF Trust (2007). Copyright (C) The IETF Trust (2007).
Abstract Abstract
This document describes two Fully-Specified FEC Schemes, LDPC- This document describes two Fully-Specified FEC Schemes, LDPC-
Staircase and LDPC-Triangle, and their application to the reliable Staircase and LDPC-Triangle, and their application to the reliable
delivery of objects on packet erasure channels. These systematic FEC delivery of data objects on the packet erasure channel (i.e., a
communication path where packets are either received without any
corruption or discarded during transmission). These systematic FEC
codes belong to the well known class of ``Low Density Parity Check'' codes belong to the well known class of ``Low Density Parity Check''
(LDPC) codes, and are large block FEC codes in the sense of RFC3453. (LDPC) codes, and are large block FEC codes in the sense of RFC3453.
Table of Contents Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Requirements notation . . . . . . . . . . . . . . . . . . . . 5 2. Requirements notation . . . . . . . . . . . . . . . . . . . . 5
3. Definitions, Notations and Abbreviations . . . . . . . . . . . 6 3. Definitions, Notations and Abbreviations . . . . . . . . . . . 6
3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 6 3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 6
3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 6
skipping to change at page 3, line 24 skipping to change at page 2, line 34
4.1. FEC Payload IDs . . . . . . . . . . . . . . . . . . . . . 8 4.1. FEC Payload IDs . . . . . . . . . . . . . . . . . . . . . 8
4.2. FEC Object Transmission Information . . . . . . . . . . . 8 4.2. FEC Object Transmission Information . . . . . . . . . . . 8
4.2.1. Mandatory Element . . . . . . . . . . . . . . . . . . 8 4.2.1. Mandatory Element . . . . . . . . . . . . . . . . . . 8
4.2.2. Common Elements . . . . . . . . . . . . . . . . . . . 8 4.2.2. Common Elements . . . . . . . . . . . . . . . . . . . 8
4.2.3. Scheme-Specific Elements . . . . . . . . . . . . . . . 9 4.2.3. Scheme-Specific Elements . . . . . . . . . . . . . . . 9
4.2.4. Encoding Format . . . . . . . . . . . . . . . . . . . 9 4.2.4. Encoding Format . . . . . . . . . . . . . . . . . . . 9
5. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.2. Determining the Maximum Source Block Length (B) . . . . . 13 5.2. Determining the Maximum Source Block Length (B) . . . . . 13
5.3. Determining the Encoding Symbol Length (E) and Number 5.3. Determining the Encoding Symbol Length (E) and Number
of Encoding Symbols per Group (G) . . . . . . . . . . . . 13 of Encoding Symbols per Group (G) . . . . . . . . . . . . 14
5.4. Determining the Number of Encoding Symbols of a Block . . 15 5.4. Determining the Maximum Number of Encoding Symbols
5.5. Identifying the Symbols of an Encoding Symbol Group . . . 16 Generated for Any Source Block (max_n) . . . . . . . . . . 15
5.6. Pseudo Random Number Generator . . . . . . . . . . . . . . 19 5.5. Determining the Number of Encoding Symbols of a Block
6. Full Specification of the LDPC-Staircase Scheme . . . . . . . 21 (n) . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.6. Identifying the G Symbols of an Encoding Symbol Group . . 16
6.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 21 5.7. Pseudo Random Number Generator . . . . . . . . . . . . . . 20
6.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 22 6. Full Specification of the LDPC-Staircase Scheme . . . . . . . 22
6.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 23 6.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 22
7. Full Specification of the LDPC-Triangle Scheme . . . . . . . . 24 6.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 22
7.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 24
7.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 24 6.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 24
7.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 24 7. Full Specification of the LDPC-Triangle Scheme . . . . . . . . 26
7.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 25 7.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 26
8. Security Considerations . . . . . . . . . . . . . . . . . . . 26 7.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 26
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 27 7.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 26
10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 28 7.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 27
11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 29 8. Security Considerations . . . . . . . . . . . . . . . . . . . 28
11.1. Normative References . . . . . . . . . . . . . . . . . . . 29 8.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 28
11.2. Informative References . . . . . . . . . . . . . . . . . . 29 8.2. Attacks Against the Data Flow . . . . . . . . . . . . . . 28
Appendix A. Trivial Decoding Algorithm (Informative Only) . . . . 31 8.2.1. Access to Confidential Objects . . . . . . . . . . . . 28
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 33 8.2.2. Content Corruption . . . . . . . . . . . . . . . . . . 29
Intellectual Property and Copyright Statements . . . . . . . . . . 34 8.3. Attacks Against the FEC Parameters . . . . . . . . . . . . 30
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 31
10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 32
11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 33
11.1. Normative References . . . . . . . . . . . . . . . . . . . 33
11.2. Informative References . . . . . . . . . . . . . . . . . . 33
Appendix A. Pseudo Random Number Generator Example
Implementation (Informative Only) . . . . . . . . . . 35
Appendix B. Trivial Decoding Algorithm (Informative Only) . . . . 37
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 39
Intellectual Property and Copyright Statements . . . . . . . . . . 40
1. Introduction 1. Introduction
RFC 3453 [3] introduces large block FEC codes as an alternative to [RFC3453] introduces large block FEC codes as an alternative to small
small block FEC codes like Reed-Solomon. The main advantage of such block FEC codes like Reed-Solomon. The main advantage of such large
large block codes is the possibility to operate efficiently on source block codes is the possibility to operate efficiently on source
blocks of size several tens of thousands (or more) source symbols. blocks of size several tens of thousands (or more) source symbols.
The present document introduces the Fully-Specified FEC Encoding ID 3 The present document introduces the Fully-Specified FEC Encoding ID 3
that is intended to be used with the LDPC-Staircase FEC codes, and that is intended to be used with the LDPC-Staircase FEC codes, and
the Fully-Specified FEC Encoding ID 4 that is intended to be used the Fully-Specified FEC Encoding ID 4 that is intended to be used
with the LDPC-Triangle FEC codes [6][9]. Both schemes belong to the with the LDPC-Triangle FEC codes [RN04][MK03]. Both schemes belong
broad class of large block codes. to the broad class of large block codes. For a definition of the
term Fully-Specified Scheme, see [RFC5052], section 4.
LDPC codes rely on a dedicated matrix, called a "Parity Check LDPC codes rely on a dedicated matrix, called a "Parity Check
Matrix", at the encoding and decoding ends. The parity check matrix Matrix", at the encoding and decoding ends. The parity check matrix
defines relationships (or constraints) between the various encoding defines relationships (or constraints) between the various encoding
symbols (i.e. source symbols and repair symbols), that are later used symbols (i.e., source symbols and repair symbols), that are later
by the decoder to reconstruct the original k source symbols if some used by the decoder to reconstruct the original k source symbols if
of them are missing. These codes are systematic, in the sense that some of them are missing. These codes are systematic, in the sense
the encoding symbols include the source symbols in addition to the that the encoding symbols include the source symbols in addition to
repair symbols. the repair symbols.
Since the encoder and decoder must operate on the same parity check Since the encoder and decoder must operate on the same parity check
matrix, information must be communicated between them as part of the matrix, information must be communicated between them as part of the
FEC Object Transmission Information. FEC Object Transmission Information.
A publicly available reference implementation of these codes is A publicly available reference implementation of these codes is
available and distributed under a GNU/LGPL license [8]. available and distributed under a GNU/LGPL license [LDPC-codec].
Besides, the code extracts included in this document (except
Appendix A that is only provided as an example) are directly
contributed to the IETF process by the authors of this document and
by Radford M. Neal.
2. Requirements notation 2. Requirements notation
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [1]. document are to be interpreted as described in [RFC2119].
