draft-ietf-rmt-bb-fec-ldpc-07.txt   draft-ietf-rmt-bb-fec-ldpc-08.txt 
RMT V. Roca RMT V. Roca
Internet-Draft INRIA Internet-Draft INRIA
Intended status: Standards Track C. Neumann Intended status: Standards Track C. Neumann
Expires: May 19, 2008 Thomson Expires: July 26, 2008 Thomson
D. Furodet D. Furodet
STMicroelectronics STMicroelectronics
November 16, 2007 January 23, 2008
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-07.txt draft-ietf-rmt-bb-fec-ldpc-08.txt
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Copyright Notice Copyright Notice
Copyright (C) The IETF Trust (2007). Copyright (C) The IETF Trust (2008).
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 data objects on the packet erasure channel (i.e., a delivery of data objects on the packet erasure channel (i.e., a
communication path where packets are either received without any communication path where packets are either received without any
corruption or discarded during transmission). These systematic FEC 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 . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Requirements notation . . . . . . . . . . . . . . . . . . . . 5 2. Requirements notation . . . . . . . . . . . . . . . . . . . . 6
3. Definitions, Notations and Abbreviations . . . . . . . . . . . 6 3. Definitions, Notations and Abbreviations . . . . . . . . . . . 7
3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 6 3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 7
3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3. Abbreviations . . . . . . . . . . . . . . . . . . . . . . 7 3.3. Abbreviations . . . . . . . . . . . . . . . . . . . . . . 8
4. Formats and Codes . . . . . . . . . . . . . . . . . . . . . . 8 4. Formats and Codes . . . . . . . . . . . . . . . . . . . . . . 9
4.1. FEC Payload IDs . . . . . . . . . . . . . . . . . . . . . 8 4.1. FEC Payload IDs . . . . . . . . . . . . . . . . . . . . . 9
4.2. FEC Object Transmission Information . . . . . . . . . . . 8 4.2. FEC Object Transmission Information . . . . . . . . . . . 9
4.2.1. Mandatory Element . . . . . . . . . . . . . . . . . . 8 4.2.1. Mandatory Element . . . . . . . . . . . . . . . . . . 9
4.2.2. Common Elements . . . . . . . . . . . . . . . . . . . 8 4.2.2. Common Elements . . . . . . . . . . . . . . . . . . . 9
4.2.3. Scheme-Specific Elements . . . . . . . . . . . . . . . 9 4.2.3. Scheme-Specific Elements . . . . . . . . . . . . . . . 10
4.2.4. Encoding Format . . . . . . . . . . . . . . . . . . . 9 4.2.4. Encoding Format . . . . . . . . . . . . . . . . . . . 10
5. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 12 5.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 13
5.2. Determining the Maximum Source Block Length (B) . . . . . 13 5.2. Determining the Maximum Source Block Length (B) . . . . . 14
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) . . . . . . . . . . . . 14 of Encoding Symbols per Group (G) . . . . . . . . . . . . 15
5.4. Determining the Maximum Number of Encoding Symbols 5.4. Determining the Maximum Number of Encoding Symbols
Generated for Any Source Block (max_n) . . . . . . . . . . 15 Generated for Any Source Block (max_n) . . . . . . . . . . 16
5.5. Determining the Number of Encoding Symbols of a Block 5.5. Determining the Number of Encoding Symbols of a Block
(n) . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 (n) . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
5.6. Identifying the G Symbols of an Encoding Symbol Group . . 16 5.6. Identifying the G Symbols of an Encoding Symbol Group . . 17
5.7. Pseudo Random Number Generator . . . . . . . . . . . . . . 20 5.7. Pseudo Random Number Generator . . . . . . . . . . . . . . 21
6. Full Specification of the LDPC-Staircase Scheme . . . . . . . 22 6. Full Specification of the LDPC-Staircase Scheme . . . . . . . 23
6.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 22 6.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 23
6.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 22 6.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 23
6.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 25
6.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 25
7. Full Specification of the LDPC-Triangle Scheme . . . . . . . . 26 7. Full Specification of the LDPC-Triangle Scheme . . . . . . . . 27
7.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 26 7.1. General . . . . . . . . . . . . . . . . . . . . . . . . . 27
7.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 26 7.2. Parity Check Matrix Creation . . . . . . . . . . . . . . . 27
7.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 26 7.3. Encoding . . . . . . . . . . . . . . . . . . . . . . . . . 28
