Internet Engineering Task Force (IETF) V. Roca
Request for Comments: 6865 INRIA
Category: Standards Track M. Cunche
ISSN: 2070-1721 INSA-Lyon/INRIA
J. Lacan
ISAE, Univ. of Toulouse
A. Bouabdallah
CDTA
K. Matsuzono
Keio University
February 2013
Simple Reed-Solomon Forward Error Correction (FEC) Scheme for FECFRAME
Abstract
This document describes a fully-specified simple Forward Error
Correction (FEC) scheme for Reed-Solomon codes over the finite field
(also known as the Galois Field) GF(2^^m), with 2 <= m <= 16, that
can be used to protect arbitrary media streams along the lines
defined by FECFRAME. The Reed-Solomon codes considered have
attractive properties, since they offer optimal protection against
packet erasures and the source symbols are part of the encoding
symbols, which can greatly simplify decoding. However, the price to
pay is a limit on the maximum source block size, on the maximum
number of encoding symbols, and a computational complexity higher
than that of the Low-Density Parity Check (LDPC) codes, for instance.
Status of This Memo
This is an Internet Standards Track document.
This document is a product of the Internet Engineering Task Force
(IETF). It represents the consensus of the IETF community. It has
received public review and has been approved for publication by the
Internet Engineering Steering Group (IESG). Further information on
Internet Standards is available in Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc6865.
Roca, et al. Standards Track [Page 1]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
Copyright Notice
Copyright (c) 2013 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents
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include Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Roca, et al. Standards Track [Page 2]
RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 5
3. Definitions Notations and Abbreviations . . . . . . . . . . . 5
3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 5
3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3. Abbreviations . . . . . . . . . . . . . . . . . . . . . . 8
4. Common Procedures Related to the ADU Block and Source
Block Creation . . . . . . . . . . . . . . . . . . . . . . . . 9
4.1. Restrictions . . . . . . . . . . . . . . . . . . . . . . . 9
4.2. ADU Block Creation . . . . . . . . . . . . . . . . . . . . 9
4.3. Source Block Creation . . . . . . . . . . . . . . . . . . 10
5. Simple Reed-Solomon FEC Scheme over GF(2^^m) for Arbitrary
ADU Flows . . . . . . . . . . . . . . . . . . . . . . . . . . 12
5.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 12
5.1.1. FEC Framework Configuration Information . . . . . . . 12
5.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . . 14
5.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 15
5.2. Procedures . . . . . . . . . . . . . . . . . . . . . . . . 17
5.3. FEC Code Specification . . . . . . . . . . . . . . . . . . 17
6. Security Considerations . . . . . . . . . . . . . . . . . . . 17
6.1. Attacks Against the Data Flow . . . . . . . . . . . . . . 17
6.1.1. Access to Confidential Content . . . . . . . . . . . . 17
6.1.2. Content Corruption . . . . . . . . . . . . . . . . . . 18
6.2. Attacks Against the FEC Parameters . . . . . . . . . . . . 18
6.3. When Several Source Flows Are to Be Protected Together . . 19
6.4. Baseline Secure FECFRAME Operation . . . . . . . . . . . . 19
7. Operations and Management Considerations . . . . . . . . . . . 19
7.1. Operational Recommendations: Finite Field Size (m) . . . . 19
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 20
9. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 20
10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 21
10.1. Normative References . . . . . . . . . . . . . . . . . . . 21
10.2. Informative References . . . . . . . . . . . . . . . . . . 21
Roca, et al. Standards Track [Page 3]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
1. Introduction
The use of the Forward Error Correction (FEC) codes is a classic
solution to improve the reliability of unicast, multicast, and
broadcast Content Delivery Protocols (CDP) and applications.
[RFC6363] describes a generic framework to use FEC schemes with media
delivery applications, and for instance with real-time streaming
media applications based on the Real-time Transport Protocol (RTP).
Similarly, [RFC5052] describes a generic framework to use FEC schemes
with object delivery applications (where the objects are files, for
example) based on the Asynchronous Layered Coding (ALC) [RFC5775] and
NACK-Oriented Reliable Multicast (NORM) [RFC5740] transport
protocols.
More specifically, the [RFC5053] and [RFC5170] FEC schemes introduce
erasure codes based on sparse parity-check matrices for object
delivery protocols like ALC and NORM. These codes are efficient in
terms of processing but not optimal in terms of erasure recovery
capabilities when dealing with "small" objects.
