Random Linear Codes (RLC) Forward Error Correction (FEC) Scheme for FECFRAME
draft-roca-tsvwg-rlc-fec-scheme-00

Abstract

This document describes a fully-specified FEC scheme for the convolutional Random Linear Codes (RLC) over GF(2^^m), where m equals 1 (binary case), 4 or 8, that can be used to protect arbitrary media streams along the lines defined by FECFRAME extended to convolutional codes. These convolutional FEC codes rely on an encoding window that slides over the source symbols, generating new repair symbols whenever needed. Compared to block FEC codes, these convolutional FEC codes offer key advantages in terms of reduced FEC-related latency while often providing improved erasure recovery capabilities.

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Table of Contents

• 1. Introduction
• 1.1. Limits of Block Codes with Real-Time Flows
• 1.2. Lower Latency and Better Protection with RLC Convolutional Codes
• 1.3. Small Transmission Overheads with the RLC FEC Scheme
• 1.4. Document Organization
• 2. Definitions and Abbreviations
• 3. Procedures
• 3.1. RLC parameters derivation
• 3.2. ADU, ADUI and Source Symbols Mappings
• 3.3. Encoding Window Management
• 3.4. Pseudo-Random Number Generator
• 3.5. Coding Coefficients Generation Function
• 4. RLC FEC Scheme for Arbitrary ADU Flows
• 4.1. Formats and Codes
• 4.1.1. FEC Framework Configuration Information
• 4.1.2. Explicit Source FEC Payload ID
• 4.1.3. Repair FEC Payload ID
• 4.1.4. Additional Procedures
• 5. FEC Code Specification
• 6. Implementation Status
• 7. Security Considerations
• 8. Operations and Management Considerations
• 9. IANA Considerations
• 10. Acknowledgments
• 11. References
• 11.1. Normative References
• 11.2. Informative References
• Appendix A. Decoding Beyond Maximum Latency Optimization
• Author's Address

1. Introduction

Application-Level Forward Erasure Correction (AL-FEC) codes are a key element of telecommunication systems. They are used to recover from packet erasures during content delivery sessions to a large number of receivers (multicast/broadcast transmissions). This is the case with the FLUTE/ALC protocol [RFC6726] in case of reliable file transfers over lossy networks, and the FECFRAME protocol for reliable continuous media transfers over lossy networks.

The present document focusses only on the FECFRAME protocol, used in multicast/broadcast delivery mode, with contents that feature stringent real-time constraints: each source packet has a maximum validity period after which it will not be considered by the destination application.

1.1. Limits of Block Codes with Real-Time Flows

With FECFRAME, there is a single FEC encoding point (either a end-host/server (source) or a middlebox) and a single FEC decoding point (either a end-host (receiver) or middlebox). In this context, currently standardized AL-FEC codes for FECFRAME like Reed-Solomon [RFC6865], LDPC-Staircase [RFC6816], or Raptor/RaptorQ, are all linear block codes: they require the data flow to be segmented into blocks of a predefined maximum size. The block size is a balance between robustness (in particular in front of long erasure bursts for which there is an incentive to increase the block size) and maximum decoding latency (for which there is an incentive to decrease the block size). Therefore, with a multicast/broadcast session, the block code is dimensioned by considering the worst communication channel one wants to support, and this choice impacts all receivers, no matter their individual channel quality.

1.2. Lower Latency and Better Protection with RLC Convolutional Codes

This document introduces a fully-specified FEC scheme that follows a totally different approach: the Random Linear Codes (RLC) over GF(2^^m), where m equals 1, 4 or 8. This FEC scheme is used to protect arbitrary media streams along the lines defined by FECFRAME extended to convolutional codes [fecframe-ext]. This FEC scheme is extremmely efficient in case of media with real-time constraints, sent within a multicast/broadcast session.

The RLC codes belong to the broad class of convolutional AL-FEC codes. The encoding process is based on an encoding window that slides over the set of source packets (in fact source symbols as we will see in Section 3.2), and which is either of fixed or variable size (elastic window). Repair packets (symbols) are generated and sent on-the-fly, after computing a random linear combination of the source symbols present in the current encoding window.

At the receiver, a linear system is managed from the set of received source and repair packets. New variables (representing source symbols) and equations (representing the linear combination of each repair symbol received) are added upon receiving new packets. Variables are removed when they are too old with respect to their validity period (real-time constraints), as well as the associated equations they are involved in (Appendix A introduces an optimisation that extends the time a variable is considered in the system). Erased source symbols are then recovered thanks this linear system whenever its rank permits it.

With RLC (more generally with convolutional codes), the protection of a multicast/broadcast session also needs to be dimensioned by considering the worst communication channel one wants to support. However the receivers experiencing a good to medium channel quality observe a FEC-related latency close to zero [Roca16] since an isolated erased source packet is quickly recovered by the following repair packet. On the opposite, with a block code, recovering an isolated erased source packet always requires waiting the end of the block for the first repair packet to arrive. Additionally, under certain situations (e.g., with a limited FEC-related latency budget and with constant bit rate transmissions after FECFRAME encoding), convolutional codes achieve more easily a target transmission quality (e.g., measured by the residual loss after FEC decoding) by sending fewer repair packets (i.e., higher code rate) than block codes.