3. Definitions, Notations and Abbreviations 3. Definitions, Notations and Abbreviations
3.1. Definitions 3.1. Definitions
This document uses the same terms and definitions as those specified This document uses the same terms and definitions as those specified
in [2]. Additionally, it uses the following definitions: in [RFC5052]. Additionally, it uses the following definitions:
Source symbol: unit of data used during the encoding process
Encoding symbol: unit of data generated by the encoding process
Repair symbol: encoding symbol that is not a source symbol
Code rate: the k/n ratio, i.e., the ratio between the number of
source symbols and the number of encoding symbols. The code rate
belongs to a ]0; 1] interval. A code rate close to 1 indicates
that a small number of repair symbols have been produced during
the encoding process
Systematic code: FEC code in which the source symbols are part of
the encoding symbols
Source block: a block of k source symbols that are considered
together for the encoding
Encoding Symbol Group: a group of encoding symbols that are sent Encoding Symbol Group: a group of encoding symbols that are sent
together, within the same packet, and whose relationships to the together, within the same packet, and whose relationships to the
source object can be derived from a single Encoding Symbol ID. source object can be derived from a single Encoding Symbol ID
Source Packet: a data packet containing only source symbols. Source Packet: a data packet containing only source symbols
Repair Packet: a data packet containing only repair symbols. Repair Packet: a data packet containing only repair symbols
Packet Erasure Channel: a communication path where packets are
either dropped (e.g., by a congested router, or because the number
of transmission errors exceeds the correction capabilities of the
physical layer codes) or received. When a packet is received, it
is assumed that this packet is not corrupted
3.2. Notations 3.2. Notations
This document uses the following notations: This document uses the following notations:
L denotes the object transfer length in bytes L denotes the object transfer length in bytes
k denotes the source block length in symbols, i.e. the number of k denotes the source block length in symbols, i.e., the number of
source symbols of a source block source symbols of a source block
n denotes the encoding block length, i.e., the number of encoding
n denotes the encoding block length, i.e. the number of encoding
symbols generated for a source block symbols generated for a source block
E denotes the encoding symbol length in bytes E denotes the encoding symbol length in bytes
B denotes the maximum source block length in symbols, i.e. the B denotes the maximum source block length in symbols, i.e., the
maximum number of source symbols per source block maximum number of source symbols per source block
N denotes the number of source blocks into which the object shall N denotes the number of source blocks into which the object shall
be partitioned be partitioned
G denotes the number of encoding symbols per group, i.e. the G denotes the number of encoding symbols per group, i.e. the
number of symbols sent in the same packet number of symbols sent in the same packet
rate denotes the "code rate", i.e. the k/n ratio CR denotes the "code rate", i.e., the k/n ratio
max_n denotes the maximum number of encoding symbols generated for max_n denotes the maximum number of encoding symbols generated for
any source block any source block. This is in particular the number of encoding
symbols generated for a source block of size B
H denotes the parity check matrix H denotes the parity check matrix
srand(s) denotes the initialization function of the pseudo-random srand(s) denotes the initialization function of the pseudo-random
number generator, where s is the seed (s > 0) number generator, where s is the seed (s > 0)
rand(m) denotes a pseudo-random number generator that returns a rand(m) denotes a pseudo-random number generator that returns a
new random integer in [0; m-1] each time it is called new random integer in [0; m-1] each time it is called
3.3. Abbreviations 3.3. Abbreviations
This document uses the following abbreviations: This document uses the following abbreviations:
ESI: Encoding Symbol ID ESI: Encoding Symbol ID
FEC OTI: FEC Object Transmission Information FEC OTI: FEC Object Transmission Information
skipping to change at page 8, line 27 skipping to change at page 8, line 27
The Encoding Symbol ID (20 bit field) identifies which encoding The Encoding Symbol ID (20 bit field) identifies which encoding
symbol(s) generated from the source block is(are) carried in the symbol(s) generated from the source block is(are) carried in the
packet payload. There are a maximum of 2^^20 encoding symbols per packet payload. There are a maximum of 2^^20 encoding symbols per
block. The first k values (0 to k-1) identify source symbols, the block. The first k values (0 to k-1) identify source symbols, the
remaining n-k values (k to n-k-1) identify repair symbols. remaining n-k values (k to n-k-1) identify repair symbols.
There MUST be exactly one FEC Payload ID per packet. In case of an There MUST be exactly one FEC Payload ID per packet. In case of an
Encoding Symbol Group, when multiple encoding symbols are sent in the Encoding Symbol Group, when multiple encoding symbols are sent in the
same packet, the FEC Payload ID refers to the first symbol of the same packet, the FEC Payload ID refers to the first symbol of the
packet. The other symbols can be deduced from the ESI of the first packet. The other symbols can be deduced from the ESI of the first
symbol thanks to a dedicated function, as explained in Section 5.5 symbol thanks to a dedicated function, as explained in Section 5.6
0 1 2 3 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 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Number | Encoding Symbol ID (20 bits) | | Source Block Number | Encoding Symbol ID (20 bits) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 1: FEC Payload ID encoding format for FEC Encoding ID 3 and 4 Figure 1: FEC Payload ID encoding format for FEC Encoding ID 3 and 4
4.2. FEC Object Transmission Information 4.2. FEC Object Transmission Information
4.2.1. Mandatory Element 4.2.1. Mandatory Element
o FEC Encoding ID: the LDPC-Staircase and LDPC-Triangle Fully- o FEC Encoding ID: the LDPC-Staircase and LDPC-Triangle Fully-
Specified FEC Schemes use respectively the FEC Encoding ID 3 Specified FEC Schemes use respectively the FEC Encoding ID 3
(Staircase) and 4 (Triangle). (Staircase) and 4 (Triangle).
4.2.2. Common Elements 4.2.2. Common Elements
The following elements MUST be defined with the present FEC Scheme: The following elements MUST be defined with the present FEC Schemes:
o Transfer-Length (L): a non-negative integer indicating the length o Transfer-Length (L): a non-negative integer indicating the length
of the object in bytes. There are some restrictions on the of the object in bytes. There are some restrictions on the
maximum Transfer-Length that can be supported: maximum Transfer-Length that can be supported:
maximum transfer length = 2^^12 * B * E maximum transfer length = 2^^12 * B * E
For instance, if B=2^^19 (because of a code rate of 1/2, For instance, if B=2^^19 (because of a code rate of 1/2,
Section 5.2), and if E=1024 bytes, then the maximum transfer Section 5.2), and if E=1024 bytes, then the maximum transfer
length is 2^^41 bytes (or 2 TB). The upper limit, with symbols of length is 2^^41 bytes (or 2 TB). The upper limit, with symbols of
skipping to change at page 9, line 34 skipping to change at page 9, line 34
max_n value. In particular max_n is at most equal to 2^^20. max_n value. In particular max_n is at most equal to 2^^20.
Section 5 explains how to define the values of each of these Section 5 explains how to define the values of each of these
elements. elements.
4.2.3. Scheme-Specific Elements 4.2.3. Scheme-Specific Elements
The following elements MUST be defined with the present FEC Scheme: The following elements MUST be defined with the present FEC Scheme:
o G: a non-negative integer indicating the number of encoding o G: a non-negative integer indicating the number of encoding
symbols per group (i.e. per packet). The default value is 1, symbols per group (i.e., per packet). The default value is 1,
meaning that each packet contains exactly one symbol. Values meaning that each packet contains exactly one symbol. Values
greater than 1 can also be defined, as explained in Section 5.3. greater than 1 can also be defined, as explained in Section 5.3.
o PRNG seed: the seed is a 32 bit unsigned integer between 1 and o PRNG seed: the seed is a 32 bit unsigned integer between 1 and
0x7FFFFFFE (i.e. 2^^31-2) inclusive. This value is used to 0x7FFFFFFE (i.e., 2^^31-2) inclusive. This value is used to
initialize the Pseudo Random Number Generator (Section 5.6). This initialize the Pseudo Random Number Generator (Section 5.7).
element is optional. Whether or not it is present in the FEC OTI
is signaled in the associated encoding format through an
appropriate mechanism (Section 4.2.4). When the PRNG seed is not
carried within the FEC OTI, it is assumed that encoder and
decoders use another way to communicate the information, or use a
fixed, predefined value.
4.2.4. Encoding Format 4.2.4. Encoding Format
This section shows two possible encoding formats of the above FEC This section shows two possible encoding formats of the above FEC
OTI. The present document does not specify when or how these OTI. The present document does not specify when or how these
encoding formats should be used. encoding formats should be used.
4.2.4.1. Using the General EXT_FTI Format 4.2.4.1. Using the General EXT_FTI Format
The FEC OTI binary format is the following, when the EXT_FTI The FEC OTI binary format is the following, when the EXT_FTI
mechanism is used (e.g. within the ALC [13] or NORM [15] protocols). mechanism is used (e.g., within the ALC
[draft-ietf-rmt-pi-alc-revised] or NORM
[draft-ietf-rmt-pi-norm-revised] protocols).
0 1 2 3 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 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| HET = 64 | HEL (=4 or 5) | | | HET = 64 | HEL = 5 | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ + +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| Transfer-Length (L) | | Transfer-Length (L) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) | G | B (MSB) | | Encoding Symbol Length (E) | G | B (MSB) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| B (LSB) | Max Nb of Enc. Symbols (max_n) | | B (LSB) | Max Nb of Enc. Symbols (max_n) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
. Optional PRNG seed . | PRNG seed |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: EXT_FTI Header for FEC Encoding ID 3 and 4. Figure 2: EXT_FTI Header for FEC Encoding ID 3 and 4.
In particular: In particular:
o The HEL (Header Extension Length) indicates whether the optional
PRNG seed is present (HEL=5) or not (HEL=4).
o The Transfer-Length (L) field size (48 bits) is larger than the o The Transfer-Length (L) field size (48 bits) is larger than the
size required to store the maximum transfer length (Section 4.2.2) size required to store the maximum transfer length (Section 4.2.2)
for field alignment purposes. for field alignment purposes.
o The Maximum-Source-Block-Length (B) field (20 bits) is split into o The Maximum-Source-Block-Length (B) field (20 bits) is split into
two parts: the 8 most significant bits (MSB) are in the third 32- two parts: the 8 most significant bits (MSB) are in the third 32-
bit word of the EXT_FTI, and the remaining 12 least significant bit word of the EXT_FTI, and the remaining 12 least significant
bits (LSB) are in the fourth 32-bit word. bits (LSB) are in the fourth 32-bit word.