The Reed-Solomon FEC codes described in this document belong to the
class of Maximum Distance Separable (MDS) codes that are optimal in
terms of erasure recovery capability. It means that a receiver can
recover the k source symbols from any set of exactly k encoding
symbols. These codes are also systematic codes, which means that the
k source symbols are part of the encoding symbols. However, they are
limited in terms of maximum source block size and number of encoding
symbols. Since the real-time constraints of media delivery
applications usually limit the maximum source block size, this is not
considered to be a major issue in the context of FECFRAME for many
(but not necessarily all) use cases. Additionally, if the encoding/
decoding complexity is higher with Reed-Solomon codes than it is with
[RFC5053] or [RFC5170] codes, it remains reasonable for most use
cases, even in case of a software codec.
Many applications dealing with reliable content transmission or
content storage already rely on packet-based Reed-Solomon erasure
recovery codes. In particular, many of them use the Reed-Solomon
codec of Luigi Rizzo [RS-codec] [Rizzo97]. The goal of the present
document is to specify a simple Reed-Solomon scheme that is
compatible with this codec.
More specifically, [RFC5510] introduced such Reed-Solomon codes and
several associated FEC schemes that are compatible with the [RFC5052]
framework. The present document inherits from Section 8 of
[RFC5510], "Reed-Solomon Codes Specification for the Erasure
Roca, et al. Standards Track [Page 4]
RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
Channel", the specifications of the core Reed-Solomon codes based on
Vandermonde matrices and specifies a simple FEC scheme that is
compatible with FECFRAME [RFC6363]:
The Fully-Specified FEC Scheme with FEC Encoding ID 8 specifies a
simple way of using of Reed-Solomon codes over GF(2^^m), with
2 <= m <= 16, in order to protect arbitrary Application Data Unit
(ADU) flows.
Therefore, Sections 4, 5, 6, and 7 of [RFC5510] that define
[RFC5052]-specific Formats and Procedures are not considered and are
replaced by FECFRAME-specific Formats and Procedures.
For instance, with this scheme, a set of Application Data Units
(ADUs) coming from one or several media delivery applications (e.g.,
a set of RTP packets), are grouped in an ADU block and FEC encoded as
a whole. With Reed-Solomon codes over GF(2^^8), there is a strict
limit over the number of ADUs that can be protected together, since
the number of encoded symbols, n, must be inferior or equal to 255.
This constraint is relaxed when using a higher finite field size (m >
8), at the price of an increased computational complexity.
2. Terminology
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
3. Definitions Notations and Abbreviations
3.1. Definitions
This document uses the following terms and definitions. Some of
these terms and definitions are FEC scheme specific and are in line
with [RFC5052]:
Source symbol: unit of data used during the encoding process. In
this specification, there is always one source symbol per ADU.
Encoding symbol: unit of data generated by the encoding process.
With systematic codes, source symbols are part of the encoding
symbols.
Repair symbol: encoding symbol that is not a source symbol.
Roca, et al. Standards Track [Page 5]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
Code rate: the k/n ratio, i.e., the ratio between the number of
source symbols and the number of encoding symbols. By definition,
the code rate is such that: 0 < code rate <= 1. A code rate close
to 1 indicates that a small number of repair symbols have been
produced during the encoding process.
Systematic code: FEC code in which the source symbols are part of
the encoding symbols. The Reed-Solomon codes introduced in this
document are systematic.
Source Block: a block of k source symbols that are considered
together for the encoding.
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.
Some of these terms and definitions are FECFRAME specific and are in
line with [RFC6363]:
Application Data Unit (ADU): The unit of source data provided as
payload to the transport layer. Depending on the use case, an ADU
may use an RTP encapsulation.
(Source) ADU Flow: A sequence of ADUs associated with a transport-
layer flow identifier (such as the standard 5-tuple {Source IP
address, source port, destination IP address, destination port,
transport protocol}). Depending on the use case, several ADU
flows may be protected together by FECFRAME.
ADU Block: a set of ADUs that are considered together by the
FECFRAME instance for the purpose of the FEC scheme. Along with
the flow ID (F[]), length (L[]), and padding (Pad[]) fields, they
form the set of source symbols over which FEC encoding will be
performed.
ADU Information (ADUI): a unit of data constituted by the ADU and
the associated Flow ID, Length and Padding fields (Section 4.3).
This is the unit of data that is used as source symbol.
FEC Framework Configuration Information (FFCI): Information that
controls the operation of FECFRAME. The FFCI enables the
synchronization of the FECFRAME sender and receiver instances.
