TSVWG V. Roca
Internet-Draft B. Teibi
Intended status: Standards Track INRIA
Expires: November 7, 2018 May 6, 2018
Sliding Window Random Linear Code (RLC) Forward Erasure Correction (FEC)
Schemes for FECFRAME
draft-ietf-tsvwg-rlc-fec-scheme-03
Abstract
This document describes two fully-specified Forward Erasure
Correction (FEC) Schemes for Sliding Window Random Linear Codes
(RLC), one for RLC over GF(2) (binary case), a second one for RLC
over GF(2^^8), both of them with the possibility of controlling the
code density. They can protect arbitrary media streams along the
lines defined by FECFRAME extended to sliding window FEC codes.
These sliding window 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 sliding window FEC codes
offer key advantages with real-time flows in terms of reduced FEC-
related latency while often providing improved packet erasure
recovery capabilities.
Status of This Memo
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Copyright Notice
Copyright (c) 2018 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Limits of Block Codes with Real-Time Flows . . . . . . . 3
1.2. Lower Latency and Better Protection of Real-Time Flows
with the Sliding Window RLC Codes . . . . . . . . . . . . 4
1.3. Small Transmission Overheads with the Sliding Window RLC
FEC Scheme . . . . . . . . . . . . . . . . . . . . . . . 5
1.4. Document Organization . . . . . . . . . . . . . . . . . . 6
2. Definitions and Abbreviations . . . . . . . . . . . . . . . . 6
3. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1. Possible Parameter Derivation . . . . . . . . . . . . . . 7
3.1.1. Detailed Parameter Derivation for CBR Real-Time Flows 8
3.1.2. Parameter Derivation for Other Real-Time Flows . . . 10
3.1.3. Parameter Derivation for Non Real-Time Flows . . . . 10
3.2. ADU, ADUI and Source Symbols Mappings . . . . . . . . . . 11
3.3. Encoding Window Management . . . . . . . . . . . . . . . 12
3.4. Pseudo-Random Number Generator . . . . . . . . . . . . . 13
3.5. Coding Coefficients Generation Function . . . . . . . . . 14
3.6. Linear Combination of Source Symbols Computation . . . . 16
4. Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary ADU
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 17
4.1.1. FEC Framework Configuration Information . . . . . . . 17
4.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 18
4.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 19
4.1.4. Additional Procedures . . . . . . . . . . . . . . . . 20
5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary ADU
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 21
5.1.1. FEC Framework Configuration Information . . . . . . . 21
5.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 21
5.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 21
5.1.4. Additional Procedures . . . . . . . . . . . . . . . . 21
6. FEC Code Specification . . . . . . . . . . . . . . . . . . . 21
6.1. Encoding Side . . . . . . . . . . . . . . . . . . . . . . 21
6.2. Decoding Side . . . . . . . . . . . . . . . . . . . . . . 22
7. Implementation Status . . . . . . . . . . . . . . . . . . . . 23
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8. Security Considerations . . . . . . . . . . . . . . . . . . . 23
8.1. Attacks Against the Data Flow . . . . . . . . . . . . . . 24
8.1.1. Access to Confidential Content . . . . . . . . . . . 24
8.1.2. Content Corruption . . . . . . . . . . . . . . . . . 24
8.2. Attacks Against the FEC Parameters . . . . . . . . . . . 24
8.3. When Several Source Flows are to be Protected Together . 25
8.4. Baseline Secure FEC Framework Operation . . . . . . . . . 25
9. Operations and Management Considerations . . . . . . . . . . 25
9.1. Operational Recommendations: Finite Field GF(2) Versus
GF(2^^8) . . . . . . . . . . . . . . . . . . . . . . . . 25
9.2. Operational Recommendations: Coding Coefficients Density
Threshold . . . . . . . . . . . . . . . . . . . . . . . . 25
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 26
11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 26
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 26
12.1. Normative References . . . . . . . . . . . . . . . . . . 26
12.2. Informative References . . . . . . . . . . . . . . . . . 27
Appendix A. Decoding Beyond Maximum Latency Optimization . . . . 29
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 30
1. Introduction
Application-Level Forward Erasure Correction (AL-FEC) codes, or
simply FEC codes, are a key element of communication systems. They
are used to recover from packet losses (or erasures) during content
delivery sessions to a large number of receivers (multicast/broadcast
transmissions). This is the case with the FLUTE/ALC protocol
[RFC6726] when used for reliable file transfers over lossy networks,
and the FECFRAME protocol when used for reliable continuous media
transfers over lossy networks.
The present document only focusses 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.