4.2.4.2. Using the FDT Instance (FLUTE specific) 4.2.4.2. Using the FDT Instance (FLUTE specific)
When it is desired that the FEC OTI be carried in the FDT Instance of When it is desired that the FEC OTI be carried in the FDT Instance of
a FLUTE session [14], the following XML attributes must be described a FLUTE session [draft-ietf-rmt-flute-revised], the following XML
for the associated object: attributes must be described for the associated object:
o FEC-OTI-FEC-Encoding-ID o FEC-OTI-FEC-Encoding-ID
o FEC-OTI-Transfer-length o FEC-OTI-Transfer-length
o FEC-OTI-Encoding-Symbol-Length o FEC-OTI-Encoding-Symbol-Length
o FEC-OTI-Maximum-Source-Block-Length o FEC-OTI-Maximum-Source-Block-Length
o FEC-OTI-Max-Number-of-Encoding-Symbols o FEC-OTI-Max-Number-of-Encoding-Symbols
o FEC-OTI-Scheme-Specific-Info o FEC-OTI-Scheme-Specific-Info
The FEC-OTI-Scheme-Specific-Info contains the string resulting from The FEC-OTI-Scheme-Specific-Info contains the string resulting from
the Base64 encoding (in the XML Schema xs:base64Binary sense) of the the Base64 encoding (in the XML Schema xs:base64Binary sense) of the
following value: following value:
skipping to change at page 11, line 25 skipping to change at page 11, line 18
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 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| PRNG seed | | PRNG seed |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| G | | G |
+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+
Figure 3: FEC OTI Scheme Specific Information to be Included in the Figure 3: FEC OTI Scheme Specific Information to be Included in the
FDT Instance for FEC Encoding ID 3 and 4. FDT Instance for FEC Encoding ID 3 and 4.
When no PRNG seed is to be carried in the FEC OTI, the seed field During Base64 encoding, the 5 bytes of the FEC OTI Scheme Specific
MUST be set to 0 (which is not a valid seed value). Otherwise the
seed field contains a valid value as explained in Section 4.2.3.
After Base64 encoding, the 5 bytes of the FEC OTI Scheme Specific
Information are transformed into a string of 8 printable characters Information are transformed into a string of 8 printable characters
(in the 64-character alphabet) and added to the FEC-OTI-Scheme- (in the 64-character alphabet) that is added to the FEC-OTI-Scheme-
Specific-Info attribute. Specific-Info attribute.
5. Procedures 5. Procedures
This section defines procedures that are common to FEC Encoding IDs 3 This section defines procedures that are common to FEC Encoding IDs 3
and 4. and 4.
5.1. General 5.1. General
The B (maximum source block length in symbols) and E (encoding symbol The B (maximum source block length in symbols), E (encoding symbol
length in bytes) parameters are first determined, as explained in the length in bytes) and G (number of encoding symbols per group)
following sections. parameters are first determined. The algorithms of Section 5.2 and
Section 5.3 MAY be used to that purpose. Using other algorithms is
possible without compromising interoperability since the B, E and G
parameters are communicated to the receiver by means of the FEC OTI.
The source object is then partitioned using the block partitioning Then, the source object MUST be partitioned using the block
algorithm specified in [2]. To that purpose, the B, L (object partitioning algorithm specified in [RFC5052]. To that purpose, the
transfer length in bytes), and E arguments are provided. As a B, L (object transfer length in bytes), and E arguments are provided.
result, the object is partitioned into N source blocks. These blocks As a result, the object is partitioned into N source blocks. These
are numbered consecutively from 0 to N-1. The first I source blocks blocks are numbered consecutively from 0 to N-1. The first I source
consist of A_large source symbols, the remaining N-I source blocks blocks consist of A_large source symbols, the remaining N-I source
consist of A_small source symbols. Each source symbol is E bytes in blocks consist of A_small source symbols. Each source symbol is E
length, except perhaps the last symbol which may be shorter. bytes in length, except perhaps the last symbol which may be shorter.
For each block the actual number of encoding symbols is determined, Then, the max_n (maximum number of encoding symbols generated for any
as explained in the following section. source block) parameter is determined. The algorithm of Section 5.4
MAY be used to that purpose. Using another algorithm is possible
without compromising interoperability since the max_n parameter is
communicated to the receiver by means of the FEC OTI.
For each block, the actual number of encoding symbols, n, MUST then
be determined using the "n-algorithm" detailed in Section 5.5.
Then, FEC encoding and decoding can be done block per block, Then, FEC encoding and decoding can be done block per block,
independently. To that purpose, a parity check matrix is created, independently. To that purpose, a parity check matrix is created,
that forms a system of linear equations between the source and repair that forms a system of linear equations between the source and repair
symbols of a given block, where the basic operator is XOR. symbols of a given block, where the basic operator is XOR.
This parity check matrix is logically divided into two parts: the This parity check matrix is logically divided into two parts: the
left side (from column 0 to k-1) which describes the occurrence of left side (from column 0 to k-1) describes the occurrences of each
each source symbol in the equation system; and the right side (from source symbol in the system of linear equations; the right side (from
column k to n-1) which describes the occurrence of each repair symbol column k to n-1) describes the occurrences of each repair symbol in
in the equation system. An entry (a "1") in the matrix at position the system of linear equations. The only difference between the
(i,j) (i.e. at row i and column j) means that the symbol with ESI i LDPC-Staircase and LDPC-Triangle schemes is the construction of this
appears in equation j of the system. The only difference between the right sub-matrix. An entry (a "1") in the matrix at position (i,j)
LDPC-Staircase and LDPC-Triangle schemes is the construction of the (i.e., at row i and column j) means that the symbol with ESI j
right sub-matrix. appears in equation i of the system.
When the parity symbols have been created, the sender will transmit When the parity symbols have been created, the sender transmits
source and parity symbols. The way this transmission occurs can source and parity symbols. The way this transmission occurs can
largely impact the erasure recovery capabilities of the LDPC-* FEC. largely impact the erasure recovery capabilities of the LDPC-* FEC.
In particular, sending parity symbols in sequence is suboptimal. In particular, sending parity symbols in sequence is suboptimal.
Instead it is usually recommended the shuffle these symbols. The Instead it is usually recommended the shuffle these symbols. The
interested reader will find more details in [7]. interested reader will find more details in [NRFF05].
The following sections detail how the B, E, and n parameters are The following sections detail how the B, E, G, max_nand n parameters
determined (respectively in Section 5.2, Section 5.3 and are determined (respectively in Section 5.2, Section 5.3, Section 5.4
Section 5.4), how encoding symbol groups are created (Section 5.5), and Section 5.5), how encoding symbol groups are created
and finally specify the PRNG (Section 5.6). (Section 5.6), and finally Section 5.7 details the PRNG.
5.2. Determining the Maximum Source Block Length (B) 5.2. Determining the Maximum Source Block Length (B)
The B parameter (maximum source block length in symbols) depends on The B parameter (maximum source block length in symbols) depends on
several parameters: the code rate (rate), the Encoding Symbol ID several parameters: the code rate (CR), the Encoding Symbol ID field
field length of the FEC Payload ID (20 bits), as well as possible length of the FEC Payload ID (20 bits), as well as possible internal
internal codec limitations. codec limitations.
The B parameter cannot be larger than the following values, derived The B parameter cannot be larger than the following values, derived
from the FEC Payload ID limitations, for a given code rate: from the FEC Payload ID limitations, for a given code rate:
max1_B = 2^^(20 - ceil(Log2(1/rate))) max1_B = 2^^(20 - ceil(Log2(1/CR)))
Some common max1_B values are: Some common max1_B values are:
o rate == 1 (no repair symbol): max1_B = 2^^20 = 1,048,576 o CR == 1 (no repair symbol): max1_B = 2^^20 = 1,048,576
o 1/2 <= rate < 1: max1_B = 2^^19 = 524,288 symbols o 1/2 <= CR < 1: max1_B = 2^^19 = 524,288 symbols
o 1/4 <= rate < 1/2: max1_B = 2^^18 = 262,144 symbols o 1/4 <= CR < 1/2: max1_B = 2^^18 = 262,144 symbols
o 1/8 <= rate < 1/4: max1_B = 2^^17 = 131,072 symbols o 1/8 <= CR < 1/4: max1_B = 2^^17 = 131,072 symbols
Additionally, a codec MAY impose other limitations on the maximum Additionally, a codec MAY impose other limitations on the maximum
block size. This is the case for instance when the codec uses block size. For instance, this is the case when the codec uses
internally 16 bit unsigned integers to store the Encoding Symbol ID, internally 16 bit unsigned integers to store the Encoding Symbol ID,
since it does not enable to store all the possible values of a 20 bit since it does not enable to store all the possible values of a 20 bit
field. In that case, if for instance 1/2 <= rate < 1, then the field. In that case, if for instance 1/2 <= CR < 1, then the maximum
maximum source block length is 2^^15. Other limitations may also source block length is 2^^15. Other limitations may also apply, for
apply, for instance because of a limited working memory size. This instance because of a limited working memory size. This decision
decision MUST be clarified at implementation time, when the target MUST be clarified at implementation time, when the target use case is
use case is known. This results in a max2_B limitation. known. This results in a max2_B limitation.
Then, B is given by: Then, B is given by:
B = min(max1_B, max2_B) B = min(max1_B, max2_B)
Note that this calculation is only required at the coder, since the B Note that this calculation is only required at the coder, since the B
parameter is communicated to the decoder through the FEC OTI. parameter is communicated to the decoder through the FEC OTI.
5.3. Determining the Encoding Symbol Length (E) and Number of Encoding 5.3. Determining the Encoding Symbol Length (E) and Number of Encoding
Symbols per Group (G) Symbols per Group (G)
The E parameter usually depends on the maximum transmission unit on The E parameter usually depends on the maximum transmission unit on
the path (PMTU) from the source to the receivers. In order to the path (PMTU) from the source to each receiver. In order to
minimize the protocol header overhead (e.g. the LCT/UDP/IPv4 or IPv6 minimize the protocol header overhead (e.g., the LCT/UDP/IPv4 or IPv6
headers in case of ALC), E is chosen as large as possible. In that headers in case of ALC), E is chosen as large as possible. In that
case, E is chosen so that the size of a packet composed of a single case, E is chosen so that the size of a packet composed of a single
symbol (G=1) remains below but close to the PMTU. symbol (G=1) remains below but close to the PMTU.