Roca, et al. Standards Track [Page 6]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
FEC Source Packet: At a sender (respectively, at a receiver) a
payload submitted to (respectively, received from) the transport
protocol containing an ADU along with an Explicit Source FEC
Payload ID (that must be present in the FEC scheme defined by the
present document, see Section 5.1.2).
FEC Repair Packet: At a sender (respectively, at a receiver) a
payload submitted to (respectively, received from) the transport
protocol containing one repair symbol along with a Repair FEC
Payload ID and possibly an RTP header.
The above terminology is illustrated in Figure 1 (sender's point of
view):
+----------------------+
| Application |
+----------------------+
|
| (1) Application Data Units (ADUs)
|
v
+----------------------+ +----------------+
| FECFRAME | | |
| |-------------------------->| FEC Scheme |
|(2) Construct source |(3) Source Block | |
| blocks | |(4) FEC Encoding|
|(6) Construct FEC |<--------------------------| |
| source and repair | | |
| packets |(5) Explicit Source FEC | |
+----------------------+ Payload IDs +----------------+
| Repair FEC Payload IDs
| Repair symbols
|
|(7) FEC source and repair packets
v
+----------------------+
| Transport Layer |
| (e.g., UDP) |
+----------------------+
Figure 1: Terminology used in this document (sender).
3.2. Notations
This document uses the following notations. Some of them are FEC
scheme specific.
k denotes the number of source symbols in a source block.
Roca, et al. Standards Track [Page 7]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
max_k denotes the maximum number of source symbols for any source
block.
n denotes the number of encoding symbols generated for a source
block.
E denotes the encoding symbol length in bytes.
GF(q) denotes a finite field (also known as the Galois Field) with q
elements. We assume that q = 2^^m in this document.
m defines the length of the elements in the finite field, in
bits. In this document, m is such that 2 <= m <= 16.
q defines the number of elements in the finite field. We have:
q = 2^^m in this specification.
CR denotes the "code rate", i.e., the k/n ratio.
a^^b denotes a raised to the power b.
Some of them are FECFRAME specific:
B denotes the number of ADUs per ADU block.
max_B denotes the maximum number of ADUs for any ADU block.
3.3. Abbreviations
This document uses the following abbreviations:
ADU stands for Application Data Unit.
ADUI stands for Application Data Unit Information.
ESI stands for Encoding Symbol ID.
FEC stands for Forward Error (or Erasure) Correction code.
FFCI stands for FEC Framework Configuration Information.
FSSI stands for FEC Scheme-Specific Information.
MDS stands for Maximum Distance Separable code.
SBN stands for Source Block Number.
SDP stands for Session Description Protocol.
Roca, et al. Standards Track [Page 8]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
4. Common Procedures Related to the ADU Block and Source Block Creation
This section introduces the procedures that are used during the ADU
block and the related source block creation for the FEC scheme
considered.
4.1. Restrictions
This specification has the following restrictions:
o there MUST be exactly one source symbol per ADUI, and therefore
per ADU;
o there MUST be exactly one repair symbol per FEC Repair Packet;
o there MUST be exactly one source block per ADU block.
4.2. ADU Block Creation
Two kinds of limitations exist that impact the ADU block creation:
o at the FEC Scheme level: the finite field size (m parameter)
directly impacts the maximum source block size and the maximum
number of encoding symbols;
o at the FECFRAME instance level: the target use case can have real-
time constraints that can/will define a maximum ADU block size.
Note that terms "maximum source block size" and "maximum ADU block
size" depend on the point of view that is adopted (FEC Scheme versus
FECFRAME instance). However, in this document, both refer to the
same value since Section 4.1 requires there is exactly one source
symbol per ADU. We now detail each of these aspects.
The finite field size parameter m defines the number of non-zero
elements in this field, which is equal to: q - 1 = 2^^m - 1. This q
- 1 value is also the theoretical maximum number of encoding symbols
that can be produced for a source block. For instance, when m = 8
(default) there is a maximum of 2^^8 - 1 = 255 encoding symbols. So:
k < n <= 255. Given the target FEC code rate (e.g., provided by the
end-user or upper application when starting the FECFRAME instance,
and taking into account the known or estimated packet loss rate), the
sender calculates:
max_k = floor((2^^m - 1) * CR)
Roca, et al. Standards Track [Page 9]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
This max_k value leaves enough room for the sender to produce the
desired number of repair symbols. Since there is one source symbol
per ADU, max_k is also an upper bound to the maximum number of ADUs
per ADU block.