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To define this block size, it is required to find an appropriate
balance between robustness and decoding latency: the larger the block
size, the higher the robustness (e.g., in front of long packet
erasure bursts), but also the higher the maximum decoding latency
(i.e., the maximum time required to recover a lost (erased) packet
thanks to FEC protection). Therefore, with a multicast/broadcast
session where different receivers experience different packet loss
rates, the block size should be chosen by considering the worst
communication conditions one wants to support, but without exceeding
the desired maximum decoding latency. This choice then impacts the
FEC-related latency of all receivers, even those experiencing a good
communication quality, since no FEC encoding can happen until all the
source data of the block is available at the sender, which directly
depends on the block size.
1.2. Lower Latency and Better Protection of Real-Time Flows with the
Sliding Window RLC Codes
This document introduces two fully-specified FEC Schemes that follow
a totally different approach: the Sliding Window Random Linear Codes
(RLC) over either Finite Field GF(2) or GF(8). These FEC Schemes are
used to protect arbitrary media streams along the lines defined by
FECFRAME extended to sliding window FEC codes [fecframe-ext]. These
FEC Schemes, and more generally Sliding Window FEC codes, are
recommended for instance with media that feature real-time
constraints sent within a multicast/broadcast session [Roca17].
The RLC codes belong to the broad class of sliding window AL-FEC
codes (A.K.A. convolutional 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 on-the-fly, computing a random linear
combination of the source symbols present in the current encoding
window, and passed to the transport layer.
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 optimization
that extends the time a variable is considered in the system). Lost
source symbols are then recovered thanks to this linear system
whenever its rank permits it.
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With RLC codes (more generally with sliding window codes), the
protection of a multicast/broadcast session also needs to be
dimensioned by considering the worst communication conditions one
wants to support. However the receivers experiencing a good to
medium communication quality will observe a reduced FEC-related
latency compared to block codes [Roca17] since an isolated lost
source packet is quickly recovered with the following repair packet.
On the opposite, with a block code, recovering an isolated lost
source packet always requires waiting for the first repair packet to
arrive after the end of the block. Additionally, under certain
situations (e.g., with a limited FEC-related latency budget and with
constant bitrate transmissions after FECFRAME encoding), sliding
window codes can more efficiently achieve 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 Sliding Window RLC FEC
Scheme
The Sliding Window RLC FEC Scheme is designed to limit the packet
header overhead. The main requirement is that each repair packet
header must enable a receiver to reconstruct the set of source
symbols plus the associated coefficients used during the encoding
process. In order to minimize packet overhead, the set of source
symbols in the encoding window as well as the set of coefficients
over GF(2^^m) (where m is 1 or 8, depending on the FEC Scheme) used
in the linear combination are not individually listed in the repair
packet header. Instead, each FEC Repair Packet header contains:
o 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 reconstruct the set
of source symbols considered during encoding, the only constraint
being that there cannot be any gap;
o 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, called Repair FEC Payload ID (Figure 7). Similarly, each FEC
Source Packet features a fixed 32-bit long trailer, 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).
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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 signalling
information associated to each source or repair symbol. It also
defines the FEC Framework Configuration Information (FFCI)
carrying signalling 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:
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 equal to 1 or 8
ADU: Application Data Unit
ADUI: Application Data Unit Information (includes the F, L and
padding fields in addition to the ADU)
E: size of an encoding symbol (i.e., source or repair symbol),
assumed fixed (in bytes)
br_in: transmission bitrate at the input of the FECFRAME sender,
assumed fixed (in bits/s)
br_out: transmission bitrate at the output of the FECFRAME sender,
assumed fixed (in bits/s)
max_lat: maximum FEC-related latency within FECFRAME (in seconds)
cr: RLC coding rate, ratio between the total number of source
symbols and the total number of source plus repair symbols
ew_size: encoding window current size at a sender (in symbols)
ew_max_size: encoding window maximum size at a sender (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)
PRNG: pseudo-random number generator
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pmms_rand(maxv): PRNG defined in Section 3.4 and used in this
specification, that returns a new random integer in [0; maxv-1]
DT: coding coefficients density threshold, an integer between 0 and
15 (inclusive) the controls the fraction of coefficients that are
non zero
3. Procedures
This section introduces the procedures that are used by these FEC
Schemes.
3.1. Possible Parameter Derivation
The Sliding Window RLC FEC Scheme relies on several 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). The maximum FEC-related
latency budget, max_lat, accounts for all sources of latency added
by FEC encoding (at a sender) and FEC decoding (at a receiver).
Other sources of latency (e.g., added by network communications)
are out of scope and must be considered separately (said
differently, they have already been deducted from max_lat).
max_lat can be regarded as the latency budget permitted for all
FEC-related operations. This is an input parameter that enables
to derive other internal parameters as explained below;
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. At session start, the encoding window will
probably be small and then progressively increase until it reaches
its maximum value. At any time:
ew_size <= ew_max_size
Decoding window maximum size, dw_max_size (in symbols): at a
receiver, this parameter denotes the maximum number of received or
lost source symbols in the linear system (i.e., the variables)
that are still within their latency budget;
Linear system maximum size, ls_max_size (in symbols): The linear
system maximum size managed by a receiver SHOULD NOT be smaller
than this decoding window maximum size, since it would mean that,
after receiving a sufficient number of FEC Repair Packets, an ADU
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may not be recovered just because it has been removed from the
linear system, and not because it has timed-out. This would be
counter-productive. On the opposite, the linear system MAY grow
beyond this value with old source symbols kept in the linear
system whereas their associated ADUs timed-out (Appendix A);
Symbol size, E (in bytes) and RLC code rate (cr): the E parameter
determines the source and repair symbol sizes (necessarily equal).
