LDPC Staircase FEC: Simple Low-Density Parity Check (LDPC) Staircase Forward Error Correction (FEC) Scheme for FECFRAME

Internet Engineering Task Force (IETF)                           V. Roca
Request for Comments: 6816                                         INRIA
Category: Standards Track                                      M. Cunche
ISSN: 2070-1721                                          INSA-Lyon/INRIA
                                                                J. Lacan
                                                 ISAE, Univ. of Toulouse
                                                           December 2012


            Simple Low-Density Parity Check (LDPC) Staircase
           Forward Error Correction (FEC) Scheme for FECFRAME

Abstract

   This document describes a fully specified simple Forward Error
   Correction (FEC) scheme for Low-Density Parity Check (LDPC) Staircase
   codes that can be used to protect media streams along the lines
   defined by FECFRAME.  These codes have many interesting properties:
   they are systematic codes, they perform close to ideal codes in many
   use-cases, and they also feature very high encoding and decoding
   throughputs.  LDPC-Staircase codes are therefore a good solution to
   protect a single high bitrate source flow or to protect globally
   several mid-rate flows within a single FECFRAME instance.  They are
   also a good solution whenever the processing load of a software
   encoder or decoder must be kept to a minimum.

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/rfc6816.

Copyright Notice

   Copyright (c) 2012 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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   described in the Simplified BSD License.

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 ..................................................8
      4.1. Restrictions ...............................................9
      4.2. ADU Block Creation .........................................9
      4.3. Source Block Creation .....................................11
   5. LDPC-Staircase FEC Scheme for Arbitrary ADU Flows ..............13
      5.1. Formats and Codes .........................................13
           5.1.1. FEC Framework Configuration Information ............13
           5.1.2. Explicit Source FEC Payload ID .....................14
           5.1.3. Repair FEC Payload ID ..............................16
      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 FEC Framework Operation ...................19
   7. Operations and Management Considerations .......................19
      7.1. Operational Recommendations ...............................19
   8. IANA Considerations ............................................21
   9. Acknowledgments ................................................21
   10. References ....................................................21
      10.1. Normative References .....................................21
      10.2. Informative References ...................................22

1.  Introduction

   The use of Forward Error Correction (FEC) codes is a classic solution
   to improve the reliability of unicast, multicast, and broadcast
   Content Delivery Protocols (CDPs) and applications [RFC3453].
   "Forward Error Correction (FEC) Framework" [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 RTP real-time protocol.  Similarly, "Forward Error Correction
   (FEC) Building Block" [RFC5052] describes a generic framework to use
   FEC schemes with objects (e.g., files) delivery applications based on
   either the Asynchronous Layered Coding (ALC) [RFC5775] or the NACK-
   Oriented Reliable Multicast (NORM) [RFC5740] protocols.

   More specifically, the [RFC5053] (Raptor) and [RFC5170] (LDPC-
   Staircase and LDPC-Triangle) FEC schemes introduce erasure codes
   based on sparse parity check matrices for object delivery protocols
   like ALC and NORM.  Similarly, "Reed-Solomon Forward Error Correction
   (FEC) Schemes" [RFC5510] introduces Reed-Solomon codes based on
   Vandermonde matrices for the same object delivery protocols.  All
   these codes are systematic codes, meaning that the k source symbols
   are part of the n encoding symbols.  Additionally, the Reed-Solomon
   FEC codes belong to the class of Maximum Distance Separable (MDS)
   codes that are optimal in terms of erasure recovery capabilities.  It
   means that a receiver can recover the k source symbols from any set
   of exactly k encoding symbols out of n.  This is not the case with
   either Raptor or LDPC-Staircase codes, and these codes require a
   certain number of encoding symbols in excess to k.  However, this
   number is small in practice when an appropriate decoding scheme is
   used at the receiver [Cunche08].  Another key difference is the high
   encoding/decoding complexity of Reed-Solomon codecs compared to
   Raptor or LDPC-Staircase codes.  A difference of one or more orders
   of magnitude in terms of encoding/decoding speed exists between the
   Reed-Solomon and LDPC-Staircase software codecs
   [Cunche08][CunchePHD10].  Finally, Raptor and LDPC-Staircase codes
   are large block FEC codes, in the sense of [RFC3453], since they can
   efficiently deal with a large number of source symbols.