The source ADU flows can have real-time constraints. When there are
multiple flows, with different real-time constraints, let us consider
the most stringent constraints (see [RFC6363], Section 10.2, item 6
for recommendations when several flows are globally protected). In
that case, the maximum number of ADUs of an ADU block must not exceed
a certain threshold since it directly impacts the decoding delay.
The larger the ADU block size, the longer a decoder may have to wait
until it has received a sufficient number of encoding symbols for
decoding to succeed, and therefore the larger the decoding delay.
When the target use case is known, these real-time constraints result
in an upper bound to the ADU block size, max_rt.
For instance, if the use case specifies a maximum decoding latency l,
and if each source ADU covers a duration d of a continuous media (we
assume here the simple case of a constant bit-rate ADU flow), then
the ADU block size must not exceed:
max_rt = floor(l / d)
After encoding, this block will produce a set of at most n = max_rt /
CR encoding symbols. These n encoding symbols will have to be sent
at a rate of n / l packets per second. For instance, with d = 10 ms,
l = 1 s, max_rt = 100 ADUs.
If we take into account all these constraints, we find:
max_B = min(max_k, max_rt)
This max_B parameter is an upper bound to the number of ADUs that can
constitute an ADU block.
4.3. Source Block Creation
In their most general form, FECFRAME and the Reed-Solomon FEC scheme
are meant to protect a set of independent flows. Since the flows
have no relationship to one another, the ADU size of each flow can
potentially vary significantly. Even in the special case of a single
flow, the ADU sizes can largely vary (e.g., the various frames of a
"Group of Pictures" (GOP) of an H.264 flow will have different
sizes). This diversity must be addressed since the Reed-Solomon FEC
scheme requires a constant encoding symbol size (E parameter) per
Roca, et al. Standards Track [Page 10]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
source block. Since this specification requires that there is only
one source symbol per ADU, E must be large enough to contain all the
ADUs of an ADU block along with their prepended 3 bytes (see below).
In situations where E is determined per source block (default,
specified by the FFCI/FSSI with S = 0, Section 5.1.1.2), E is equal
to the size of the largest ADU of this source block plus 3 (for the
prepended 3 bytes; see below). In this case, upon receiving the
first FEC Repair Packet for this source block, since this packet MUST
contain a single repair symbol (Section 5.1.3), a receiver determines
the E parameter used for this source block.
In situations where E is fixed (specified by the FFCI/FSSI with
S = 1, Section 5.1.1.2), then E must be greater or equal to the size
of the largest ADU of this source block plus 3 (for the prepended 3
bytes; see below). If this is not the case, an error is returned.
How to handle this error is use-case specific (e.g., a larger E
parameter may be communicated to the receivers in an updated FFCI
message using an appropriate mechanism) and is not considered by this
specification.
The ADU block is always encoded as a single source block. There are
a total of B <= max_B ADUs in this ADU block. For the ADU i, with
0 <= i <= B-1, 3 bytes are prepended (Figure 2):
o The first byte, F[i] (Flow ID), contains the integer identifier
associated to the source ADU flow to which this ADU belongs to.
It is assumed that a single byte is sufficient, or said
differently, that no more than 256 flows will be protected by a
single instance of FECFRAME.
o The following 2 bytes, L[i] (Length), contain the length of this
ADU, in network byte order (i.e., big endian). This length is for
the ADU itself and does not include the F[i], L[i], or Pad[i]
fields.
Then zero padding is added to ADU i (if needed), in field Pad[i], for
alignment purposes up to a size of exactly E bytes. The data unit
resulting from the ADU i and the F[i], L[i], and Pad[i] fields, is
called ADU Information (or ADUI). Each ADUI contributes to exactly
one source symbol of the source block.
Roca, et al. Standards Track [Page 11]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
Encoding Symbol Length (E)
< ----------------------------------------------------------------- >
+----+--------+-----------------------+-----------------------------+
|F[0]| L[0] | ADU[0] | Pad[0] |
+----+--------+----------+------------+-----------------------------+
|F[1]| L[1] | ADU[1] | Pad[1] |
+----+--------+----------+------------------------------------------+
|F[2]| L[2] | ADU[2] |
+----+--------+------+----------------------------------------------+
|F[3]| L[3] |ADU[3]| Pad[3] |
+----+--------+------+----------------------------------------------+
\_________________________________ ________________________________/
\/
simple FEC encoding
+-------------------------------------------------------------------+
| Repair 4 |
+-------------------------------------------------------------------+
. .
. .
+-------------------------------------------------------------------+
| Repair 7 |
+-------------------------------------------------------------------+
Figure 2: Source block creation, for code rate 1/2 (equal number of
source and repair symbols; 4 in this example), and S = 0.