The cr parameter determines the code rate, i.e., the amount of
redundancy added to the flow (i.e., cr is the ratio between the
total number of source symbols and the total number of source plus
repair symbols). These two parameters are input parameters that
enable to derive other internal parameters as explained below. An
implementation at a sender SHOULD fix the E parameter and
communicate it as part of the FEC Scheme-Specific Information
(Section 4.1.1.2). However there is no need to communicate the cr
parameter per see (it's not required to process a repair packet at
a receiver). This code rate parameter can be fixed. However, in
specific use-cases (e.g., with unicast transmissions in presence
of a feedback mechanism that estimates the communication quality,
out-of-scope of FECFRAME), the code rate may be adjusted
dynamically.
The FEC Schemes specified in this document can be used in various
manners. They can protect one or more source ADU flows having real-
time constraints, or they can protect non-realtime source ADU flows.
The source ADU flows may be Constant Bitrate (CBR) flows, while other
may be of Variable Bitrate (VBR). The FEC Schemes can be used in
various environments like the Internet or over a CBR channel. It
follows that the FEC Scheme parameters can be derived in different
ways, as described in the following sections.
3.1.1. Detailed Parameter Derivation for CBR Real-Time Flows
In the following, we consider a real-time flow with max_lat latency
budget. The encoding symbol size (E, in bytes) is constant. The
code rate (cr) is also constant, in line with the expected
communication loss model. However the choice of this cr value is out
of scope for this document.
In a first configuration, the source ADU flow bitrate at the input of
the FECFRAME sender is fixed (br_in, in bits/s). It means that the
transmission bitrate at the output of the FECFRAME sender will be
higher, depending on the added repair flow overhead. In order to
comply with the maximum FEC-related latency budget, we have:
dw_max_size = (max_lat * br_in) / (8 * E)
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In a second configuration, the FECFRAME sender generates a fixed
bitrate flow, equal to the CBR channel bitrate (br_out, in bits/s),
as in [Roca17]. The maximum source flow bitrate needs to be such
that, with the added repair flow overhead, the total transmission
bitrate remains (inferior or) equal to br_out. Here we have:
dw_max_size = (max_lat * br_out * cr) / (8 * E)
For decoding to be possible, it is required that the encoding window
maximum size be at most equal to the decoding window maximum size.
So, once the dw_max_size has been determined, the ew_max_size SHOULD
be computed with ([Roca17]):
ew_max_size = dw_max_size * 0.75
The ew_max_size is the main parameter, used by a FECFRAME sender.
Whenever the FEC protection (i.e., cr value) is sufficient in front
of the packet loss model, the ew_max_size guaranties that the
recovery of lost ADUs will happen at a FECFRAME receiver on time.
The dw_max_size is computed by a FECFRAME sender but not explicitly
communicated to a FECFRAME receiver. However a FECFRAME receiver can
easily evaluate the ew_max_size by observing the maximum Number of
Source Symbols (NSS) value contained in the Repair FEC Payload ID of
received FEC Repair Packets (Section 4.1.3). A receiver can then
easily compute dw_max_size:
dw_max_size = max_NSS_observed / 0.75
and chose an appropriate maximum linear system size. Having a
limited linear system size is a practical requirement that enables to
forget old source symbols, no longer needed. We have:
ls_max_size >= dw_max_size
Using the same maximum size is the minimum. But it is good practice
to use a larger value for ls_max_size as explained in Appendix A,
without impacting maximum latency nor interoperability.
The particular case of session start needs to be managed
appropriately. Here the ew_size progressively increases, upon
receiving new source ADUs at the FECFRAME sender, until it reaches
the ew_max_size value, A FECFRAME receiver SHOULD continuously
observe the received FEC Repair Packets, since the NSS value carried
in the Repair FEC Payload ID will increase too, and adjust the
ls_max_size accordingly.
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3.1.2. Parameter Derivation for Other Real-Time Flows
There are situations where the real-time source ADU flow is of
variable bitrate (VBR). A first possibility is to consider the peak
bitrate of the source ADU flow, when this parameter is known, and to
reuse the derivation of Section 3.1.1.
There are also situations where the peak bitrate is not know. In
that case the previous parameter derivation cannot be directly
applied. An approach in that case consists in using ADU timing
information when present (e.g., using the timestamp field of an RTP
packet header) to manage the encoding window accordingly, in
particular removing old symbols whose associated ADUs timed-out.