   The present document focuses on LDPC-Staircase codes that belong to
   the well-known class of "Low Density Parity Check" codes.  Because of
   their key features, these codes are a good solution in many
   situations, as detailed in Section 7.

   This document inherits from [RFC5170], Section 6 "Full Specification
   of the LDPC-Staircase Scheme", the specifications of the core LDPC-
   Staircase codes, and from Section 5.7 "Pseudo-Random Number
   Generator", the specifications of the PRNG used by these codes.
   Therefore, this document specifies only the information specific to
   the FECFRAME context and refers to [RFC5170] for the core
   specifications of the codes.  To that purpose, the present document
   introduces:

   o  the Fully Specified FEC Scheme with FEC Encoding ID 7 that
      specifies a simple way of using LDPC-Staircase codes in order to
      protect arbitrary Application Data Unit (ADU) flows.

   Therefore Sections 4 and 5 (except Section 5.7, see above) of
   [RFC5170], that define [RFC5052] specific Formats and Procedures, are
   not considered and are replaced by FECFRAME specific Formats and
   Procedures.

   Finally, publicly available reference implementations of these codes
   are available [LDPC-codec] [LDPC-codec-OpenFEC].

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.  Those in the
   list below 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.

   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 LDPC-Staircase 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.

   The following 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 the FEC Framework.  The FFCI enables the
      synchronization of the FECFRAME sender and receiver instances.

   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 optional Explicit Source
      FEC Payload ID.

   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
   +----------------------+                           +----------------+
   |    FEC Framework     |                           |                |
   |                      |-------------------------->|   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.  Those in the list below
   are FEC scheme specific:

   k      denotes the number of source symbols in a source block.

   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.

   CR     denotes the "code rate", i.e., the k/n ratio.

   N1     denotes the target number of "1s" per column in the left side
          of the parity check matrix.

   N1m3   denotes the value N1 - 3.

   G      G denotes the number of encoding symbols per group, i.e., the
          number of symbols sent in the same packet.

   a^^b   denotes a raised to the power b.

   The following 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    Application Data Unit

   ESI    Encoding Symbol ID

   FEC    Forward Error (or Erasure) Correction

   FFCI   FEC Framework Configuration Information

   FSSI   FEC Scheme-Specific Information

   LDPC   Low-Density Parity Check

   MDS    Maximum Distance Separable

   PRNG   Pseudo-Random Number Generator

   SDP    Session Description Protocol

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 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;

   o  the use of the LDPC-Staircase scheme is such that there MUST be
      exactly one encoding symbol per group; i.e., G MUST be equal to 1
      [RFC5170];

4.2.  ADU Block Creation

   Two kinds of limitations exist that impact the ADU block creation:

   o  at the FEC scheme level: the FEC scheme and the FEC codec have
      limitations that define a maximum source block size;

   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 the use of the terminology "maximum source block size" and
   "maximum ADU block size" depends 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 be
   exactly one source symbol per ADU.  We now detail each of these
   aspects.

   The maximum source block size in symbols, max_k, depends on several
   parameters: the code rate (CR) and the Encoding Symbol ID (ESI) field
   length in the Explicit Source/Repair FEC Payload ID (16 bits), as
   well as possible internal codec limitations.  More specifically,
   max_k cannot be larger than the following values, derived from the
   ESI field size limitation, for a given code rate:

      max1_k = 2^^(16 - ceil(Log2(1/CR)))

   Some common max1_k values are:

   o  CR == 1 (no repair symbol): max1_k = 2^^16 = 65536 symbols

   o  1/2 <= CR < 1: max1_k = 2^^15 = 32,768 symbols

   o  1/4 <= CR < 1/2: max1_k = 2^^14 = 16,384 symbols
   Additionally, a codec can impose other limitations on the maximum
   source block size, for instance, because of a limited working memory
   size.  This decision MUST be clarified at implementation time, when
   the target use-case is known.  This results in a max2_k limitation.