Note that neither the initial 3 bytes nor the optional padding are
sent over the network. However, they are considered during FEC
encoding. It means that a receiver who lost a certain FEC source
packet (e.g., the UDP datagram containing this FEC source packet)
will be able to recover the ADUI if FEC decoding succeeds. Thanks to
the initial 3 bytes, this receiver will get rid of the padding (if
any) and identify the corresponding ADU flow.
5. Simple Reed-Solomon FEC Scheme over GF(2^^m) for Arbitrary ADU Flows
This Fully-Specified FEC Scheme specifies the use of Reed-Solomon
codes over GF(2^^m), with 2 <= m <= 16, with a simple FEC encoding
for arbitrary packet flows.
5.1. Formats and Codes
5.1.1. FEC Framework Configuration Information
The FEC Framework Configuration Information (or FFCI) includes
information that must be communicated between the sender and
receiver(s) [RFC6363]. More specifically, it enables the
Roca, et al. Standards Track [Page 12]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
synchronization of the FECFRAME sender and receiver instances. It
includes both mandatory elements and scheme-specific elements, as
detailed below.
5.1.1.1. Mandatory Information
o FEC Encoding ID: the value assigned to this Fully-Specified FEC
scheme MUST be 8, as assigned by IANA (Section 8).
When SDP is used to communicate the FFCI, this FEC Encoding ID MUST
be carried in the 'encoding-id' parameter of the 'fec-repair-flow'
attribute specified in RFC 6364 [RFC6364].
5.1.1.2. FEC Scheme-Specific Information
The FEC Scheme-Specific Information (FSSI) includes elements that are
specific to the present FEC scheme. More precisely:
o Encoding Symbol Length (E): a non-negative integer, inferior to
2^^16, that indicates either the length of each encoding symbol in
bytes ("strict" mode, i.e., if S = 1), or the maximum length of
any encoding symbol (i.e., if S = 0).
o Strict (S) flag: when set to 1, this flag indicates that the E
parameter is the actual encoding symbol length value for each
block of the session (unless otherwise notified by an updated FFCI
if this possibility is considered by the use case or CDP). When
set to 0, this flag indicates that the E parameter is the maximum
encoding symbol length value for each block of the session (unless
otherwise notified by an updated FFCI if this possibility is
considered by the use case or CDP).
o m parameter (m): an integer that defines the length of the
elements in the finite field, in bits. We have: 2 <= m <= 16.
These elements are required both by the sender (Reed-Solomon encoder)
and the receiver(s) (Reed-Solomon decoder).
When SDP is used to communicate the FFCI, this FEC scheme-specific
information MUST be carried in the 'fssi' parameter of the
'fec-repair-flow' attribute, in textual representation as specified
in RFC 6364 [RFC6364]. For instance:
a=fec-repair-flow: encoding-id=8; fssi=E:1400,S:0,m:8
If another mechanism requires the FSSI to be carried as an opaque
octet string (for instance after a Base64 encoding), the encoding
format consists of the following 3 octets of Figure 3:
Roca, et al. Standards Track [Page 13]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
o Encoding symbol length (E): 16-bit field.
o Strict (S) flag: 1-bit field.
o m parameter (m): 7-bit field.
0 1 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) |S| m |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: FSSI encoding format.
5.1.2. Explicit Source FEC Payload ID
A FEC source packet MUST contain an Explicit Source FEC Payload ID
that is appended to the end of the packet as illustrated in Figure 4.
+--------------------------------+
| IP Header |
+--------------------------------+
| Transport Header |
+--------------------------------+
| ADU |
+--------------------------------+
| Explicit Source FEC Payload ID |
+--------------------------------+
Figure 4: Structure of a FEC Source Packet with the Explicit Source
FEC Payload ID.
More precisely, the Explicit Source FEC Payload ID is composed of the
Source Block Number, the Encoding Symbol ID, and the Source Block
Length. The length of the first 2 fields depends on the m parameter
(transmitted separately in the FFCI, Section 5.1.1.2):
o Source Block Number (SBN) ((32-m)-bit field): this field
identifies the source block to which this FEC source packet
belongs.
o Encoding Symbol ID (ESI) (m-bit field): this field identifies the
source symbol contained in this FEC source packet. This value is
such that 0 <= ESI <= k - 1 for source symbols.