No matter the choice of the FECFRAME sender, a FECFRAME receiver can
still easily evaluate the ew_max_size by observing the maximum Number
of Source Symbols (NSS) value contained in the Repair FEC Payload ID
of received FEC Repair Packets. A receiver can then compute
dw_max_size and derive an appropriate maximum linear system size,
ls_max_size.
When the observed NSS fluctuates significantly and perhaps slowly, a
FECFRAME receiver may want to adapt its ls_max_size accordingly in
order to avoid managing linear systems that would be significantly
too large. It is worth noticing however that it is preferable to use
an ls_max_size too large than the opposite.
Beyond these general guidelines, the details of how to manage these
situations at a FECFRAME sender and receiver remain out of scope of
this document.
3.1.3. Parameter Derivation for Non Real-Time Flows
Finally there are situations where there is no known real-time
constraints. FECFRAME and the FEC Schemes defined in this document
can still be used. The choice of appropriate parameter values can be
directed by practical considerations. It can be an estimation of the
maximum memory amount that could be dedicated to the linear system at
a FECFRAME receiver, or CPU computation requirements at a FECFRAME
receiver, both of them depending on the ls_max_size. The same
considerations can also apply to the FECFRAME sender, where maximum
memory and CPU computation requirements depend on the ew_max_size.
Here also, the NSS value contained in FEC Repair Packets is used to
inform a FECFRAME receiver of the current coding window size (and
ew_max_size by observing its maximum value over the time).
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Beyond these general guidelines, the details of how to manage these
situations at a FECFRAME sender and receiver remain out of scope of
this document.
3.2. ADU, ADUI and Source Symbols Mappings
At a sender, an ADU coming from the application cannot directly be
mapped to source symbols. When multiple source flows (e.g., media
streams) are mapped onto the same FECFRAME instance, each flow is
assigned its own Flow ID value (see below). At a sender, this
identifier is prepended to each ADU before FEC encoding. This way,
FEC decoding at a receiver also recovers this Flow ID and a recovered
ADU can be assigned to the right source flow (note that transport
port numbers and IP addresses cannot be used to that purpose as they
are not recovered during FEC decoding).
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 MUST 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 session instance.
Length (L) (16-bit field): this unsigned integer contains 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 the 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).
The data unit resulting from the ADU and the F, L, and Pad fields is
called ADUI. Since ADUs can have different sizes, this is also the
case for ADUIs. However an ADUI always contributes to an integral
number of source symbols.
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symbol length, E E E
< ------------------ >< ------------------ >< ------------------ >
+-+--+---------------------------------------------+-------------+
|F| L| ADU | Pad |
+-+--+---------------------------------------------+-------------+
Figure 1: ADUI Creation example (here 3 source symbols are created
for this ADUI).
Note that neither the initial 3 bytes nor the optional padding are
sent over the network. However, they are considered during FEC
encoding, and a receiver who lost a certain FEC Source Packet (e.g.,
the UDP datagram containing this FEC Source Packet when UDP is used
as the transport protocol) 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.
3.3. Encoding Window Management
Source symbols and the corresponding ADUs are removed from the
encoding window:
o when the sliding encoding window has reached its maximum size,
ew_max_size. In that case the oldest symbol MUST be removed
before adding a new symbol, so that the current encoding window
size always remains inferior or equal to the maximum size: ew_size
<= ew_max_size;
o when an ADU has reached its maximum validity duration in case of a
real-time flow. When this happens, all source symbols
corresponding to the ADUI that expired SHOULD be removed from the
encoding window;
Source symbols are added to the sliding encoding window each time a
new ADU arrives, once the ADU to source symbols mapping has been
performed (Section 3.2). The current size of the encoding window,
ew_size, is updated after adding new source symbols. This process
may require to remove old source symbols so that: ew_size <=
ew_max_size.
Note that a FEC codec may feature practical limits in the number of
source symbols in the encoding window (e.g., for computational
complexity reasons). This factor may further limit the ew_max_size
value, in addition to the maximum FEC-related latency budget
(Section 3.1).
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3.4. Pseudo-Random Number Generator
The RLC codes rely on the following Pseudo-Random Number Generator
(PRNG), identical to the PRNG used with LDPC-Staircase codes
([RFC5170], section 5.7).
The Park-Miler "minimal standard" PRNG [PM88] MUST be used. It
defines a simple multiplicative congruential algorithm: Ij+1 = A * Ij
(modulo M), with the following choices: A = 7^^5 = 16807 and M =
2^^31 - 1 = 2147483647. A validation criteria of such a PRNG is the
following: if seed = 1, then the 10,000th value returned MUST be
equal to 1043618065.