   Then, max_k is given by:

      max_k = min(max1_k, max2_k)

   Note that this calculation is only required at the encoder (sender),
   since the actual k parameter (k <= max_k) is communicated to the
   decoder (receiver) through the Explicit Source/Repair FEC Payload ID.

   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 its most general form, FECFRAME and the LDPC-Staircase 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).  This diversity must be
   addressed since the LDPC-Staircase FEC Scheme requires a constant
   encoding symbol size (E parameter) per source block.  Since this
   specification requires that there be 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 three (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 three (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.  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 two 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.

                        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.  LDPC-Staircase FEC Scheme for Arbitrary ADU 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).  More specifically, it enables the 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 7, as assigned by IANA (Section 8).

   When SDP is used to communicate the FFCI, this FEC Encoding ID is
   carried in the 'encoding-id' parameter.

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  PRNG seed (seed): a non-negative 32-bit integer used as the seed
      of the Pseudo-Random Number Generator, as defined in [RFC5170].

   o  Encoding symbol length (E): a non-negative integer 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  N1 minus 3 (n1m3): an integer between 0 (default) and 7,
      inclusive.  The number of "1s" per column in the left side of the
      parity check matrix, N1, is then equal to N1m3 + 3, as specified
      in [RFC5170].

   These elements are required both by the sender (LDPC-Staircase
   encoder) and the receiver(s) (LDPC-Staircase decoder).

   When SDP is used to communicate the FFCI, this FEC scheme-specific
   information is carried in the 'fssi' parameter in textual
   representation as specified in [RFC6364].  For instance:

   fssi=seed:1234,E:1400,S:0,n1m3:0

   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 7 octets:

   o  PRNG seed (seed): 32-bit field.

   o  Encoding symbol length (E): 16-bit field.

   o  Strict (S) flag: 1-bit field.

   o  Reserved: a 4-bit field that MUST be set to zero.

   o  N1m3 parameter (n1m3): 3-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
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                      PRNG seed (seed)                         |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |   Encoding Symbol Length (E)  |S| resvd | n1m3|
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      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
   following fields (Figure 5):

   o  Source Block Number (SBN) (16-bit field): this field identifies
      the source block to which this FEC source packet belongs.

   o  Encoding Symbol ID (ESI) (16-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.

   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.

    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 (SBN)   |   Encoding Symbol ID (ESI)    |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |    Source Block Length (k)    |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

              Figure 5: Source FEC Payload ID Encoding Format

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 6.  There
   MUST be a single repair symbol per FEC repair packet.
                  +--------------------------------+
                  |           IP Header            |
                  +--------------------------------+
                  |        Transport Header        |
                  +--------------------------------+
                  |     Repair FEC Payload ID      |
                  +--------------------------------+
                  |         Repair Symbol          |
                  +--------------------------------+

              Figure 6: Structure of a FEC Repair Packet with
                           the Repair Payload ID

   More precisely, the Repair FEC Payload ID is composed of the
   following fields (Figure 7):

   o  Source Block Number (SBN) (16-bit field): this field identifies
      the source block to which the FEC repair packet belongs.

   o  Encoding Symbol ID (ESI) (16-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.

   o  Number of Encoding Symbols (n) (16-bit field): this field provides
      the number of encoding symbols for this source block, i.e., the n
      parameter.

    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 (SBN)   |   Encoding Symbol ID (ESI)    |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |    Source Block Length (k)    |  Number Encoding Symbols (n)  |
   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

              Figure 7: Repair FEC Payload ID Encoding Format

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^^16
      - 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 [RFC5170] the specification of the
   core LDPC-Staircase codes for a packet erasure transmission channel
   (see Section 1).

   Because of the requirement to have exactly one encoding symbol per
   group, i.e., because G MUST be equal to 1 (Section 4.1), several
   parts of [RFC5170] are not of use.  In particular, this is the case
   of Section 5.6, "Identifying the G Symbols of an Encoding Symbol
   Group".