However other considerations can exist. For instance, the E However other considerations can exist. For instance, the E
parameter can be made a function of the object transfer length. parameter can be made a function of the object transfer length.
Indeed, LDPC codes are known to offer better protection for large Indeed, LDPC codes are known to offer better protection for large
blocks. In case of small objects, it can be advantageous to reduce blocks. In case of small objects, it can be advantageous to reduce
the encoding symbol length (E) in order to artificially increase the the encoding symbol length (E) in order to artificially increase the
number of symbols, and therefore the block size. number of symbols, and therefore the block size.
In order to minimize the protocol header overhead, several symbols In order to minimize the protocol header overhead, several symbols
can be grouped in the same Encoding Symbol Group (i.e. G > 1). can be grouped in the same Encoding Symbol Group (i.e., G > 1).
Depending on how many symbols are grouped (G) and on the packet loss Depending on how many symbols are grouped (G) and on the packet loss
rate (G symbols are lost for each packet erasure), this strategy rate (G symbols are lost for each packet erasure), this strategy
might or might not be appropriate. A balance must therefore be might or might not be appropriate. A balance must therefore be
found. found.
The current specification does not mandate any value for either E or The current specification does not mandate any value for either E or
G. The current specification only provides an example of possible G. The current specification only provides an example of possible
choices for E and G. Note that this choice is done by the sender. choices for E and G. Note that this choice is done by the sender, and
Then the E and G parameters are communicated to the receivers thanks the E and G parameters are then communicated to the receiver thanks
to the FEC OTI. to the FEC OTI. Note also that the decoding algorithm used
influences the choice of the E and G parameters. Indeed, increasing
the number of symbols will negatively impact the processing load when
decoding is based (in part or totally) on Gaussian elimination,
whereas the impacts will be rather low when decoding is based on the
trivial algorithm sketched in Section 6.4.
Example: Example:
First define the target packet payload size, pkt_sz (at most equal to Let us assume that the trivial decoding algorithm sketched in
the PMTU minus the size of the various protocol headers). The pkt_sz Section 6.4 is used. First define the target packet payload size,
must be chosen in such a way that the symbol size is an integer. pkt_sz (at most equal to the PMTU minus the size of the various
This can require that pkt_sz be a multiple of 4, 8 or 16 (see the protocol headers). The pkt_sz must be chosen in such a way that the
table below). Then calculate the number of packets in the object: symbol size is an integer. This can require that pkt_sz be a
nb_pkts = ceil(L / pkt_sz). Finally, thanks to nb_pkts, use the multiple of 4, 8 or 16 (see the table below). Then calculate the
following table to find a possible G value. number of packets in the object: nb_pkts = ceil(L / pkt_sz).
Finally, thanks to nb_pkts, use the following table to find a
possible G value.
+------------------------+----+-------------+-------------------+ +------------------------+----+-------------+-------------------+
| Number of packets | G | Symbol size | k | | Number of packets | G | Symbol size | k |
+------------------------+----+-------------+-------------------+ +------------------------+----+-------------+-------------------+
| 4000 <= nb_pkts | 1 | pkt_sz | 4000 <= k | | 4000 <= nb_pkts | 1 | pkt_sz | 4000 <= k |
| | | | | | | | | |
| 1000 <= nb_pkts < 4000 | 4 | pkt_sz / 4 | 4000 <= k < 16000 | | 1000 <= nb_pkts < 4000 | 4 | pkt_sz / 4 | 4000 <= k < 16000 |
| | | | | | | | | |
| 500 <= nb_pkts < 1000 | 8 | pkt_sz / 8 | 4000 <= k < 8000 | | 500 <= nb_pkts < 1000 | 8 | pkt_sz / 8 | 4000 <= k < 8000 |
| | | | | | | | | |
| 1 <= nb_pkts < 500 | 16 | pkt_sz / 16 | 16 <= k < 8000 | | 1 <= nb_pkts < 500 | 16 | pkt_sz / 16 | 16 <= k < 8000 |
+------------------------+----+-------------+-------------------+ +------------------------+----+-------------+-------------------+
5.4. Determining the Number of Encoding Symbols of a Block 5.4. Determining the Maximum Number of Encoding Symbols Generated for
Any Source Block (max_n)
The following algorithm, also called "n-algorithm", explains how to
determine the actual number of encoding symbols for a given block.
AT A SENDER: The following algorithm MAY be used by a sender to determine the
maximum number of encoding symbols generated for any source block
(max_n) as a function of B and the target code rate. Since the max_n
parameter is communicated to the decoder by means of the FEC OTI,
another method MAY be used to determine max_n.
Input: Input:
B: Maximum source block length, for any source block. Section 5.2 B: Maximum source block length, for any source block. Section 5.2
explains how to determine its value. MAY be used to determine its value.
k: Current source block length. This parameter is given by the
source blocking algorithm.
rate: FEC code rate. It is provided by the user, for instance CR: FEC code rate, which is provided by the user (e.g., when
when starting a FLUTE sending application. It is expressed as a starting a FLUTE sending application). It is expressed as a
floating point value. The rate value must be such that the floating point value. The CR value must be such that the
resulting number of encoding symbols per block is at most equal to resulting number of encoding symbols per block is at most equal to
2^^20 (Section 4.1). 2^^20 (Section 4.1).
Output: Output:
max_n: Maximum number of encoding symbols generated for any source max_n: Maximum number of encoding symbols generated for any source
block block.
n: Number of encoding symbols generated for this source block
Algorithm: Algorithm:
max_n = floor(B / rate); max_n = ceil(B / CR);
if (max_n > 2^^20) then return an error ("invalid code rate"); if (max_n > 2^^20) then return an error ("invalid code rate");
(NB: if B has been defined as explained in Section 5.2, this error (NB: if B has been defined as explained in Section 5.2, this error
should never happen) should never happen)
n = floor(k * max_n / B); 5.5. Determining the Number of Encoding Symbols of a Block (n)
AT A RECEIVER: The following algorithm, also called "n-algorithm", MUST be used by
the sender and the receiver to determine the number of encoding
symbols for a given block (n) as a function of B, k, and max_n.
Input: Input:
B: Extracted from the received FEC OTI B: Maximum source block length, for any source block. At a
sender, Section 5.2 MAY be used to determine its value. At a
receiver, this value MUST be extracted from the received FEC OTI.
max_n: Extracted from the received FEC OTI k: Current source block length. At a sender or receiver, the
k: Given by the source blocking algorithm block partitioning algorithm MUST be used to determine its value.
max_n: Maximum number of encoding symbols generated for any source
block. At a sender, Section 5.4 MAY be used to determine its
value. At a receiver, this value MUST be extracted from the
received FEC OTI.
Output: Output:
n: Number of encoding symbols generated for this source block n: Number of encoding symbols generated for this source block.
Algorithm: Algorithm:
n = floor(k * max_n / B); n = floor(k * max_n / B);
5.5. Identifying the Symbols of an Encoding Symbol Group 5.6. Identifying the G Symbols of an Encoding Symbol Group
When multiple encoding symbols are sent in the same packet, the FEC When multiple encoding symbols are sent in the same packet, the FEC
Payload ID information of the packet MUST refer to the first encoding Payload ID information of the packet MUST refer to the first encoding
symbol. It MUST then be possible to identify each symbol from this symbol. It MUST then be possible to identify each symbol from this
single FEC Payload ID. To that purpose, the symbols of an Encoding single FEC Payload ID. To that purpose, the symbols of an Encoding
Symbol Group (i.e. packet): Symbol Group (i.e. packet):
o MUST all be either source symbols, or repair symbols. Therefore o MUST all be either source symbols, or repair symbols. Therefore
only source packets and repair packets are permitted, not mixed only source packets and repair packets are permitted, not mixed
ones. ones.
o are identified by a function, sender(resp. o are identified by a function, sender(resp.
receiver)_find_ESIs_of_group(), that takes as argument: receiver)_find_ESIs_of_group(), that takes as argument:
* for a sender, the index of the Encoding Symbol Group (i.e. * for a sender, the index of the Encoding Symbol Group (i.e.,
packet) that the application wants to create, packet) that the application wants to create,
* for a receiver, the ESI information contained in the FEC * for a receiver, the ESI information contained in the FEC
Payload ID. Payload ID.
and returns a list of G Encoding Symbol IDs. In case of a source and returns a list of G Encoding Symbol IDs. In case of a source
packet, the G Encoding Symbol IDs are chosen consecutively, by packet, the G Encoding Symbol IDs are chosen consecutively, by
incrementing the ESI. In case of a repair packet, the G repair incrementing the ESI. In case of a repair packet, the G repair
symbols are chosen randomly, as explained below. symbols are chosen randomly, as explained below.