7.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.4. Decoding . . . . . . . . . . . . . . . . . . . . . . . . . 28
8. Security Considerations . . . . . . . . . . . . . . . . . . . 28 8. Security Considerations . . . . . . . . . . . . . . . . . . . 29
8.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 28 8.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 29
8.2. Attacks Against the Data Flow . . . . . . . . . . . . . . 28 8.2. Attacks Against the Data Flow . . . . . . . . . . . . . . 29
8.2.1. Access to Confidential Objects . . . . . . . . . . . . 28 8.2.1. Access to Confidential Objects . . . . . . . . . . . . 29
8.2.2. Content Corruption . . . . . . . . . . . . . . . . . . 29 8.2.2. Content Corruption . . . . . . . . . . . . . . . . . . 30
8.3. Attacks Against the FEC Parameters . . . . . . . . . . . . 30 8.3. Attacks Against the FEC Parameters . . . . . . . . . . . . 31
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 31 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 32
10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 32 10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 33
11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 33 11. References . . . . . . . . . . . . . . . . . . . . . . . . . . 34
11.1. Normative References . . . . . . . . . . . . . . . . . . . 33 11.1. Normative References . . . . . . . . . . . . . . . . . . . 34
11.2. Informative References . . . . . . . . . . . . . . . . . . 33 11.2. Informative References . . . . . . . . . . . . . . . . . . 34
Appendix A. Pseudo Random Number Generator Example Appendix A. Trivial Decoding Algorithm (Informative Only) . . . . 37
Implementation (Informative Only) . . . . . . . . . . 35
Appendix B. Trivial Decoding Algorithm (Informative Only) . . . . 37
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 39 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 39
Intellectual Property and Copyright Statements . . . . . . . . . . 40 Intellectual Property and Copyright Statements . . . . . . . . . . 40
1. Introduction 1. Introduction
[RFC3453] introduces large block FEC codes as an alternative to small [RFC3453] introduces large block FEC codes as an alternative to small
block FEC codes like Reed-Solomon. The main advantage of such large block FEC codes like Reed-Solomon. The main advantage of such 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
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some of them are missing. These codes are systematic, in the sense some of them are missing. These codes are systematic, in the sense
that the encoding symbols include the source symbols in addition to that the encoding symbols include the source symbols in addition to
the 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 [LDPC-codec]. available and distributed under a GNU/LGPL license [LDPC-codec].
Besides, the code extracts included in this document (except Besides, the code extracts included in this document are directly
Appendix A that is only provided as an example) are directly
contributed to the IETF process by the authors of this document and contributed to the IETF process by the authors of this document and
by Radford M. Neal. 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 [RFC2119]. document are to be interpreted as described in [RFC2119].
3. Definitions, Notations and Abbreviations 3. Definitions, Notations and Abbreviations
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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
CR 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. This is in particular the number of encoding any source block. This is in particular the number of encoding
symbols generated for a source block of size B 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 pmms_rand(m) denotes the pseudo-random number generator defined in
number generator, where s is the seed (s > 0) Section 5.7 that returns a new random integer in [0; m-1] each
time it is called
rand(m) denotes a pseudo-random number generator that returns a
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
FPI: FEC Payload ID FPI: FEC Payload ID
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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)
following value: [RFC4648] of the following value:
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| 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
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Algorithm: Algorithm:
n = floor(k * max_n / B); n = floor(k * max_n / B);
5.6. Identifying the G 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,
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*/ */
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));
if (txseqToID == NULL || IDtoTxseq == NULL)
handle the malloc failures as appropriate...