Several implementations of this PRNG are known and discussed in the
literature. An optimized implementation of this algorithm, using
only 32-bit mathematics, and which does not require any division, can
be found in [rand31pmc]. It uses the Park and Miller algorithm
[PM88] with the optimization suggested by D. Carta in [CA90]. The
history behind this algorithm is detailed in [WI08].
This PRNG produces, natively, a 31-bit value between 1 and 0x7FFFFFFE
(2^^31-2) inclusive. Since it is desired to scale the pseudo-random
number between 0 and maxv-1 inclusive, one must keep the most
significant bits of the value returned by the PRNG (the least
significant bits are known to be less random, and modulo-based
solutions should be avoided [PTVF92]). The following algorithm MUST
be used:
Input:
raw_value: random integer generated by the inner PRNG algorithm,
between 1 and 0x7FFFFFFE (2^^31-2) inclusive.
maxv: upper bound used during the scaling operation.
Output:
scaled_value: random integer between 0 and maxv-1 inclusive.
Algorithm:
scaled_value = (unsigned long) ((double)maxv * (double)raw_value /
(double)0x7FFFFFFF);
(NB: the above C type casting to unsigned long is equivalent to
using floor() with positive floating point values.)
In this document, pmms_rand(maxv) denotes the PRNG function that
implements the Park-Miller "minimal standard" algorithm, defined
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above, and that scales the raw value between 0 and maxv-1 inclusive,
using the above scaling algorithm.
Additionally, the pmms_srand(seed) function must be provided to
enable the initialization of the PRNG with a seed before calling
pmms_rand(maxv) the first time. The seed is a 31-bit integer between
1 and 0x7FFFFFFE inclusive. In this specification, the seed is
restricted to a value between 1 and 0xFFFF inclusive, as this is the
Repair_Key 16-bit field value of the Repair FEC Payload ID
(Section 4.1.3).
3.5. Coding Coefficients Generation Function
The coding coefficients, used during the encoding process, are
generated at the RLC encoder by the generate_coding_coefficients()
function each time a new repair symbol needs to be produced. The
fraction of coefficients that are non zero (i.e., the density) is
controlled by the DT (Density Threshold) parameter. When DT equals
15, the maximum value, the function guaranties that all coefficients
are non zero (i.e., maximum density). When DT is between 0 (minimum
value) and strictly inferior to 15, the average probability of having
a non zero coefficient equals (DT +1) / 16.
These considerations apply both the RLC over GF(2) and RLC over
GF(2^^8), the only difference being the value of the m parameter.
With the RLC over GF(2) FEC Scheme (Section 5), m MUST be equal to 1.
With RLC over GF(2^^8) FEC Scheme (Section 4), m MUST be equal to 8.
<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. This
* parameter is ignored (useless) if m=2 and dt=15
* (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) dt integer between 0 and 15 (inclusive) that
* controls the density. With value 15, all
* coefficients are guaranteed to be non zero
* (i.e. equal to 1 with GF(2) and equal to a
* value in {1,... 255} with GF(2^^8)), otherwise
* a fraction of them will be 0.
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* (in) m Finite Field GF(2^^m) parameter. In this
* document only values 1 and 8 are considered.
* (out) returns an error code
*/
int generate_coding_coefficients (UINT16 repair_key,
UINT8 cc_tab[],
UINT16 cc_nb,
UINT8 dt,
UINT8 m)
{
UINT32 i;
if (dt > 15) {
return SOMETHING_WENT_WRONG; /* bad dt parameter */
}
if (repair_key == 0 && dt != 15 && m != 2) {
return SOMETHING_WENT_WRONG; /* bad repair_key parameter */
}
switch (m) {
case 1:
if (dt == 15) {
/* all coefficients are 1 */
memset(cc_tab, 1, cc_nb);
} else {
/* here coefficients are either 0 or 1 */
pmms_srand(repair_key);
pmms_rand(16); /* skip the first PRNG value */
for (i = 0 ; i < cc_nb ; i++) {
if (pmms_rand(16) <= dt) {
cc_tab[i] = (UINT8) 1;
} else {
cc_tab[i] = (UINT8) 0;
}
}
}
break;
case 8:
pmms_srand(repair_key);
pmms_rand(256); /* skip the first PRNG value */
if (dt == 15) {
/* coefficient 0 is avoided here in order to include
* all the source symbols */
for (i = 0 ; i < cc_nb ; i++) {
do {
cc_tab[i] = (UINT8) pmms_rand(256);
} while (cc_tab[i] == 0);
}
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} else {
/* here a certain fraction of coefficients should be 0 */
for (i = 0 ; i < cc_nb ; i++) {
if (pmms_rand(16) <= dt) {
do {
cc_tab[i] = (UINT8) pmms_rand(256);
} while (cc_tab[i] == 0);
} else {
cc_tab[i] = 0;
}
}
}
break;
default:
/* bad parameter m */
return SOMETHING_WENT_WRONG;
}
return EVERYTHING_IS_OKAY;
}
<CODE ENDS>
Figure 2: Coding Coefficients Generation Function pseudo-code
One can note in the above function that each call to pmms_srand()
(PRNG initialisation) is immediately followed by a call to
pmms_rand() whose return value is ignored. This extra call is
motivated by a possible bias in the first value generated depending
on the way the repair key is managed by a FECFRAME implementation.