skipping to change at page 17, line 22 skipping to change at page 18, line 22
void void
initialize_tables () initialize_tables ()
{ {
int i; int i;
int randInd; int randInd;
int backup; int backup;
txseqToID = malloc((n-k) * sizeof(int)); txseqToID = malloc((n-k) * sizeof(int));
IDtoTxseq = malloc((n-k) * sizeof(int)); IDtoTxseq = malloc((n-k) * sizeof(int));
/* initialize the two tables that map ID /* initialize the two tables that map ID
* (i.e. ESI-k) to/from TxSequence. */ * (i.e., ESI-k) to/from TxSequence. */
for (i = 0; i < n - k; i++) { for (i = 0; i < n - k; i++) {
IDtoTxseq[i] = i; IDtoTxseq[i] = i;
txseqToID[i] = i; txseqToID[i] = i;
} }
/* now randomize everything */ /* now randomize everything */
for (i = 0; i < n - k; i++) { for (i = 0; i < n - k; i++) {
randInd = rand(n - k); randInd = rand(n - k);
backup = IDtoTxseq[i]; backup = IDtoTxseq[i];
IDtoTxseq[i] = IDtoTxseq[randInd]; IDtoTxseq[i] = IDtoTxseq[randInd];
IDtoTxseq[randInd] = backup; IDtoTxseq[randInd] = backup;
skipping to change at page 18, line 37 skipping to change at page 19, line 37
for (i = 0; i < G; i++) { for (i = 0; i < G; i++) {
ESIs[i] = ESIs[i] =
k + k +
txseqToID[(i + (PktIdx - nbSourcePkts) * G) txseqToID[(i + (PktIdx - nbSourcePkts) * G)
% (n - k)]; % (n - k)];
} }
} }
return; return;
} }
Similarly, upon receiving an Encoding Symbol Group (i.e. packet), a Similarly, upon receiving an Encoding Symbol Group (i.e., packet), a
receiver can determine the sequence of G Encoding Symbol IDs from the receiver can determine the sequence of G Encoding Symbol IDs from the
first ESI, esi0, that is contained in the FEC Payload ID. first ESI, esi0, that is contained in the FEC Payload ID.
/* /*
* Determine the sequence of ESIs for the packet received. * Determine the sequence of ESIs for the packet received.
* Warning: use only when G > 1. * Warning: use only when G > 1.
* esi0 (IN): : ESI contained in the FEC Payload ID * esi0 (IN): : ESI contained in the FEC Payload ID
* ESIs[] (OUT): list of ESIs for the packet * ESIs[] (OUT): list of ESIs for the packet
*/ */
void void
skipping to change at page 19, line 34 skipping to change at page 20, line 34
/* this is a repair packet */ /* this is a repair packet */
for (i = 0; i < G; i++) { for (i = 0; i < G; i++) {
ESIs[i] = ESIs[i] =
k + k +
txseqToID[(i + IDtoTxseq[esi0 - k]) txseqToID[(i + IDtoTxseq[esi0 - k])
% (n - k)]; % (n - k)];
} }
} }
} }
5.6. Pseudo Random Number Generator 5.7. Pseudo Random Number Generator
The present FEC Encoding ID relies on a pseudo-random number The FEC Encoding IDs 3 and 4 rely on a pseudo-random number generator
generator (PRNG) that must be fully specified, in particular in order (PRNG) that must be fully specified, in particular in order to enable
to enable the receivers and the senders to build the same parity the receivers and the senders to build the same parity check matrix.
check matrix. The minimal standard generator [10] is used. It
defines a simple multiplicative congruential algorithm: Ij+1 = A * Ij
(modulo M), with the following choices: A = 7^^5 = 16807 and M =
2^^31 - 1 = 2147483647. Several implementations of this PRNG are
known and discussed in the literature. All of them provide the same
sequence of pseudo random numbers. A validation criteria of such a
PRNG is the following: if seed = 1, then the 10,000th value returned
MUST be equal to 1043618065.
The following implementation uses the Park and Miller algorithm with The minimal standard generator [PM88] MUST be used. It defines a
the optimization suggested by D. Carta in [11]. simple multiplicative congruential algorithm: Ij+1 = A * Ij (modulo
M), with the following choices: A = 7^^5 = 16807 and M = 2^^31 - 1 =
2147483647. Several implementations of this PRNG are known and
discussed in the literature. All of them provide the same sequence
of pseudo random numbers. A validation criteria of such a PRNG is
the following: if seed = 1, then the 10,000th value returned MUST be
equal to 1043618065.
unsigned long seed; An optimized implementation of this algorithm, using only 32 bit
mathematics which does not require any division, is provided, as an
example, in Appendix A. Yet any other implementation of the PRNG
algorithm that matches the above validation criteria is appropriate.
/* This PRNG produces a 31 bit value between 1 and 0x7FFFFFFE (2^^31-2)
* Initialize the PRNG with a seed between inclusive. When it is desired to scale the pseudo random number
* 1 and 0x7FFFFFFE (i.e. 2^^31-2) inclusive. between 0 and maxv-1 inclusive, one must keep the most significant
*/ bits of the value returned by the PRNG (the least significant bits
void srand (unsigned long s) are known to be less random and modulo based solutions should be
{ avoided [PTVF92]). The following algorithm MUST be used:
if ((s > 0) && (s < 0x7FFFFFFF))
seed = s;
else
exit(-1);
}
/* Input:
* Returns a random integer in [0; maxv-1]
* Derived from rand31pmc, Robin Whittle,
* September 20th, 2005.
* http://www.firstpr.com.au/dsp/rand31/
* 16807 multiplier constant (7^^5)
* 0x7FFFFFFF modulo constant (2^^31-1)
* The inner PRNG produces a value between 1 and
* 0x7FFFFFFE (2^^31-2) inclusive.
* This value is then scaled between 0 and maxv-1
* inclusive.
*/
unsigned long
rand (unsigned long maxv)
{
unsigned long hi, lo;
lo = 16807 * (seed & 0xFFFF); raw_value: random integer generated by the inner PRNG algorithm,
hi = 16807 * (seed >> 16); /* binary shift to right */ between 1 and 0x7FFFFFFE (2^^31-2) inclusive.
lo += (hi & 0x7FFF) < < 16; /* binary shift to left */
lo += hi >> 15; maxv: upper bound used during the scaling operation.
if (lo > 0x7FFFFFFF)
lo -= 0x7FFFFFFF; Output:
seed = (long)lo;
/* don't use modulo, least significant bits are less random scaled_value: random integer between 0 and maxv-1 inclusive.
* than most significant bits [Numerical Recipes in C] */
return ((unsigned long) Algorithm:
((double)seed * (double)maxv / (double)0x7FFFFFFF));
} scaled_value = (unsigned long) ((double)maxv * (double)raw_value /
(double)0x7FFFFFFF);
(NB: the above C type casting to unsigned long is equivalent to
using floor() with positive floating point values)
6. Full Specification of the LDPC-Staircase Scheme 6. Full Specification of the LDPC-Staircase Scheme
6.1. General 6.1. General
The LDPC-Staircase scheme is identified by the Fully-Specified FEC The LDPC-Staircase scheme is identified by the Fully-Specified FEC
Encoding ID 3. Encoding ID 3.
The PRNG used by the LDPC-Staircase scheme must be initialized by a The PRNG used by the LDPC-Staircase scheme must be initialized by a
seed. This PRNG seed is an optional instance-specific FEC OTI seed. This PRNG seed is an instance-specific FEC OTI attribute
attribute (Section 4.2.3). When this PRNG seed is not carried within (Section 4.2.3).
the FEC OTI, it is assumed that encoder and decoders either use
another way to communicate the seed value or use a fixed, predefined
value.
6.2. Parity Check Matrix Creation 6.2. Parity Check Matrix Creation
The LDPC-Staircase matrix can be divided into two parts: the left The LDPC-Staircase matrix can be divided into two parts: the left
side of the matrix defines in which equations the source symbols are side of the matrix defines in which equations the source symbols are
involved; the right side of the matrix defines in which equations the involved; the right side of the matrix defines in which equations the
repair symbols are involved. repair symbols are involved.
The left side is generated with the following algorithm: The left side is generated with the following algorithm:
/*
* Derived from: "Software for Low Density Parity Check Codes"
* Version of 2001-11-18, Radford M. Neal, Univ. of Toronto.
* Copyright (c) 1995, 1996, 2000, 2001 by Radford M. Neal
* http://www.cs.toronto.edu/~radford/ldpc.software.html
*/
/* initialize a list of all possible choices in order to /* initialize a list of all possible choices in order to
* guarantee a homogeneous "1" distribution */ * guarantee a homogeneous "1" distribution */
for (h = 3*k-1; h >= 0; h--) { for (h = 3*k-1; h >= 0; h--) {
u[h] = h % (n-k); u[h] = h % (n-k);
} }
/* left limit within the list of possible choices, u[] */ /* left limit within the list of possible choices, u[] */
t = 0; t = 0;
for (j = 0; j < k; j++) { /* for each source symbol column */ for (j = 0; j < k; j++) { /* for each source symbol column */
for (h = 0; h < 3; h++) { /* add 3 "1s" */ for (h = 0; h < 3; h++) { /* add 3 "1s" */
skipping to change at page 22, line 24 skipping to change at page 23, line 44
matrix_insert_entry(i, j); matrix_insert_entry(i, j);
} }
} }
} }
/* Add extra bits to avoid rows with less than two "1s". /* Add extra bits to avoid rows with less than two "1s".