/* 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 = pmms_rand(n - k);
backup = IDtoTxseq[i]; backup = IDtoTxseq[i];
IDtoTxseq[i] = IDtoTxseq[randInd]; IDtoTxseq[i] = IDtoTxseq[randInd];
IDtoTxseq[randInd] = backup; IDtoTxseq[randInd] = backup;
txseqToID[IDtoTxseq[i]] = i; txseqToID[IDtoTxseq[i]] = i;
txseqToID[IDtoTxseq[randInd]] = randInd; txseqToID[IDtoTxseq[randInd]] = randInd;
} }
return; return;
} }
It is then possible, at the sender, to determine the sequence of G It is then possible, at the sender, to determine the sequence of G
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} }
} }
} }
5.7. Pseudo Random Number Generator 5.7. Pseudo Random Number Generator
The FEC Encoding IDs 3 and 4 rely on a pseudo-random number generator The FEC Encoding IDs 3 and 4 rely on a pseudo-random number generator
(PRNG) that must be fully specified, in particular in order to enable (PRNG) that must be fully specified, in particular in order to enable
the receivers and the senders to build the same parity check matrix. the receivers and the senders to build the same parity check matrix.
The minimal standard generator [PM88] MUST be used. It defines a The Park-Miler "minimal standard" PRNG [PM88] MUST be used. It
simple multiplicative congruential algorithm: Ij+1 = A * Ij (modulo defines a simple multiplicative congruential algorithm: Ij+1 = A * Ij
M), with the following choices: A = 7^^5 = 16807 and M = 2^^31 - 1 = (modulo M), with the following choices: A = 7^^5 = 16807 and M =
2147483647. Several implementations of this PRNG are known and 2^^31 - 1 = 2147483647. A validation criteria of such a PRNG is the
discussed in the literature. All of them provide the same sequence following: if seed = 1, then the 10,000th value returned MUST be
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. equal to 1043618065.
An optimized implementation of this algorithm, using only 32 bit Several implementations of this PRNG are known and discussed in the
mathematics which does not require any division, is provided, as an literature. An optimized implementation of this algorithm, using
example, in Appendix A. Yet any other implementation of the PRNG only 32 bit mathematics and which does not require any division, can
algorithm that matches the above validation criteria is appropriate. be found in [rand31pmc]. It uses the Park and Miller algorithm
[PM88] with the optimization suggested by D. Carta in [CA90]. The
history behind this algorithm is detailed in [WI08]. Yet any other
implementation of the PRNG algorithm that matches the above
validation criteria, like the ones detailed in [PM88], is
appropriate.
This PRNG produces a 31 bit value between 1 and 0x7FFFFFFE (2^^31-2) This PRNG produces natively a 31 bit value between 1 and 0x7FFFFFFE
inclusive. When it is desired to scale the pseudo random number (2^^31-2) inclusive. Since it is desired to scale the pseudo random
between 0 and maxv-1 inclusive, one must keep the most significant number between 0 and maxv-1 inclusive, one must keep the most
bits of the value returned by the PRNG (the least significant bits significant bits of the value returned by the PRNG (the least
are known to be less random and modulo based solutions should be significant bits are known to be less random and modulo based
avoided [PTVF92]). The following algorithm MUST be used: solutions should be avoided [PTVF92]). The following algorithm MUST
be used:
Input: Input:
raw_value: random integer generated by the inner PRNG algorithm, raw_value: random integer generated by the inner PRNG algorithm,
between 1 and 0x7FFFFFFE (2^^31-2) inclusive. between 1 and 0x7FFFFFFE (2^^31-2) inclusive.
maxv: upper bound used during the scaling operation. maxv: upper bound used during the scaling operation.
Output: Output:
scaled_value: random integer between 0 and maxv-1 inclusive. scaled_value: random integer between 0 and maxv-1 inclusive.
Algorithm: Algorithm:
scaled_value = (unsigned long) ((double)maxv * (double)raw_value / scaled_value = (unsigned long) ((double)maxv * (double)raw_value /
(double)0x7FFFFFFF); (double)0x7FFFFFFF);
(NB: the above C type casting to unsigned long is equivalent to (NB: the above C type casting to unsigned long is equivalent to
using floor() with positive floating point values) using floor() with positive floating point values)
In this document, pmms_rand(maxv) denotes the PRNG function that
implements the Park-Miller "minimal standard" algorithm defined above
and that scales the raw value between 1 and maxv-1 inclusive, using
the above scaling algorithm. Additionally, a function should be
provided to enable the initialization of the PRNG with a seed (i.e.,
a 31 bit interger between 1 and 0x7FFFFFFE inclusive) before calling
pmms_rand(maxv) the first time.