1.3. Small Transmission Overheads with the RLC FEC Scheme

The RLC FEC scheme is designed so as to reduce the transmission overhead. The main requirement is that each repair packet header must enable a receiver to reconstruct the list of source symbols and the associated random coefficients used during the encoding process. In order to minimize packet overhead, the set of symbols in the encoding window as well as the set of coefficients over GF(2^^m) used in the linear combination are not individually listed in the repair packet header. Instead, each FEC repair packet header contains:

• the Encoding Symbol Identifier (ESI) of the first source symbol in the encoding window as well as the number of symbols (since this number may vary with a variable size, elastic window). These two pieces of information enable each receiver to easily reconstruct the set of source symbols considered during encoding, the only constraint being that there cannot be any gap;
• the seed used by a coding coefficients generation function (Section 3.5). This information enables each receiver to generate the same set of coding coefficients over GF(2^^m) as the sender;

Therefore, no matter the number of source symbols present in the encoding window, each FEC repair packet features a fixed 64-bit long header, also called Repair FEC Payload ID (Figure 7). Similarly, each FEC source packet features a fixed 32-bit lon trailer, also called Explicit Source FEC Payload ID (Figure 5), that contains the ESI of the first source symbol (see the ADUI and source symbol mapping, Section 3.2).

1.4. Document Organization

This fully-specified FEC scheme follows the structure required by [RFC6363], section 5.6. "FEC Scheme Requirements", namely:

3. Procedures:

This section describes procedures specific to this FEC scheme, namely: RLC parameters derivation, ADUI and source symbols mapping, pseudo-random number generator, and coding coefficients generation function;

4. Formats and Codes:

This section defines the Source FEC Payload ID and Repair FEC Payload ID formats, carrying the signaling information associated to each source or repair symbol. It also defines the FEC Framework Configuration Information (FFCI) carrying signaling information for the session;

5. FEC Code Specification:

Finally this section provides the code specification.

2. Definitions and Abbreviations

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 [RFC2119].

This document uses the following definitions and abbreviations:

ADU:

Application Data Unit

E:

encoding symbol size (i.e., source or repair symbol), assumed fixed (in bytes)

bw_out:

transmission bandwidth at the output of the FECFRAME sender, assumed fixed (in bits/s)

max_lat:

maximum FEC-related latency within FECFRAME (in seconds)

cr:

AL-FEC coding rate

plr:

packet loss rate on the erasure channel

ew_size:

encoding window current size at a sender (in symbols)

ew_max_size:

encoding window maximum size at a sender (in symbols)

dw_size:

decoding window current size at a receiver (in symbols).

dw_max_size:

decoding window maximum size at a receiver (in symbols)

ls_max_size:

linear system maximum size (or width) at a receiver (in symbols)

ls_size:

linear system current size (or width) at a receiver (in symbols)

PRNG:

pseudo-random number generator

pmms_rand(maxv):

PRNG defined in Section 3.4 and used in this specification, that returns a new random integer in [0; maxv-1]

3. Procedures

This section introduces the procedures that are used by this FEC scheme.

3.1. RLC parameters derivation

The RLC FEC Scheme relies on several key internal parameters:

Maximum FEC-related latency budget, max_lat (in seconds)

A source ADU flow can have real-time constraints, and therefore any FECFRAME related operation must take place within the validity period of each ADU. When there are multiple flows with different real-time constraints, we consider the most stringent constraints (see [RFC6363], Section 10.2, item 6, for recommendations when several flows are globally protected). This maximum FEC-related latency accounts for all sources of latency added by FEC encoding (sender) and FEC decoding (receiver). Any other source of latency (e.g., added by network communications) is not considered in this latency budget; It can be regarded as the latency budget permitted for all FEC-related operations. This is also an input parameter that enables to derive other internal parameters;

Encoding window current (resp. maximum) size, ew_size (resp. ew_max_size) (in symbols):

these parameters are used by a sender during FEC encoding. More precisely, each repair symbol is a linear combination of the ew_size source symbols present in the encoding window when RLC encoding took place. In all situations, we MUST have ew_size ≤ ew_max_size;

Decoding window current (resp. maximum) size, dw_size (resp. dw_max_size) (in symbols):

these parameters are used by a receiver when managing the linear system used for decoding. dw_size is the current size of the decoding window, i.e., the set of received or erased source symbols that are currently part of the linear system. In all situations, we MUST have dw_size ≤ dw_max_size;

In order to comply with the maximum FEC-related latency budget, assuming a constant transmission bandwidth at the output of the FECFRAME sender (bw_out), encoding symbol size (E), and code rate (cr), we have:

• dw_max_size = (max_lat * bw_out * cr) / (8 * E)

This dw_max_size defines the maximum delay after which an old source symbol may be recovered: after this delay, this old source symbol symbol will be removed from the decoding window.