6.  Security Considerations

   The FEC Framework 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 LDPC-Staircase codes.

6.1.  Attacks against the Data Flow

6.1.1.  Access to Confidential Content

   The LDPC-Staircase 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] be used, with special considerations
   to the way this solution is applied (e.g., Is encryption applied
   before or after FEC protection?  Is it 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.

6.1.2.  Content Corruption

   The LDPC-Staircase 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] be 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.  Contrarily, 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  N1 minus 3 (n1m3): changing this parameter leads the receiver to
      consider a different code, which enables an attacker to create a
      DoS.

   Therefore, it is RECOMMENDED that security measures be 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), or the Number Encoding Symbols (n), 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 be 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 LDPC-Staircase FEC Scheme specified in this document does not
   change the recommendations of [RFC6363].

6.4.  Baseline Secure FEC Framework Operation

   The LDPC-Staircase 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 the FEC
   Framework operates.

7.  Operations and Management Considerations

   The FEC Framework 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 LDPC-Staircase codes as specified in
   this document.

7.1.  Operational Recommendations

   LDPC-Staircase codes have excellent erasure recovery capabilities
   with large source blocks, close to ideal MDS codes.  For instance,
   independently of FECFRAME, let us consider a source block of size
   k=1024 symbols, CR=2/3 (i.e., 512 repair symbols are added), N1=7,
   G=1, a transmission scheme where all the symbols are sent in a random
   order, and a hybrid ITerative/Maximum Likelihood (IT/ML) decoder (see
   below).  An ideal MDS code with code rate 2/3 can recover from
   erasures up to a 33.33% channel loss rate.  With LDPC-Staircase
   codes, the average overhead amounts to 0.237% (i.e., receiving 2.43
   symbols in addition to k, which corresponds to a 33.18% channel loss
   rate, enables a successful decoding with a probability 0.5), and an
   overhead of 1.46% (i.e., receiving 15 symbols in addition to k, which
   corresponds to a 32.36% channel loss rate) is sufficient to reduce
   the probability that decoding fails down to 8.2*10^^-5.  This is why
   these codes are a good solution to protect a single high bitrate
   source flow as in [Matsuzono10] or to protect globally several mid-
   rate source flows within a single FECFRAME instance: in both cases,
   the source block size can be assumed to be equal to a few hundred (or
   more) source symbols.

   LDPC-Staircase codes are also a good solution whenever the processing
   load at a software encoder or decoder must be kept to a minimum.
   This is true when the decoder uses an IT decoding algorithm, an ML
   algorithm (we use a Gaussian Elimination as the ML algorithm) when
   carefully implemented, or a mixture of both techniques, which is the
   recommended solution [Cunche08][CunchePHD10][LDPC-codec-OpenFEC].
   Let us consider the same conditions as above (k=1024 source symbols,
   CR=2/3, N1=7, G=1), with encoding symbols of size 1024 bytes.  With
   an Intel Xeon 5120/1.86 GHz workstation running Linux/64 bits, the
   average decoding speed is between 1.78 Gbps (overhead of 2 symbols in
   addition to k, corresponding to a very bad channel with a 33.20% loss
   rate, close to the theoretical decoding limit, where ML decoding is
   required) and 3.91 Gbps (corresponding to a good channel with a 5%
   loss rate only, where IT decoding is sufficient).  Under the same
   conditions, on a Samsung Galaxy SII smartphone (GT-I9100P model,
   featuring an ARM Cortex-A9/1.2 GHz processor and running Android
   2.3.4), the decoding speed is between 397 Mbps (bad channel with a
   33.20% loss rate, close to the theoretical decoding limit) and 813
   Mbps (good channel with a 5% loss rate only).

