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rfc:rfc6865

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
 (http://trustee.ietf.org/license-info) in effect on the date of
 publication of this document.  Please review these documents
 carefully, as they describe your rights and restrictions with respect
 to this document.  Code Components extracted from this document must
 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]

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