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 instance-specific FEC OTI attribute seed. This PRNG seed is an instance-specific FEC OTI attribute
(Section 4.2.3). (Section 4.2.3).
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 MUST be generated by using the following function:
/* initialize a list of all possible choices in order to /*
* Initialize the left side of the parity check matrix.
* This function assumes that an empty matrix of size n-k * k has
* previously been allocated/reset and that the matrix_has_entry(),
* matrix_insert_entry() and degree_of_row() functions can access it.
* (IN): the k and n parameters.
*/
void left_matrix_init (int k, int n)
{
int i; /* row index or temporary variable */
int j; /* column index */
int h;
int t; /* left limit within the list of possible choices u[] */
int u[3*MAX_K]; /* table used to have a homogeneous 1 distrib. */
/* 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[] */
t = 0;
/* Initialize the matrix with 3 "1s" per column, homogeneously */
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" */
/* check that valid available choices remain */ /* check that valid available choices remain */
for (i = t; i < 3*k && matrix_has_entry(u[i], j); i++); for (i = t; i < 3*k && matrix_has_entry(u[i], j); i++);
if (i < 3*k) { if (i < 3*k) {
/* choose one index within the list of possible /* choose one index within the list of possible
* choices */ * choices */
do { do {
i = t + rand(3*k-t); i = t + pmms_rand(3*k-t);
} while (matrix_has_entry(u[i], j)); } while (matrix_has_entry(u[i], j));
matrix_insert_entry(u[i], j); matrix_insert_entry(u[i], j);
/* replace with u[t] which has never been chosen */ /* replace with u[t] which has never been chosen */
u[i] = u[t]; u[i] = u[t];
t++; t++;
} else { } else {
/* no choice left, choose one randomly */ /* no choice left, choose one randomly */
do { do {
i = rand(n-k); i = pmms_rand(n-k);
} while (matrix_has_entry(i, j)); } while (matrix_has_entry(i, j));
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 = pmms_rand(k);
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 = pmms_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 }
algorithm:
The right side (the staircase) MUST be generated by using the
following function:
/*
* Initialize the right side of the parity check matrix with a
* staircase structure.
* (IN): the k and n parameters.
*/
void right_matrix_staircase_init (int k, int n)
{
int i; /* row index */
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 5.6) 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
skipping to change at page 24, line 44 skipping to change at page 25, line 52
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 [ZP74]: given a set of linear equations, following trivial algorithm [ZP74]: given a set of linear equations,
if one of them has only one remaining unknown variable, then the if one of them has only one remaining unknown variable, then the
value of this variable is that of the constant term. So, replace value of this variable is that of the constant term. So, replace
this 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 B sketches a possible implementation of this algorithm. Appendix A 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 26, line 22 skipping to change at page 27, line 22
seed. This PRNG seed is an instance-specific FEC OTI attribute seed. This PRNG seed is an instance-specific FEC OTI attribute
(Section 4.2.3). (Section 4.2.3).
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 MUST be generated by using the same left_matrix_init()
Staircase (Section 6.2). function as with LDPC-Staircase (Section 6.2).
The right side (the triangle) is generated with the following The right side (the triangle) MUST be generated by using the
algorithm: following function:
/*
* Initialize the right side of the parity check matrix with a
* triangle structure.
* (IN): the k and n parameters.
*/
void right_matrix_staircase_init (int k, int n)
{
int i; /* row index */
int j; /* randomly chosen column indexes in 0..n-k-2 */
int l; /* limitation of the # of "1s" added per row */
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 */
/* 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 = pmms_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 5.6) 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 of ESI i is equal to the sum of all source and repair symbols symbol of ESI i is equal to the sum of all source and repair symbols
skipping to change at page 28, line 43 skipping to change at page 29, line 43
(e.g., by sending forged symbols) or against the FEC parameters that (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- are sent either in-band (e.g., in an EXT_FTI or FDT Instance) or out-
of-band (e.g., in a session description). of-band (e.g., in a session description).