   As the source block size decreases, the erasure recovery capabilities
   of LDPC codes in general also decrease.  In the case of LDPC-
   Staircase codes, in order to limit this phenomenon, it is recommended
   to use a value of the N1 parameter at least equal to 7 (e.g.,
   experiments carried out in [Matsuzono10] use N1=7 if k=170 symbols,
   and N1=5 otherwise).  For instance, independently of FECFRAME, with a
   source block of size k=256 symbols, CR=2/3 (i.e., 128 repair symbols
   are added), N1=7, and G=1, the average overhead amounts to 0.706%
   (i.e., receiving 1.8 symbols in addition to k enables a successful
   decoding with a probability 0.5), and an overhead of 5.86% (i.e.,
   receiving 15 symbols in addition to k) is sufficient to reduce the
   decoding failure probability to 5.9*10^^-5.

   The processing load also decreases with the source block size.  For
   instance, under these conditions (k=256 source symbols, CR=2/3, N1=7,
   and G=1), with encoding symbols of size 1024 bytes, on a Samsung
   Galaxy SII smartphone, the decoding speed is between 518 Mbps (bad
   channel) and 863 Mbps (good channel with a 5% loss rate only).

   With very small source blocks (e.g., a few tens of symbols), using
   for instance Reed-Solomon codes [SIMPLE_RS] or 2D parity check codes
   may be more appropriate.

   The way the FEC repair packets are transmitted is of high importance.
   A good strategy, that works well for any kind of channel loss model,
   consists in sending FEC repair packets in random order (rather than
   in sequence) while FEC source packets are sent first and in sequence.
   Sending all packets in a random order is another possibility, but it
   requires that all repair symbols for a source block be produced
   first, which adds some extra delay at a sender.

8.  IANA Considerations

   This document registers one value in the "FEC Framework (FECFRAME)
   FEC Encoding IDs" registry [RFC6363] as follows:

   o  7 refers to the Simple LDPC-Staircase FEC Scheme for Arbitrary
      Packet Flows, as defined in Section 5 of this document.

9.  Acknowledgments

   The authors want to thank K. Matsuzono, J. Detchart, and H. Asaeda
   for their contributions in evaluating the use of LDPC-Staircase codes
   in the context of FECFRAME [Matsuzono10].

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.

   [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.

   [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

   [Cunche08]   Cunche, M. and V. Roca, "Optimizing the Error Recovery
                Capabilities of LDPC-Staircase Codes Featuring a
                Gaussian Elimination Decoding Scheme",  10th IEEE
                International Workshop on Signal Processing for Space
                Communications (SPSC'08), October 2008.

   [CunchePHD10]
                Cunche, M., "High performances AL-FEC codes for the
                erasure channel : variation around LDPC codes", PhD
                dissertation (in French) (http://
                tel.archives-ouvertes.fr/tel-00451336/en/), June 2010.

   [LDPC-codec]
                Cunche, M., Roca, V., Neumann, C., and J.  Laboure,
                "LDPC-Staircase/LDPC-Triangle Codec Reference
                Implementation", INRIA Rhone-Alpes and
                STMicroelectronics,
                <http://planete-bcast.inrialpes.fr/>.

   [LDPC-codec-OpenFEC]
                "The OpenFEC project", <http://openfec.org/>.

   [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.

   [RFC3453]    Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley,
                M., and J. Crowcroft, "The Use of Forward Error
                Correction (FEC) in Reliable Multicast", RFC 3453,
                December 2002.

   [RFC5052]    Watson, M., Luby, M., and L. Vicisano, "Forward Error
                Correction (FEC) Building Block", RFC 5052, August 2007.

   [RFC5053]    Luby, M., Shokrollahi, A., Watson, M., and T.
                Stockhammer, "Raptor Forward Error Correction Scheme for
                Object Delivery", RFC 5053, October 2007.

   [RFC5510]    Lacan, J., Roca, V., Peltotalo, J., and S.  Peltotalo,
                "Reed-Solomon Forward Error Correction (FEC) Schemes",
                RFC 5510, April 2009.

   [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.

   [SIMPLE_RS]  Roca, V., Cunche, M., Lacan, J., Bouabdallah, A., and K.
                Matsuzono, "Simple Reed-Solomon Forward Error Correction
                (FEC) Scheme for FECFRAME", Work in Progress, October
                2012.

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/