* This is needed when the code rate is smaller than 2/5. */ * This is needed when the code rate is smaller than 2/5. */
for (i = 0; i < n-k; i++) { /* for each row */ for (i = 0; i < n-k; i++) { /* for each row */
if (degree_of_row(i) == 0) { if (degree_of_row(i) == 0) {
j = rand(k); j = rand(k);
e = matrix_insert_entry(i, j); matrix_insert_entry(i, j);
} }
if (degree_of_row(i) == 1) { if (degree_of_row(i) == 1) {
do { do {
j = rand(k); j = rand(k);
} while (matrix_has_entry(i, j)); } while (matrix_has_entry(i, j));
matrix_insert_entry(i, j); matrix_insert_entry(i, j);
} }
} }
The right side (the staircase) is generated by the following The right side (the staircase) is generated by the following
algorithm: algorithm:
matrix_insert_entry(0, k); /* first row */ matrix_insert_entry(0, k); /* first row */
for (i = 1; i < n-k; i++) { /* for the following rows */ for (i = 1; i < n-k; i++) { /* for the following rows */
matrix_insert_entry(i, k+i); /* identity */ matrix_insert_entry(i, k+i); /* identity */
matrix_insert_entry(i, k+i-1); /* staircase */ matrix_insert_entry(i, k+i-1); /* staircase */
} }
Note that just after creating this parity check matrix, when encoding Note that just after creating this parity check matrix, when encoding
skipping to change at page 22, line 44 skipping to change at page 24, line 14
The right side (the staircase) is generated by the following The right side (the staircase) is generated by the following
algorithm: algorithm:
matrix_insert_entry(0, k); /* first row */ matrix_insert_entry(0, k); /* first row */
for (i = 1; i < n-k; i++) { /* for the following rows */ for (i = 1; i < n-k; i++) { /* for the following rows */
matrix_insert_entry(i, k+i); /* identity */ matrix_insert_entry(i, k+i); /* identity */
matrix_insert_entry(i, k+i-1); /* staircase */ matrix_insert_entry(i, k+i-1); /* staircase */
} }
Note that just after creating this parity check matrix, when encoding Note that just after creating this parity check matrix, when encoding
symbol groups are used (i.e. G > 1), the function initializing the symbol groups are used (i.e., G > 1), the function initializing the
two random permutation tables (Section 5.5) MUST be called. This is two random permutation tables (Section 5.6) MUST be called. This is
true both at a sender and at a receiver. true both at a sender and at a receiver.
6.3. Encoding 6.3. Encoding
Thanks to the staircase matrix, repair symbol creation is Thanks to the staircase matrix, repair symbol creation is
straightforward: each repair symbol is equal to the sum of all source straightforward: each repair symbol is equal to the sum of all source
symbols in the associated equation, plus the previous repair symbol symbols in the associated equation, plus the previous repair symbol
(except for the first repair symbol). Therefore encoding MUST follow (except for the first repair symbol). Therefore encoding MUST follow
the natural repair symbol order: start with the first repair symbol, the natural repair symbol order: start with the first repair symbol,
and generate repair symbol with ESI i before symbol ESI i+1. and generate repair symbol with ESI i before symbol with ESI i+1.
6.4. Decoding 6.4. Decoding
Decoding basically consists in solving a system of n-k linear Decoding basically consists in solving a system of n-k linear
equations whose variables are the n source and repair symbols. Of equations whose variables are the n source and repair symbols. Of
course, the final goal is to recover the value of the k source course, the final goal is to recover the value of the k source
symbols only. symbols only.
To that purpose, many techniques are possible. One of them is the To that purpose, many techniques are possible. One of them is the
following trivial algorithm [12]: given a set of linear equations, if following trivial algorithm [ZP74]: given a set of linear equations,
one of them has only one remaining unknown variable, then the value if one of them has only one remaining unknown variable, then the
of this variable is that of the constant term. So, replace this value of this variable is that of the constant term. So, replace
variable by its value in all the remaining linear equations and this variable by its value in all the remaining linear equations and
reiterate. The value of several variables can therefore be found reiterate. The value of several variables can therefore be found
recursively. Applied to LDPC FEC codes working over an erasure recursively. Applied to LDPC FEC codes working over an erasure
channel, the parity check matrix defines a set of linear equations channel, the parity check matrix defines a set of linear equations
whose variables are the source symbols and repair symbols. Receiving whose variables are the source symbols and repair symbols. Receiving
or decoding a symbol is equivalent to having the value of a variable. or decoding a symbol is equivalent to having the value of a variable.
Appendix A sketches a possible implementation of this algorithm. Appendix B sketches a possible implementation of this algorithm.
A Gaussian elimination (or any optimized derivative) is another A Gaussian elimination (or any optimized derivative) is another
possible decoding technique. Hybrid solutions that start by using possible decoding technique. Hybrid solutions that start by using
the trivial algorithm above and finish with a Gaussian elimination the trivial algorithm above and finish with a Gaussian elimination
are also possible. are also possible.
Because interoperability does not depend on the decoding algorithm Because interoperability does not depend on the decoding algorithm
used, the current document does not recommend any particular used, the current document does not recommend any particular
technique. This choice is left to the codec developer. technique. This choice is left to the codec developer.
skipping to change at page 24, line 12 skipping to change at page 26, line 12
the above trivial algorithm. Depending on the target use case, the the above trivial algorithm. Depending on the target use case, the
codec developer will favor one feature or the other. codec developer will favor one feature or the other.
7. Full Specification of the LDPC-Triangle Scheme 7. Full Specification of the LDPC-Triangle Scheme
7.1. General 7.1. General
LDPC-Triangle is identified by the Fully-Specified FEC Encoding ID 4. LDPC-Triangle is identified by the Fully-Specified FEC Encoding ID 4.
The PRNG used by the LDPC-Triangle scheme must be initialized by a The PRNG used by the LDPC-Triangle scheme must be initialized by a
seed. This PRNG seed is an optional instance-specific FEC OTI seed. This PRNG seed is an instance-specific FEC OTI attribute
attribute (Section 4.2.3). When this PRNG seed is not carried within (Section 4.2.3).
the FEC OTI, it is assumed that encoder and decoders either use
another way to communicate the seed value or use a fixed, predefined
value.
7.2. Parity Check Matrix Creation 7.2. Parity Check Matrix Creation
The LDPC-Triangle matrix can be divided into two parts: the left side The LDPC-Triangle matrix can be divided into two parts: the left side
of the matrix defines in which equations the source symbols are of the matrix defines in which equations the source symbols are
involved; the right side of the matrix defines in which equations the involved; the right side of the matrix defines in which equations the
repair symbols are involved. repair symbols are involved.
The left side is generated with the same algorithm as that of LDPC- The left side is generated with the same algorithm as that of LDPC-
Staircase (Section 6.2). Staircase (Section 6.2).
skipping to change at page 24, line 44 skipping to change at page 26, line 41
matrix_insert_entry(i, k+i-1); /* staircase */ matrix_insert_entry(i, k+i-1); /* staircase */
/* now fill the triangle */ /* now fill the triangle */
j = i-1; j = i-1;
for (l = 0; l < j; l++) { /* limit the # of "1s" added */ for (l = 0; l < j; l++) { /* limit the # of "1s" added */
j = rand(j); j = rand(j);
matrix_insert_entry(i, k+j); matrix_insert_entry(i, k+j);
} }
} }
Note that just after creating this parity check matrix, when encoding Note that just after creating this parity check matrix, when encoding
symbol groups are used (i.e. G > 1), the function initializing the symbol groups are used (i.e., G > 1), the function initializing the
two random permutation tables (Section 5.5) MUST be called. This is two random permutation tables (Section 5.6) MUST be called. This is
true both at a sender and at a receiver. true both at a sender and at a receiver.
7.3. Encoding 7.3. Encoding
Here also repair symbol creation is straightforward: each repair Here also repair symbol creation is straightforward: each repair
symbol is equal to the sum of all source symbols in the associated symbol of ESI i is equal to the sum of all source and repair symbols
equation, plus the repair symbols in the triangle. Therefore (with ESI lower than i) in the associated equation. Therefore
encoding MUST follow the natural repair symbol order: start with the encoding MUST follow the natural repair symbol order: start with the
first repair symbol, and generate repair symbol with ESI i before first repair symbol, and generate repair symbol with ESI i before
symbol ESI i+1. symbol with ESI i+1.
7.4. Decoding 7.4. Decoding
Decoding basically consists in solving a system of n-k linear Decoding basically consists in solving a system of n-k linear
equations, whose variables are the n source and repair symbols. Of equations, whose variables are the n source and repair symbols. Of
course, the final goal is to recover the value of the k source course, the final goal is to recover the value of the k source
symbols only. To that purpose, many techniques are possible, as symbols only. To that purpose, many techniques are possible, as
explained in Section 6.4. explained in Section 6.4.
Because interoperability does not depend on the decoding algorithm Because interoperability does not depend on the decoding algorithm
used, the current document does not recommend any particular used, the current document does not recommend any particular
technique. This choice is left to the codec implementer. technique. This choice is left to the codec implementer.
8. Security Considerations 8. Security Considerations
Data delivery can be subject to denial-of-service attacks by 8.1. Problem Statement
attackers which send corrupted packets that are accepted as
legitimate by receivers. This is particularly a concern for
multicast delivery because a corrupted packet may be injected into
the session close to the root of the multicast tree, in which case
the corrupted packet will arrive at many receivers. This is
particularly a concern for the FEC building block because the use of
even one corrupted packet containing encoding data may result in the
decoding of an object that is completely corrupted and unusable. It
is thus RECOMMENDED that source authentication and integrity checking
are applied to decoded objects before delivering objects to an
application. For example, a SHA-1 hash [4] of an object may be
appended before transmission, and the SHA-1 hash is computed and
checked after the object is decoded but before it is delivered to an
application. Source authentication SHOULD be provided, for example
by including a digital signature verifiable by the receiver computed
on top of the hash value. It is also RECOMMENDED that a packet
authentication protocol such as TESLA [5] be used to detect and
discard corrupted packets upon arrival. Furthermore, it is
RECOMMENDED that Reverse Path Forwarding checks be enabled in all
network routers and switches along the path from the sender to
receivers to limit the possibility of a bad agent successfully
injecting a corrupted packet into the multicast tree data path.