Indeed, the PRNG sequences produced by two seeds in sequence have a
high probability of starting with the same value since I1 = A * seed
(modulo M) which is further scaled to a small range (either {0, ...
15} or {0, ... 255}). Producing several times the same first coding
coefficient could reduce the protection of the first source symbol if
multiple repair symbols are produced with the same coding window's
left edge. The extra call avoids such side effects.
3.6. Linear Combination of Source Symbols Computation
The two RLC FEC Schemes require the computation of a linear
combination of source symbols, using the coding coefficients produced
by the generate_coding_coefficients() function and stored in the
cc_tab[] array.
With the RLC over GF(2^^8) FEC Scheme, a linear combination of the
ew_size source symbol present in the encoding window, say src_0 to
src_ew_size_1, in order to generate a repair symbol, is computed as
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follows. For each byte of position i in each source and the repair
symbol, where i belongs to {0; E-1}, compute:
repair[i] = cc_tab[0] * src_0[i] + cc_tab[1] * src_1[i] + ... +
cc_tab[ew_size - 1] * src_ew_size_1[i]
where * is the multiplication over GF(2^^8) and + is an XOR
operation. In practice various optimizations need to be used in
order to make this computation efficient (see in particular [PGM13]).
With the RLC over GF(2) FEC Scheme (binary case), a linear
combination is computed as follows. The repair symbol is the XOR sum
of all the source symbols corresponding to a coding coefficient
cc_tab[j] equal to 1 (i.e., the source symbols corresponding to zero
coding coefficients are ignored). The XOR sum of the byte of
position i in each source is computed and stored in the corresponding
byte of the repair symbol, where i belongs to {0; E-1}. In practice,
the XOR sums will be computed several bytes at a time (e.g., on 64
bit words, or on arrays of 16 or more bytes when using SIMD CPU
extensions).
With both FEC Schemes, the details of how to optimize the computation
of these linear combinations are of high practical importance but out
of scope of this document.
4. Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary ADU Flows
This fully-specified FEC Scheme defines the Sliding Window Random
Linear Codes (RLC) over GF(2^^8).
4.1. Formats and Codes
4.1.1. FEC Framework Configuration Information
Following the guidelines of [RFC6363], section 5.6, this section
provides the FEC Framework Configuration Information (or FFCI). This
FCCI needs to be shared (e.g., using SDP) between the FECFRAME sender
and receiver instances in order to synchronize them. It includes a
FEC Encoding ID, mandatory for any FEC Scheme specification, plus
scheme-specific elements.
4.1.1.1. FEC Encoding ID
o FEC Encoding ID: the value assigned to this fully specified FEC
Scheme MUST be XXXX, as assigned by IANA (Section 10).
When SDP is used to communicate the FFCI, this FEC Encoding ID is
carried in the 'encoding-id' parameter.
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4.1.1.2. FEC Scheme-Specific Information
The FEC Scheme-Specific Information (FSSI) includes elements that are
specific to the present FEC Scheme. More precisely:
Encoding symbol size (E): a non-negative integer that indicates the
size of each encoding symbol in bytes;
This element is required both by the sender (RLC encoder) and the
receiver(s) (RLC 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=E:1400
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 2 octets:
Encoding symbol length (E): 16-bit field.
0 1
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: FSSI Encoding Format
4.1.2. 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 an FEC Source Packet with the Explicit Source
FEC Payload ID
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More precisely, the Explicit Source FEC Payload ID is composed of the
following field (Figure 5):
Encoding Symbol ID (ESI) (32-bit field): this unsigned integer
identifies the first source symbol of the ADUI corresponding to
this FEC Source Packet. The ESI is incremented for each new
source symbol, and after reaching the maximum value (2^32-1),
wrapping to zero occurs.
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) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: Source FEC Payload ID Encoding Format
4.1.3. Repair FEC Payload ID
A FEC Repair Packet MAY contain one or more repair symbols. When
there are several repair symbols, all of them MUST have been
generated from the same encoding window, using Repair_Key values that
are managed as explained below. A receiver can easily deduce the
number of repair symbols within a FEC Repair Packet by comparing the
received FEC Repair Packet size (equal to the UDP payload size when
UDP is the underlying transport protocol) and the symbol size, E,
communicated in the FFCI.
A FEC Repair Packet MUST contain a Repair FEC Payload ID that is
prepended to the repair symbol as illustrated in Figure 6.