8.2. Attacks Against the Data Flow 8.2. Attacks Against the Data Flow
First of all, let us consider the attacks against the data flow. First of all, let us consider the attacks against the data flow.
8.2.1. Access to Confidential Objects 8.2.1. Access to Confidential Objects
Access control to the object being transmitted is typically provided Access control to a confidential object being transmitted is
by means of encryption. This encryption can be done over the whole typically provided by means of encryption. This encryption can be
object (e.g., by the content provider, before the FEC encoding done over the whole object (e.g., by the content provider, before the
process), or be done on a packet per packet basis (e.g., when IPSec/ FEC encoding process), or be done on a packet per packet basis (e.g.,
ESP is used [RFC4303]). If access control is a concern, it is when IPsec/ESP is used [RFC4303]). If confidentiality is a concern,
RECOMMENDED that one of these solutions be used. Even if we mention it is RECOMMENDED that one of these solutions be used. Even if we
these attacks here, they are not related nor facilitated by the use mention these attacks here, they are not related nor facilitated by
of FEC. the use of FEC.
8.2.2. Content Corruption 8.2.2. Content Corruption
Protection against corruptions (e.g., after sending forged packets) Protection against corruptions (e.g., after sending forged packets)
is achieved by means of a content integrity verification/sender is achieved by means of a content integrity verification/sender
authentication scheme. This service can be provided at the object authentication scheme. This service can be provided at the object
level, but in that case a receiver has no way to identify which 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. 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, 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 after removing all forged packets, the object may be in some case
skipping to change at page 29, line 26 skipping to change at page 30, line 26
o at the object level, the object MAY be digitally signed (with o at the object level, the object MAY be digitally signed (with
public key cryptography), for instance by using RSASSA-PKCS1-v1_5 public key cryptography), for instance by using RSASSA-PKCS1-v1_5
[RFC3447]. This signature enables a receiver to check the object [RFC3447]. This signature enables a receiver to check the object
integrity, once this latter has been fully decoded. Even if integrity, once this latter has been fully decoded. Even if
digital signatures are computationally expensive, this calculation digital signatures are computationally expensive, this calculation
occurs only once per object, which is usually acceptable; occurs only once per object, which is usually acceptable;
o at the packet level, each packet can be digitally signed. A major o at the packet level, each packet can be digitally signed. A major
limitation is the high computational and transmission overheads limitation is the high computational and transmission overheads
that this solution requires (unless Elliptic Curve Cryptography that this solution requires (unless perhaps if Elliptic Curve
(ECC) is used). To avoid this problem, the signature may span a Cryptography (ECC) is used). To avoid this problem, the signature
set of symbols (instead of a single one) in order to amortize the may span a set of symbols (instead of a single one) in order to
signature calculation. But if a single symbol is missing, the amortize the signature calculation. But if a single symbol is
integrity of the whole set cannot be checked; missing, the integrity of the whole set cannot be checked;
o at the packet level, a Group Message Authentication Code (MAC) o at the packet level, a Group Message Authentication Code (MAC)
[RFC2104] scheme can be used, for instance by using HMAC-SHA-1 [RFC2104] scheme can be used, for instance by using HMAC-SHA-1
with a secret key shared by all the group members, senders and with a secret key shared by all the group members, senders and
receivers. This technique creates a cryptographically secured receivers. This technique creates a cryptographically secured
(thanks to the secret key) digest of a packet that is sent along (thanks to the secret key) digest of a packet that is sent along
with the packet. The Group MAC scheme does not create prohibitive with the packet. The Group MAC scheme does not create prohibitive
processing load nor transmission overhead, but it has a major processing load nor transmission overhead, but it has a major
limitation: it only provides a group authentication/integrity limitation: it only provides a group authentication/integrity
service since all group members share the same secret group key, service since all group members share the same secret group key,
which means that each member can send a forged packet. It is which means that each member can send a forged packet. It is
therefore restricted to situations where group members are fully therefore restricted to situations where group members are fully
trusted (or in association with another technique as a pre-check); trusted (or in association with another technique as a pre-check);
o at the packet level, TESLA [RFC4082] is a very attractive and o at the packet level, TESLA [RFC4082] is an attractive solution
efficient solution that is robust to losses, provides a true that is robust to losses, provides a true authentication/integrity
authentication/integrity service, and does not create any service, and does not create any prohibitive processing load or
prohibitive processing load or transmission overhead. Yet transmission overhead. Yet checking a packet requires a small
checking a packet requires a small delay (a second or more) after delay (a second or more) after its reception;
its reception;
Techniques relying on public key cryptography (digital signatures and Techniques relying on public key cryptography (digital signatures and
TESLA during the bootstrap process, when used) require that public TESLA during the bootstrap process, when used) require that public
keys be securely associated to the entities. This can be achieved by 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 a Public Key Infrastructure (PKI), or by a PGP Web of Trust, or by
pre-distributing the public keys of each group member. pre-distributing the public keys of each group member.