Another security concern is that some FEC information may be obtained A content delivery system is potentially subject to many attacks:
by receivers out-of-band in a session description, and if the session some of them target the network (e.g., to compromise the routing
description is forged or corrupted then the receivers will not use infrastructure, by compromising the congestion control component),
the correct protocol for decoding content from received packets. To others target the Content Delivery Protocol (CDP) (e.g., to
avoid these problems, it is RECOMMENDED that measures be taken to compromise its normal behavior), and finally some attacks target the
prevent receivers from accepting incorrect session descriptions, content itself. Since this document focuses on a FEC building block
e.g., by using source authentication to ensure that receivers only independently of any particular CDP (even if ALC and NORM are two
accept legitimate session descriptions from authorized senders. natural candidates), this section only discusses the additional
threats that an arbitrary CDP may be exposed to when using this
building block.
More specifically, several kinds of attacks exist:
o those that are meant to give access to a confidential content
(e.g., in case of a non-free content),
o those that try to corrupt the object being transmitted (e.g., to
inject malicious code within an object, or to prevent a receiver
from using an object),
o and those that try to compromise the receiver's behavior (e.g., by
making the decoding of an object computationally expensive).
These attacks can be launched either against the data flow itself
(e.g., by sending forged symbols) or against the FEC parameters that
are sent either in-band (e.g., in an EXT_FTI or FDT Instance) or out-
of-band (e.g., in a session description).
8.2. Attacks Against the Data Flow
First of all, let us consider the attacks against the data flow.
8.2.1. Access to Confidential Objects
Access control to the object being transmitted is typically provided
by means of encryption. This encryption can be done over the whole
object (e.g., by the content provider, before the FEC encoding
process), or be done on a packet per packet basis (e.g., when IPSec/
ESP is used [RFC4303]). If access control is a concern, it is
RECOMMENDED that one of these solutions be used. Even if we mention
these attacks here, they are not related nor facilitated by the use
of FEC.
8.2.2. Content Corruption
Protection against corruptions (e.g., after sending forged packets)
is achieved by means of a content integrity verification/sender
authentication scheme. This service can be provided at the object
level, but in that case a receiver has no way to identify which
symbol(s) is(are) corrupted if the object is detected as corrupted.
This service can also be provided at the packet level. In this case,
after removing all forged packets, the object may be in some case
recovered. Several techniques can provide this source
authentication/content integrity service:
o at the object level, the object MAY be digitally signed (with
public key cryptography), for instance by using RSASSA-PKCS1-v1_5
[RFC3447]. This signature enables a receiver to check the object
integrity, once this latter has been fully decoded. Even if
digital signatures are computationally expensive, this calculation
occurs only once per object, which is usually acceptable;
o at the packet level, each packet can be digitally signed. A major
limitation is the high computational and transmission overheads
that this solution requires (unless Elliptic Curve Cryptography
(ECC) is used). To avoid this problem, the signature may span a
set of symbols (instead of a single one) in order to amortize the
signature calculation. But if a single symbol is missing, the
integrity of the whole set cannot be checked;
o at the packet level, a Group Message Authentication Code (MAC)
[RFC2104] scheme can be used, for instance by using HMAC-SHA-1
with a secret key shared by all the group members, senders and
receivers. This technique creates a cryptographically secured
(thanks to the secret key) digest of a packet that is sent along
with the packet. The Group MAC scheme does not create prohibitive
processing load nor transmission overhead, but it has a major
limitation: it only provides a group authentication/integrity
service since all group members share the same secret group key,
which means that each member can send a forged packet. It is
therefore restricted to situations where group members are fully
trusted (or in association with another technique as a pre-check);
o at the packet level, TESLA [RFC4082] is a very attractive and
efficient solution that is robust to losses, provides a true
authentication/integrity service, and does not create any
prohibitive processing load or transmission overhead. Yet
checking a packet requires a small delay (a second or more) after
its reception;
Techniques relying on public key cryptography (digital signatures and
TESLA during the bootstrap process, when used) require that public
keys be securely associated to the entities. This can be achieved by
a Public Key Infrastructure (PKI), or by a PGP Web of Trust, or by
pre-distributing the public keys of each group member.
Techniques relying on symmetric key cryptography (group MAC) require
that a secret key be shared by all group members. This can be
achieved by means of a group key management protocol, or simply by
pre-distributing the secret key (but this manual solution has many
limitations).
It is up to the developer and deployer, who know the security
requirements and features of the target application area, to define
which solution is the most appropriate. Nonetheless, in case there
is any concern of the threat of object corruption, it is RECOMMENDED
that at least one of these techniques be used.
8.3. Attacks Against the FEC Parameters
Let us now consider attacks against the FEC parameters (or FEC OTI).
The FEC OTI can either be sent in-band (i.e., in an EXT_FTI or in an
FDT Instance containing FEC OTI for the object) or out-of-band (e.g.,
in a session description). Attacks on these FEC parameters can
prevent the decoding of the associated object: for instance modifying
the B parameter will lead to a different block partitioning.
It is therefore RECOMMENDED that security measures be taken to
guarantee the FEC OTI integrity. To that purpose, the packets
carrying the FEC parameters sent in-band in an EXT_FTI header
extension SHOULD be protected by one of the per-packet techniques
described above: digital signature, group MAC, or TESLA. When FEC
OTI is contained in an FDT Instance, this object SHOULD be protected,
for instance by digitally signing it with XML digital signatures
[RFC3275]. Finally, when FEC OTI is sent out-of-band (e.g., in a
session description) this latter SHOULD be protected, for instance by
digitally signing it.
The same considerations concerning the key management aspects apply
here also.
9. IANA Considerations 9. IANA Considerations
Values of FEC Encoding IDs and FEC Instance IDs are subject to IANA Values of FEC Encoding IDs and FEC Instance IDs are subject to IANA
registration. For general guidelines on IANA considerations as they registration. For general guidelines on IANA considerations as they
apply to this document, see [2]. apply to this document, see [RFC5052].
This document assigns the Fully-Specified FEC Encoding ID 3 under the This document assigns the Fully-Specified FEC Encoding ID 3 under the
"ietf:rmt:fec:encoding" name-space to "LDPC Staircase Codes". "ietf:rmt:fec:encoding" name-space to "LDPC Staircase Codes".
This document assigns the Fully-Specified FEC Encoding ID 4 under the This document assigns the Fully-Specified FEC Encoding ID 4 under the
"ietf:rmt:fec:encoding" name-space to "LDPC Triangle Codes". "ietf:rmt:fec:encoding" name-space to "LDPC Triangle Codes".
10. Acknowledgments 10. Acknowledgments
Section 5.4 is derived from a previous Internet-Draft, and we would Section 5.5 is derived from a previous Internet-Draft, and we would
like to thank S. Peltotalo and J. Peltotalo for their contribution. like to thank S. Peltotalo and J. Peltotalo for their contribution.
We would also like to thank Pascal Moniot, Laurent Fazio, Aurelien We would also like to thank Pascal Moniot, Laurent Fazio, Aurelien
Francillon and Shao Wenjian for their comments. Francillon, Shao Wenjian, Brian Carpenter, Magnus Westerlund, and
Alfred Hoenes for their comments.
Last but not least, the authors are grateful to Radford M. Neal
(University of Toronto) whose LDPC software
(http://www.cs.toronto.edu/~radford/ldpc.software.html) inspired this
work.
11. References 11. References
11.1. Normative References 11.1. Normative References
[1] Bradner, S., "Key words for use in RFCs to Indicate Requirement [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Levels", RFC 2119, BCP 14, March 1997. Requirement Levels", RFC 2119, BCP 14, March 1997.
[2] Watson, M., Luby, M., and L. Vicisano, "Forward Error
Correction (FEC) Building Block",
draft-ietf-rmt-fec-bb-revised-07.txt (work in progress),
April 2007.
[3] Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley, M.,
and J. Crowcroft, "The Use of Forward Error Correction (FEC) in
Reliable Multicast", RFC 3453, December 2002.
[4] "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, [RFC5052] Watson, M., Luby, M., and L. Vicisano, "Forward Error
February 1997. Correction (FEC) Building Block", RFC 5052, August 2007.
[5] "Timed Efficient Stream Loss-Tolerant Authentication (TESLA): [RFC3453] Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley,
Multicast Source Authentication Transform Introduction", M., and J. Crowcroft, "The Use of Forward Error Correction
RFC 4082, June 2005. (FEC) in Reliable Multicast", RFC 3453, December 2002.
11.2. Informative References 11.2. Informative References
[6] Roca, V. and C. Neumann, "Design, Evaluation and Comparison of [ZP74] Zyablov, V. and M. Pinsker, "Decoding Complexity of Low-
Four Large Block FEC Codecs: LDPC, LDGM, LDGM-Staircase and Density Codes for Transmission in a Channel with
LDGM-Triangle, Plus a Reed-Solomon Small Block FEC Codec", Erasures", Translated from Problemy Peredachi
INRIA Research Report RR-5225, June 2004. Informatsii, Vol.10, No. 1, pp.15-28, January-March 1974.