Roca, et al. Standards Track [Page 14]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
o Source Block Length (k) (16-bit field): this field provides the
number of source symbols for this source block, i.e., the k
parameter. If 16 bits are too much when m <= 8, it is needed when
8 < m <= 16. Therefore, we provide a single common format
regardless of m.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Number (24 bits) | Enc. Symb. ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Length (k) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: Source FEC Payload ID encoding format for m = 8 (default).
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Nb (16 bits) | Enc. Symbol ID (16 bits) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Length (k) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 6: Source FEC Payload ID encoding format for m = 16.
The format of the Source FEC Payload ID for m = 8 and m = 16 are
illustrated in Figures 5 and 6, respectively.
5.1.3. Repair FEC Payload ID
A FEC repair packet MUST contain a Repair FEC Payload ID that is
prepended to the repair symbol(s) as illustrated in Figure 7. There
MUST be a single repair symbol per FEC repair packet.
+--------------------------------+
| IP Header |
+--------------------------------+
| Transport Header |
+--------------------------------+
| Repair FEC Payload ID |
+--------------------------------+
| Repair Symbol |
+--------------------------------+
Figure 7: Structure of a FEC Repair Packet with the Repair FEC
Payload ID.
Roca, et al. Standards Track [Page 15]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
More precisely, the Repair FEC Payload ID is composed of the Source
Block Number, the Encoding Symbol ID, and the Source Block Length.
The length of the first 2 fields depends on the m parameter
(transmitted separately in the FFCI, Section 5.1.1.2):
o Source Block Number (SBN) ((32-m)-bit field): this field
identifies the source block to which the FEC repair packet
belongs.
o Encoding Symbol ID (ESI) (m-bit field): this field identifies the
repair symbol contained in this FEC repair packet. This value is
such that k <= ESI <= n - 1 for repair symbols.
o Source Block Length (k) (16-bit field): this field provides the
number of source symbols for this source block, i.e., the k
parameter. If 16 bits are too much when m <= 8, it is needed when
8 < m <= 16. Therefore, we provide a single common format
regardless of m.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Number (24 bits) | Enc. Symb. ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Length (k) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 8: Repair FEC Payload ID encoding format for m = 8 (default).
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Nb (16 bits) | Enc. Symbol ID (16 bits) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Block Length (k) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 9: Repair FEC Payload ID encoding format for m = 16.
The format of the Repair FEC Payload ID for m = 8 and m = 16 are
illustrated in Figures 8 and 9, respectively.
Roca, et al. Standards Track [Page 16]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
5.2. Procedures
The following procedures apply:
o The source block creation MUST follow the procedures specified in
Section 4.3.
o The SBN value MUST start with value 0 for the first block of the
ADU flow and MUST be incremented by 1 for each new source block.
Wrapping to zero will happen for long sessions, after value
2^^(32-m) - 1.
o The ESI of encoding symbols MUST start with value 0 for the first
symbol and MUST be managed sequentially. The first k values
(0 <= ESI <= k - 1) identify source symbols, whereas the last n-k
values (k <= ESI <= n - 1) identify repair symbols.
o The FEC repair packet creation MUST follow the procedures
specified in Section 5.1.3.
5.3. FEC Code Specification
The present document inherits from Section 8 of [RFC5510], "Reed-
Solomon Codes Specification for the Erasure Channel", the
specifications of the core Reed-Solomon codes based on Vandermonde
matrices.
6. Security Considerations
The FECFRAME document [RFC6363] provides a comprehensive analysis of
security considerations applicable to FEC schemes. Therefore, the
present section follows the security considerations section of
[RFC6363] and only discusses topics that are specific to the use of
Reed-Solomon codes.
6.1. Attacks Against the Data Flow
6.1.1. Access to Confidential Content
The Reed-Solomon FEC Scheme specified in this document does not
change the recommendations of [RFC6363]. To summarize, if
confidentiality is a concern, it is RECOMMENDED that one of the
solutions mentioned in [RFC6363] is used with special considerations
to the way this solution is applied (e.g., is encryption applied
before or after FEC protection, within the end-system or in a
middlebox) to the operational constraints (e.g., performing FEC
decoding in a protected environment may be complicated or even
impossible) and to the threat model.
Roca, et al. Standards Track [Page 17]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
6.1.2. Content Corruption
The Reed-Solomon FEC Scheme specified in this document does not
change the recommendations of [RFC6363]. To summarize, it is
RECOMMENDED that one of the solutions mentioned in [RFC6363] is used
on both the FEC Source and Repair Packets.