Techniques relying on symmetric key cryptography (group MAC) require Techniques relying on symmetric key cryptography (group MAC) require
that a secret key be shared by all group members. This can be 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 achieved by means of a group key management protocol, or simply by
pre-distributing the secret key (but this manual solution has many pre-distributing the secret key (but this manual solution has many
limitations). limitations).
It is up to the developer and deployer, who know the security It is up to the CDP developer, who knows the security requirements
requirements and features of the target application area, to define and features of the target application area, to define which solution
which solution is the most appropriate. Nonetheless, in case there is the most appropriate. Nonetheless, in case there is any concern
is any concern of the threat of object corruption, it is RECOMMENDED of the threat of object corruption, it is RECOMMENDED that at least
that at least one of these techniques be used. one of these techniques be used.
8.3. Attacks Against the FEC Parameters 8.3. Attacks Against the FEC Parameters
Let us now consider attacks against the FEC parameters (or FEC OTI). 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 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., FDT Instance containing FEC OTI for the object) or out-of-band (e.g.,
in a session description). Attacks on these FEC parameters can in a session description). Attacks on these FEC parameters can
prevent the decoding of the associated object: for instance modifying prevent the decoding of the associated object: for instance modifying
the B parameter will lead to a different block partitioning. the B parameter will lead to a different block partitioning.
It is therefore RECOMMENDED that security measures be taken to It is therefore RECOMMENDED that security measures be taken to
guarantee the FEC OTI integrity. To that purpose, the packets guarantee the FEC OTI integrity. To that purpose, the packets
carrying the FEC parameters sent in-band in an EXT_FTI header carrying the FEC parameters sent in-band in an EXT_FTI header
extension SHOULD be protected by one of the per-packet techniques extension SHOULD be protected by one of the per-packet techniques
described above: digital signature, group MAC, or TESLA. When FEC described above: digital signature, group MAC, or TESLA. When FEC
OTI is contained in an FDT Instance, this object SHOULD be protected, OTI is contained in an FDT Instance, this object SHOULD be protected,
for instance by digitally signing it with XML digital signatures for instance by digitally signing it with XML digital signatures
[RFC3275]. Finally, when FEC OTI is sent out-of-band (e.g., in a [RFC3275]. Finally, when FEC OTI is sent out-of-band (e.g., in a
session description) this latter SHOULD be protected, for instance by session description) this latter SHOULD be protected, for instance by
digitally signing it. digitally signing it with [RFC3852].
The same considerations concerning the key management aspects apply The same considerations concerning the key management aspects apply
here also. 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 [RFC5052]. apply to this document, see [RFC5052].
skipping to change at page 32, line 10 skipping to change at page 33, line 10
"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 5.5 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, Shao Wenjian, Brian Carpenter, Magnus Westerlund, and Francillon, Shao Wenjian, Magnus Westerlund, Brian Carpenter, Tim
Alfred Hoenes for their comments. Polk, Jari Arkko, Chris Newman, Robin Whittle and Alfred Hoenes for
their comments.
Last but not least, the authors are grateful to Radford M. Neal Last but not least, the authors are grateful to Radford M. Neal
(University of Toronto) whose LDPC software (University of Toronto) whose LDPC software
(http://www.cs.toronto.edu/~radford/ldpc.software.html) inspired this (http://www.cs.toronto.edu/~radford/ldpc.software.html) inspired this
work. work.