+--------------------------------+
| IP Header |
+--------------------------------+
| Transport Header |
+--------------------------------+
| Repair FEC Payload ID |
+--------------------------------+
| Repair Symbol |
+--------------------------------+
Figure 6: Structure of an FEC Repair Packet with the Repair FEC
Payload ID
More precisely, the Repair FEC Payload ID is composed of the
following fields (Figure 7):
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Repair_Key (16-bit field): this unsigned integer is used as a seed
by the coefficient generation function (Section 3.5) in order to
generate the desired number of coding coefficients. Value 0 MUST
NOT be used. When a FEC Repair Packet contains several repair
symbols, this repair key value is that of the first repair symbol.
The remaining repair keys can be deduced by incrementing by 1 this
value, up to a maximum value of 65535 after which it loops back to
1 (note that 0 is not a valid value).
Density Threshold for the coding coefficients, DT (4-bit field):
this unsigned integer carries the Density Threshold (DT) used by
the coding coefficient generation function Section 3.5. More
precisely, it controls the probability of having a non zero coding
coefficient, which equals (DT+1) / 16. When a FEC Repair Packet
contains several repair symbols, the DT value applies to all of
them;
Number of Source Symbols in the encoding window, NSS (12-bit field):
this unsigned integer indicates the number of source symbols in
the encoding window when this repair symbol was generated. When a
FEC Repair Packet contains several repair symbols, this NSS value
applies to all of them;
ESI of First Source Symbol in the encoding window, FSS_ESI (32-bit
field):
this unsigned integer indicates the ESI of the first source symbol
in the encoding window when this repair symbol was generated.
When a FEC Repair Packet contains several repair symbols, this
FSS_ESI value applies to all of them;
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 | DT |NSS (# src symb in ew) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| FSS_ESI |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: Repair FEC Payload ID Encoding Format
4.1.4. Additional Procedures
The following procedure applies:
o The ESI of source symbols MUST start with value 0 for the first
source symbol and MUST be managed sequentially. Wrapping to zero
happens after reaching the maximum 32-bit value.
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5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary ADU Flows
This fully-specified FEC Scheme defines the Sliding Window Random
Linear Codes (RLC) over GF(2) (binary case).
5.1. Formats and Codes
5.1.1. FEC Framework Configuration Information
5.1.1.1. FEC Encoding ID
o FEC Encoding ID: the value assigned to this fully specified FEC
Scheme MUST be YYYY, as assigned by IANA (Section 10).
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
All the considerations of Section 4.1.1.2 apply here.
5.1.2. Explicit Source FEC Payload ID
All the considerations of Section 4.1.1.2 apply here.
5.1.3. Repair FEC Payload ID
All the considerations of Section 4.1.1.2 apply here, with the only
exception that the Repair_Key field is useless if DT = 15 (indeed, in
that case all the coefficients are necessarily equal to 1 and the
coefficient generation function does not use any PRNG). When DT = 15
it is RECOMMENDED that the sender use value 0 for the Repair_Key
field, but a receiver SHALL ignore this field.
5.1.4. Additional Procedures
All the considerations of Section 4.1.1.2 apply here.
6. FEC Code Specification
6.1. Encoding Side
This section provides a high level description of a Sliding Window
RLC encoder.
Whenever a new FEC Repair Packet is needed, the RLC encoder instance
first gathers the ew_size source symbols currently in the sliding
encoding window. Then it chooses a repair key, which can be a non
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zero monotonically increasing integer value, incremented for each
repair symbol up to a maximum value of 65535 (as it is carried within
a 16-bit field) after which it loops back to 1 (indeed, being used as
a PRNG seed, value 0 is prohibited). This repair key is communicated
to the coefficient generation function (Section Section 3.5) in order
to generate ew_size coding coefficients. Finally, the FECFRAME
sender computes the repair symbol as a linear combination of the
ew_size source symbols using the ew_size coding coefficients. When E
is small and when there is an incentive to pack several repair
symbols within the same FEC Repair Packet, the appropriate number of
repair symbols are computed. In that case the repair key for each of
them MUST be incremented by 1, keeping the same ew_size source
symbols, since only the first repair key will be carried in the
Repair FEC Payload ID. The FEC Repair Packet can then be passed to
the transport layer for transmission. The source versus repair FEC
packet transmission order is out of scope of this document and
several approaches exist that are implementation specific.
Other solutions are possible to select a repair key value when a new
FEC Repair Packet is needed, for instance by choosing a random
integer between 1 and 65535. However, selecting the same repair key
as before (which may happen in case of a random process) is only
meaningful if the encoding window has changed, otherwise the same FEC
Repair Packet will be generated.
6.2. Decoding Side
This section provides a high level description of a Sliding Window
RLC decoder.