6.2. Attacks Against the FEC Parameters
The FEC Scheme specified in this document defines parameters that can
be the basis of several attacks. More specifically, the following
parameters of the FFCI may be modified by an attacker
(Section 5.1.1.2):
o FEC Encoding ID: changing this parameter leads the receiver to
consider a different FEC Scheme, which enables an attacker to
create a Denial of Service (DoS).
o Encoding symbol length (E): setting this E parameter to a value
smaller than the valid one enables an attacker to create a DoS
since the repair symbols and certain source symbols will be larger
than E, which is an incoherency for the receiver. Setting this E
parameter to a value larger than the valid one has similar impacts
when S = 1 since the received repair symbol size will be smaller
than expected. On the opposite, it will not lead to any
incoherency when S = 0 since the actual symbol length value for
the block is determined by the size of any received repair symbol,
as long as this value is smaller than E. However, setting this E
parameter to a larger value may have impacts on receivers that
pre-allocate memory space in advance to store incoming symbols.
o Strict (S) flag: flipping this S flag from 0 to 1 (i.e., E is now
considered as a strict value) enables an attacker to mislead the
receiver if the actual symbol size varies over different source
blocks. Flipping this S flag from 1 to 0 has no major
consequences unless the receiver requires to have a fixed E value
(e.g., because the receiver pre-allocates memory space).
o m parameter: changing this parameter triggers a DoS since the
receiver and sender will consider different codes, and the
receiver will interpret the Explicit Source FEC Payload ID and
Repair FEC Payload ID differently. Additionally, by increasing
this m parameter to a larger value (typically m = 16 rather than
8, when both values are possible in the target use case) will
create additional processing load at a receiver if decoding is
attempted.
Roca, et al. Standards Track [Page 18]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
It is therefore RECOMMENDED that security measures are taken to
guarantee the FFCI integrity, as specified in [RFC6363]. How to
achieve this depends on the way the FFCI is communicated from the
sender to the receiver, which is not specified in this document.
Similarly, attacks are possible against the Explicit Source FEC
Payload ID and Repair FEC Payload ID: by modifying the Source Block
Number (SBN), or the Encoding Symbol ID (ESI), or the Source Block
Length (k), an attacker can easily corrupt the block identified by
the SBN. Other consequences, that are use case and/or CDP dependent,
may also happen. It is therefore RECOMMENDED that security measures
are taken to guarantee the FEC Source and Repair Packets as stated in
[RFC6363].
6.3. When Several Source Flows Are to Be Protected Together
The Reed-Solomon FEC Scheme specified in this document does not
change the recommendations of [RFC6363].
6.4. Baseline Secure FECFRAME Operation
The Reed-Solomon FEC Scheme specified in this document does not
change the recommendations of [RFC6363] concerning the use of the
IPsec/ESP security protocol as a mandatory to implement (but not
mandatory to use) security scheme. This is well suited to situations
where the only insecure domain is the one over which FECFRAME
operates.
7. Operations and Management Considerations
The FECFRAME document [RFC6363] provides a comprehensive analysis of
operations and management considerations applicable to FEC schemes.
Therefore, the present section only discusses topics that are
specific to the use of Reed-Solomon codes as specified in this
document.
7.1. Operational Recommendations: Finite Field Size (m)
The present document requires that m, the length of the elements in
the finite field in bits, is such that 2 <= m <= 16. However, all
possibilities are not equally interesting from a practical point of
view. It is expected that m = 8, the default value, will be mostly
used since it offers the possibility to have small to medium sized
source blocks and/or a significant number of repair symbols (i.e., k
< n <= 255). Additionally, elements in the finite field are 8 bits
long, which makes read/write memory operations aligned on bytes
during encoding and decoding.
Roca, et al. Standards Track [Page 19]
RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
An alternative when it is known that only very small source blocks
will be used is m = 4 (i.e., k < n <= 15). Elements in the finite
field are 4 bits long, so if 2 elements are accessed at a time, read/
write memory operations are aligned on bytes during encoding and
decoding.
An alternative when very large source blocks are needed is m = 16
(i.e., k < n<= 65535). However, this choice has significant impact
on the processing load. For instance, using pre-calculated tables to
speed up operations over the finite field (as done with smaller
finite fields) may require a prohibitive amount of memory to be used
on embedded platforms. Alternative lightweight solutions (e.g., LDPC
FEC [RFC5170]) may be preferred in situations where the processing
load is an issue and the source block length is large enough
[Matsuzono10].
Since several values for the m parameter are possible, the use case
SHOULD define which value or values need to be supported. In
situations where this is not specified, the default m = 8 value MUST
be used.