11. References 11. References
11.1. Normative References 11.1. Normative References
skipping to change at page 34, line 9 skipping to change at page 35, line 9
64298-1, 2003. 64298-1, 2003.
[PM88] Park, S. and K. Miller, "Random Number Generators: Good [PM88] Park, S. and K. Miller, "Random Number Generators: Good
Ones are Hard to Find", Communications of the ACM, Vol. Ones are Hard to Find", Communications of the ACM, Vol.
31, No. 10, pp.1192-1201, 1988. 31, No. 10, pp.1192-1201, 1988.
[CA90] Carta, D., "Two Fast Implementations of the Minimal [CA90] Carta, D., "Two Fast Implementations of the Minimal
Standard Random Number Generator", Communications of the Standard Random Number Generator", Communications of the
ACM, Vol. 33, No. 1, pp.87-88, January 1990. ACM, Vol. 33, No. 1, pp.87-88, January 1990.
[WI08] Whittle, R., "Park-Miller-Carta Pseudo-Random Number
Generator", http://www.firstpr.com.au/dsp/rand31/,
January 2008.
[rand31pmc]
Whittle, R., "31 bit pseudo-random number generator", htt
p://www.firstpr.com.au/dsp/rand31/
rand31-park-miller-carta.cc.txt, September 2005.
[PTVF92] Press, W., Teukolsky, S., Vetterling, W., and B. Flannery, [PTVF92] Press, W., Teukolsky, S., Vetterling, W., and B. Flannery,
"Numerical Recipies in C; Second Edition", Cambridge "Numerical Recipies in C; Second Edition", Cambridge
University Press, ISBN: 0-521-43108-5, 1992. University Press, ISBN: 0-521-43108-5, 1992.
[draft-ietf-rmt-pi-alc-revised] [draft-ietf-rmt-pi-alc-revised]
Luby, M., Watson, M., and L. Vicisano, "Asynchronous Luby, M., Watson, M., and L. Vicisano, "Asynchronous
Layered Coding (ALC) Protocol Instantiation", 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.
skipping to change at page 35, line 5 skipping to change at page 36, line 10
RFC 2104, February 1997. RFC 2104, February 1997.
[RFC4082] "Timed Efficient Stream Loss-Tolerant Authentication [RFC4082] "Timed Efficient Stream Loss-Tolerant Authentication
(TESLA): Multicast Source Authentication Transform (TESLA): Multicast Source Authentication Transform
Introduction", RFC 4082, June 2005. Introduction", RFC 4082, June 2005.
[RFC3275] Eastlake, D., Reagle, J., and D. Solo, "(Extensible Markup [RFC3275] Eastlake, D., Reagle, J., and D. Solo, "(Extensible Markup
Language) XML-Signature Syntax and Processing", RFC 3275, Language) XML-Signature Syntax and Processing", RFC 3275,
March 2002. March 2002.
Appendix A. Pseudo Random Number Generator Example Implementation [RFC3852] Housley, R., "Cryptographic Message Syntax (CMS)",
(Informative Only) RFC 3852, July 2004.
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); [RFC4648] Josefsson, S., "The Base16, Base32, and Base64 Data
hi = 16807 * (seed >> 16); /* binary shift to right */ Encodings", RFC 4648, October 2006.
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) Appendix A. Trivial Decoding Algorithm (Informative Only)
A trivial decoding algorithm is sketched below (please see A trivial decoding algorithm is sketched below (please see
[LDPC-codec] for the details omitted here): [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;
skipping to change at page 40, line 7 skipping to change at page 40, line 7
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/
Full Copyright Statement Full Copyright Statement
Copyright (C) The IETF Trust (2007). Copyright (C) The IETF Trust (2008).
This document is subject to the rights, licenses and restrictions This document is subject to the rights, licenses and restrictions
contained in BCP 78, and except as set forth therein, the authors contained in BCP 78, and except as set forth therein, the authors
retain all their rights. retain all their rights.
This document and the information contained herein are provided on an This document and the information contained herein are provided on an
"AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY, THE IETF TRUST AND OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY, THE IETF TRUST AND
THE INTERNET ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS THE INTERNET ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF
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