[7] Neumann, C., Roca, V., Francillon, A., and D. Furodet, "Impacts [RN04] Roca, V. and C. Neumann, "Design, Evaluation and
of Packet Scheduling and Packet Loss Distribution on FEC Comparison of Four Large Block FEC Codecs: LDPC, LDGM,
Performances: Observations and Recommendations", ACM CoNEXT'05 LDGM-Staircase and LDGM-Triangle, Plus a Reed-Solomon
Conference, Toulouse, France (an extended version is available Small Block FEC Codec", INRIA Research Report RR-5225,
as INRIA Research Report RR-5578), October 2005. June 2004.
[8] Roca, V., Neumann, C., and J. Laboure, "LDPC-Staircase/ [NRFF05] Neumann, C., Roca, V., Francillon, A., and D. Furodet,
LDPC-Triangle Codec Reference Implementation", INRIA Rhone- "Impacts of Packet Scheduling and Packet Loss Distribution
Alpes and STMicroelectronics, on FEC Performances: Observations and Recommendations",
ACM CoNEXT'05 Conference, Toulouse, France (an extended
version is available as INRIA Research Report RR-5578),
October 2005.
[LDPC-codec]
Roca, V., Neumann, C., Cunche, M., and J. Laboure, "LDPC-
Staircase/LDPC-Triangle Codec Reference Implementation",
INRIA Rhone-Alpes and STMicroelectronics,
http://planete-bcast.inrialpes.fr/. http://planete-bcast.inrialpes.fr/.
[9] MacKay, D., "Information Theory, Inference and Learning [MK03] MacKay, D., "Information Theory, Inference and Learning
Algorithms", Cambridge University Press, ISBN: 0521642981, Algorithms", Cambridge University Press, ISBN: 0-521-
2003. 64298-1, 2003.
[10] Park, S. and K. Miller, "Random Number Generators: Good Ones [PM88] Park, S. and K. Miller, "Random Number Generators: Good
are Hard to Find", Communications of the ACM, Vol. 31, No. 10, Ones are Hard to Find", Communications of the ACM, Vol.
pp.1192-1201, 1988. 31, No. 10, pp.1192-1201, 1988.
[11] Carta, D., "Two Fast Implementations of the Minimal Standard [CA90] Carta, D., "Two Fast Implementations of the Minimal
Random Number Generator", Communications of the ACM, Vol. 33, Standard Random Number Generator", Communications of the
No. 1, pp.87-88, January 1990. ACM, Vol. 33, No. 1, pp.87-88, January 1990.
[12] Zyablov, V. and M. Pinsker, "Decoding Complexity of Low-Density [PTVF92] Press, W., Teukolsky, S., Vetterling, W., and B. Flannery,
Codes for Transmission in a Channel with Erasures", Translated "Numerical Recipies in C; Second Edition", Cambridge
from Problemy Peredachi Informatsii, Vol.10, No. 1, pp.15-28, University Press, ISBN: 0-521-43108-5, 1992.
January-March 1974.
[13] Luby, M., Watson, M., and L. Vicisano, "Asynchronous Layered [draft-ietf-rmt-pi-alc-revised]
Coding (ALC) Protocol Instantiation", Luby, M., Watson, M., and L. Vicisano, "Asynchronous
Layered Coding (ALC) Protocol Instantiation",
draft-ietf-rmt-pi-alc-revised-04.txt (work in progress), draft-ietf-rmt-pi-alc-revised-04.txt (work in progress),
February 2007. February 2007.
[14] Paila, T., Walsh, R., Luby, M., Lehtonen, R., and V. Roca, [draft-ietf-rmt-pi-norm-revised]
Adamson, B., Bormann, C., Handley, M., and J. Macker,
"Negative-acknowledgment (NACK)-Oriented Reliable
Multicast (NORM) Protocol",
draft-ietf-rmt-pi-norm-revised-05.txt (work in progress),
March 2007.
[draft-ietf-rmt-flute-revised]
Paila, T., Walsh, R., Luby, M., Lehtonen, R., and V. Roca,
"FLUTE - File Delivery over Unidirectional Transport", "FLUTE - File Delivery over Unidirectional Transport",
draft-ietf-rmt-flute-revised-03.txt (work in progress), draft-ietf-rmt-flute-revised-05.txt (work in progress),
January 2007. October 2007.
[15] Adamson, B., Bormann, C., Handley, M., and J. Macker, [RFC3447] Jonsson, J. and B. Kaliski, "Public-Key Cryptography
"Negative-acknowledgment (NACK)-Oriented Reliable Multicast Standards (PKCS) #1: RSA Cryptography Specifications
(NORM) Protocol", draft-ietf-rmt-pi-norm-revised-04.txt (work Version 2.1", RFC 3447, February 2003.
in progress), March 2007.
Appendix A. Trivial Decoding Algorithm (Informative Only) [RFC4303] Kent, S., "IP Encapsulating Security Payload (ESP)",
RFC 4303, December 2005.
A trivial decoding algorithm is sketched below (please see [8] for [RFC2104] "HMAC: Keyed-Hashing for Message Authentication",
the details omitted here): RFC 2104, February 1997.
[RFC4082] "Timed Efficient Stream Loss-Tolerant Authentication
(TESLA): Multicast Source Authentication Transform
Introduction", RFC 4082, June 2005.
[RFC3275] Eastlake, D., Reagle, J., and D. Solo, "(Extensible Markup
Language) XML-Signature Syntax and Processing", RFC 3275,
March 2002.
Appendix A. Pseudo Random Number Generator Example Implementation
(Informative Only)
The following is an implementation of the minimal standard generator
defined in Section 5.7 that scales the result between 0 and maxv-1
inclusive. It uses the Park and Miller algorithm [PM88] with the
optimization suggested by D. Carta in [CA90]. The inner algorithm
relies on 32 bit mathematics only and does not require any division.
unsigned long seed;
/*
* Initialize the PRNG with a seed between
* 1 and 0x7FFFFFFE (i.e., 2^^31-2) inclusive.
*/
void srand (unsigned long s)
{
if ((s > 0) && (s < 0x7FFFFFFF))
seed = s;
else
exit(-1);
}
/*
* Returns a random integer in [0; maxv-1]
* Derived from rand31pmc, Robin Whittle,
* September 20th, 2005.
* http://www.firstpr.com.au/dsp/rand31/
* 16807 multiplier constant (7^^5)
* 0x7FFFFFFF modulo constant (2^^31-1)
* The inner PRNG produces a value between 1 and
* 0x7FFFFFFE (2^^31-2) inclusive.
* This value is then scaled between 0 and maxv-1
* inclusive.
*/
unsigned long
rand (unsigned long maxv)
{
unsigned long hi, lo;
lo = 16807 * (seed & 0xFFFF);
hi = 16807 * (seed >> 16); /* binary shift to right */
lo += (hi & 0x7FFF) << 16; /* binary shift to left */
lo += hi >> 15;
if (lo > 0x7FFFFFFF)
lo -= 0x7FFFFFFF;
seed = lo;
/* don't use modulo, least significant bits are less random
* than most significant bits [PTVF92] */
return ((unsigned long)
((double)maxv * (double)seed / (double)0x7FFFFFFF));
}
Appendix B. Trivial Decoding Algorithm (Informative Only)
A trivial decoding algorithm is sketched below (please see
[LDPC-codec] for the details omitted here):
Initialization: allocate a table partial_sum[n-k] of buffers, each Initialization: allocate a table partial_sum[n-k] of buffers, each
buffer being of size the symbol size. There's one buffer being of size the symbol size. There's one
entry per equation since the buffers are meant to entry per equation since the buffers are meant to
store the partial sum of each equation; Reset all store the partial sum of each equation; Reset all
the buffers to zero; the buffers to zero;
/* /*
* For each newly received or decoded symbol, try to make progress * For each newly received or decoded symbol, try to make progress
* in the decoding of the associated source block. * in the decoding of the associated source block.
skipping to change at page 33, line 14 skipping to change at page 39, line 14
Authors' Addresses Authors' Addresses
Vincent Roca Vincent Roca
INRIA INRIA
655, av. de l'Europe 655, av. de l'Europe
Inovallee; Montbonnot Inovallee; Montbonnot
ST ISMIER cedex 38334 ST ISMIER cedex 38334
France France
Email: vincent.roca@inrialpes.fr Email: vincent.roca@inria.fr
URI: http://planete.inrialpes.fr/~roca/ URI: http://planete.inrialpes.fr/people/roca/
Christoph Neumann Christoph Neumann
Thomson Research Thomson
46, Quai A. Le Gallo 12, bd de Metz
Boulogne Cedex 92648 Rennes 35700
France France
Email: christoph.neumann@thomson.net Email: christoph.neumann@thomson.net
URI: http://planete.inrialpes.fr/~chneuman/ URI: http://planete.inrialpes.fr/people/chneuman/
David Furodet David Furodet
STMicroelectronics STMicroelectronics
12, Rue Jules Horowitz 12, Rue Jules Horowitz
BP217 BP217
Grenoble Cedex 38019 Grenoble Cedex 38019
France France
Email: david.furodet@st.com Email: david.furodet@st.com
URI: http://www.st.com/ URI: http://www.st.com/
 End of changes. 110 change blocks. 
334 lines changed or deleted 539 lines changed or added

This html diff was produced by rfcdiff 1.34. The latest version is available from http://tools.ietf.org/tools/rfcdiff/