In any case, any compliant implementation MUST support at least the
default m = 8 value.
8. IANA Considerations
Values of FEC Encoding IDs are subject to IANA registration.
[RFC6363] defines general guidelines on IANA considerations. In
particular, it defines the "FEC Framework (FECFRAME) FEC Encoding
IDs" subregistry of the "Reliable Multicast Transport (RMT) FEC
Encoding IDs and FEC Instance IDs" registry, whose registration
procedure is IETF Review.
This document registers one value in the "FEC Framework (FECFRAME)
FEC Encoding IDs" subregistry as follows:
8 refers to the Simple Reed-Solomon [RFC5510] FEC Scheme over
GF(2^^m) for Arbitrary Packet Flows.
9. Acknowledgments
The authors want to thank Hitoshi Asaeda and Ali Begen for their
valuable comments.
Roca, et al. Standards Track [Page 20]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
10. References
10.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC5052] Watson, M., Luby, M., and L. Vicisano, "Forward Error
Correction (FEC) Building Block", RFC 5052,
August 2007.
[RFC5510] Lacan, J., Roca, V., Peltotalo, J., and S. Peltotalo,
"Reed-Solomon Forward Error Correction (FEC) Schemes",
RFC 5510, April 2009.
[RFC6363] Watson, M., Begen, A., and V. Roca, "Forward Error
Correction (FEC) Framework", RFC 6363, October 2011.
[RFC6364] Begen, A., "Session Description Protocol Elements for
the Forward Error Correction (FEC) Framework",
RFC 6364, October 2011.
10.2. Informative References
[Matsuzono10] Matsuzono, K., Detchart, J., Cunche, M., Roca, V., and
H. Asaeda, "Performance Analysis of a High-Performance
Real-Time Application with Several AL-FEC Schemes",
35th Annual IEEE Conference on Local Computer
Networks (LCN 2010), October 2010.
[RFC5053] Luby, M., Shokrollahi, A., Watson, M., and T.
Stockhammer, "Raptor Forward Error Correction Scheme
for Object Delivery", RFC 5053, October 2007.
[RFC5170] Roca, V., Neumann, C., and D. Furodet, "Low Density
Parity Check (LDPC) Staircase and Triangle Forward
Error Correction (FEC) Schemes", RFC 5170, June 2008.
[RFC5740] Adamson, B., Bormann, C., Handley, M., and J. Macker,
"NACK-Oriented Reliable Multicast (NORM) Transport
Protocol", RFC 5740, November 2009.
[RFC5775] Luby, M., Watson, M., and L. Vicisano, "Asynchronous
Layered Coding (ALC) Protocol Instantiation",
RFC 5775, April 2010.
Roca, et al. Standards Track [Page 21]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
[Rizzo97] Rizzo, L., "Effective Erasure Codes for Reliable
Computer Communication Protocols", ACM SIGCOMM
Computer Communication Review, Vol.27, No.2, pp.24-36,
April 1997.
[RS-codec] Rizzo, L., "Reed-Solomon FEC codec (C language)",
original codec: http://info.iet.unipi.it/~luigi/vdm98/
vdm980702.tgz, improved codec: http://openfec.org/,
July 1998.
Authors' Addresses
Vincent Roca
INRIA
655, av. de l'Europe
Inovallee; Montbonnot
ST ISMIER cedex 38334
France
EMail: vincent.roca@inria.fr
URI: http://planete.inrialpes.fr/people/roca/
Mathieu Cunche
INSA-Lyon/INRIA
Laboratoire CITI
6 av. des Arts
Villeurbanne cedex 69621
France
EMail: mathieu.cunche@inria.fr
URI: http://mathieu.cunche.free.fr/
Jerome Lacan
ISAE, Univ. of Toulouse
10 av. Edouard Belin; BP 54032
Toulouse cedex 4 31055
France
EMail: jerome.lacan@isae.fr
URI: http://personnel.isae.fr/jerome-lacan/
Roca, et al. Standards Track [Page 22]RFC 6865 Simple Reed-Solomon FEC Scheme February 2013
Amine Bouabdallah
CDTA
Center for Development of Advanced Technologies
Cite 20 aout 1956, Baba Hassen
Algiers
Algeria
EMail: abouabdallah@cdta.dz
Kazuhisa Matsuzono
Keio University
Graduate School of Media and Governance
5322 Endo
Fujisawa, Kanagawa 252-8520
Japan
EMail: kazuhisa@sfc.wide.ad.jp
Roca, et al. Standards Track [Page 23]