It is often good practice to choose:

• ew_max_size = dw_max_size / 2

However any value ew_max_size < dw_max_size can be used without impact on the FEC-related latency budget. Finding the optimal value can depend on the erasure channel one wants to support and should be determined after simulations or field trials.

Note that the decoding beyond maximum latency optimisation (Appendix A) enables an old source symbol to be kept in the linear system beyond the FEC-related latency budget, but not delivered to the receiving application. Here we have: ls_size ≥ dw_max_size

3.2. ADU, ADUI and Source Symbols Mappings

An ADU, coming from the application, cannot be mapped to source symbols directly. Indeed, an erased ADU recovered at a receiver must contain enough information to be assigned to the right application flow (UDP port numbers and IP addresses cannot be used to that purpose as they are not protected by FEC encoding). This requires adding the flow identifier to each ADU before doing FEC encoding.

Additionally, since ADUs are of variable size, padding is needed so that each ADU (with its flow identifier) contribute to an integral number of source symbols. This requires adding the original ADU length to each ADU before doing FEC encoding. Because of these requirements, an intermediate format, the ADUI, or ADU Information, is considered [RFC6363].

For each incoming ADU, an ADUI is created as follows. First of all, 3 bytes are prepended: (Figure 1):

Flow ID (F) (8-bit field):

this unsigned byte contains the integer identifier associated to the source ADU flow to which this ADU belongs. It is assumed that a single byte is sufficient, which implies that no more than 256 flows will be protected by a single FECFRAME instance.

Length (L) (16-bit field):

this unsigned integer 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, L, or Pad fields.

Then, zero padding is added to ADU if needed:

Padding (Pad) (variable size field):

this field contains zero padding to align the F, L, ADU and padding up to a size that is multiple of E bytes (i.e., the source and repair symbol length).

Each ADUI contributes to an integral number of source symbols. The data unit resulting from the ADU and the F, L, and Pad fields is called ADU Information (or ADUI). Since ADUs can be of different size, this is also the case for ADUIs.

   symbol length, E              E                     E
< ------------------ >< ------------------ >< ------------------ >
+-+--+---------------------------------------------+-------------+
|F| L|                     ADU                     |     Pad     |
+-+--+---------------------------------------------+-------------+

<CODE BEGINS>
/*
 * Fills in the table of coding coefficients (of the right size)
 * provided with the appropriate number of coding coefficients to
 * use for the repair symbol key provided.
 *
 * (in) repair_key    key associated to this repair symbol
 * (in) cc_tab[]      pointer to a table of the right size to store
 *                    coding coefficients. All coefficients are
 *                    stored as bytes, regardless of the m parameter,
 *                    upon return of this function.
 * (in) cc_nb[]       number of entries in the table. This value is
 *                    equal to the current encoding window size.
 * (in) m             Finite Field GF(2^^m) parameter.
 * (out)              returns an error code
 */
int generate_coding_coefficients (UINT16    repair_key,
                                  UINT8     cc_tab[],
                                  UINT16    cc_nb,
                                  UINT8     m)
{
    UINT32    i;

    if (repair_key == 0) {
        return SOMETHING_WENT_WRONG;
    }
    pmms_srand(repair_key);
    if (m == 1) {
        /* 0 is a valid coefficient value in binary GF */
        for (i = 0 ; i < cc_nb ; i ++) {
            cc_tab[i] = (UINT8) pmms_rand(2);
        }
    } else {
        /* coefficient 0 is avoided in non-binary GF to consider each
         * source symbol */
        UINT32    maxv;
        maxv = get_gf_size(); /* i.e., 16 if m=4 or 256 if m=8 */
        for (i = 0 ; i < cc_nb ; i ++) {
            do {
                cc_tab[i] = (UINT8) pmms_rand(maxv);
            } while (cc_tab[i] == 0)
        }
    }
    return EVERYTHING_IS_OKAY;
}
<CODE ENDS>

 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|   Encoding Symbol Length (E)  |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
  

+--------------------------------+
|           IP Header            |
+--------------------------------+
|        Transport Header        |
+--------------------------------+
|              ADU               |
+--------------------------------+
| Explicit Source FEC Payload ID |
+--------------------------------+
  

 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                   Encoding Symbol ID (ESI)                    |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
  

+--------------------------------+
|           IP Header            |
+--------------------------------+
|        Transport Header        |
+--------------------------------+
|     Repair FEC Payload ID      |
+--------------------------------+
|         Repair Symbol          |
+--------------------------------+
  

 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|       Repair_Key              |  NSS (# source symbols in ew) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                            FSS_ESI                            |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
  

                             ls_max_size
/---------------------------------^-------------------------------\

        late source symbols
 (pot. decoded but not delivered)            dw_max_size
/--------------^-----------------\ /--------------^---------------\
src0 src1 src2 src3 src4 src5 src6 src7 src8 src9 src10 src11 src12