A FECFRAME receiver needs to maintain a linear system whose variables
are the received and lost source symbols. Upon receiving a FEC
Repair Packet, a receiver first extracts all the repair symbols it
contains (in case several repair symbols are packed together). For
each repair symbol, when at least one of the corresponding source
symbols it protects has been lost, the receiver adds an equation to
the linear system (or no equation if this repair packet does not
change the linear system rank). This equation of course re-uses the
ew_size coding coefficients that are computed by the same coefficient
generation function (Section Section 3.5), using the repair key and
encoding window descriptions carried in the Repair FEC Payload ID.
Whenever possible (i.e., when a sub-system covering one or more lost
source symbols is of full rank), decoding is performed in order to
recover lost source symbols. Each time an ADUI can be totally
recovered, padding is removed (thanks to the Length field, L, of the
ADUI) and the ADU is assigned to the corresponding application flow
(thanks to the Flow ID field, F, of the ADUI). This ADU is finally
passed to the corresponding upper application. Received FEC Source
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Packets, containing an ADU, MAY be passed to the application either
immediately or after some time to guaranty an ordered delivery to the
application. This document does not mandate any approach as this is
an operational and management decision.
With real-time flows, a lost ADU that is decoded after the maximum
latency or an ADU received after this delay has no value to the
application. This raises the question of deciding whether or not an
ADU is late. This decision MAY be taken within the FECFRAME receiver
(e.g., using the decoding window, see Section 3.1) or within the
application (e.g., using RTP timestamps within the ADU). Deciding
which option to follow and whether or not to pass all ADUs, including
those assumed late, to the application are operational decisions that
depend on the application and are therefore out of scope of this
document. Additionally, Appendix A discusses a backward compatible
optimization whereby late source symbols MAY still be used within the
FECFRAME receiver in order to improve the global robustness.
7. Implementation Status
Editor's notes: RFC Editor, please remove this section motivated by
RFC 6982 before publishing the RFC. Thanks.
An implementation of the Sliding Window RLC FEC Scheme for FECFRAME
exists:
o Organisation: Inria
o Description: This is an implementation of the Sliding Window RLC
FEC Scheme limited to GF(2^^8). It relies on a modified version
of our OpenFEC (http://openfec.org) FEC code library. It is
integrated in our FECFRAME software (see [fecframe-ext]).
o Maturity: prototype.
o Coverage: this software complies with the Sliding Window RLC FEC
Scheme.
o Lincensing: proprietary.
o Contact: vincent.roca@inria.fr
8. 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 specific topics.
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8.1. Attacks Against the Data Flow
8.1.1. Access to Confidential Content
The Sliding Window RLC 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.
8.1.2. Content Corruption
The Sliding Window RLC 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.
8.2. Attacks Against the FEC Parameters
The FEC Scheme specified in this document defines parameters that can
be the basis of attacks. More specifically, the following parameters
of the FFCI may be modified by an attacker who targets receivers
(Section 4.1.1.2):
o FEC Encoding ID: changing this parameter leads the receivers 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
different value will confuse the receivers and create a DoS. More
precisely, the FEC Repair Packets received will probably no longer
be multiple of E, leading receivers to reject them;
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 Encoding
Symbol ID (ESI), or the repair key, NSS or FSS_ESI. It is therefore
RECOMMENDED that security measures are taken to guarantee the FEC
Source and Repair Packets as stated in [RFC6363].
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8.3. When Several Source Flows are to be Protected Together
The Sliding Window RLC FEC Scheme specified in this document does not
change the recommendations of [RFC6363].
8.4. Baseline Secure FEC Framework Operation
The Sliding Window RLC 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.
9. 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 specific
topics.
9.1. Operational Recommendations: Finite Field GF(2) Versus GF(2^^8)
The present document specifies two FEC Schemes that differ on the
Finite Field used for the coding coefficients. It is expected that
the RLC over GF(2^^8) FEC Scheme will be mostly used since it
warrants a higher packet loss protection. In case of small encoding
windows, the associated processing overhead is not an issue (e.g., we
measured decoding speeds between 745 Mbps and 2.8 Gbps on an ARM
Cortex-A15 embedded board in [Roca17]). Of course the CPU overhead
will increase with the encoding window size, because more operations
in the GF(2^^8) finite field will be needed.
The RLC over GF(2) FEC Scheme offers an alternative. In that case
operations symbols can be directly XOR-ed together which warrants
high bitrate encoding and decoding operations, and can be an
advantage with large encoding windows. However packet loss
protection is significantly reduced by using this FEC Scheme.
9.2. Operational Recommendations: Coding Coefficients Density Threshold
In addition to the choice of the Finite Field, the two FEC Schemes
define a coding coefficient density threshold (DT) parameter. This
parameter enables a sender to control the code density, i.e., the
proportion of coefficients that are non zero on average. With RLC
over GF(2^^8), it is usually appropriate that small encoding windows
be associated to a density threshold equal to 15, the maximum value,
in order to warrant a high loss protection.
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On the opposite, with larger encoding windows, it is usually
appropriate that the density threshold be reduced. With large
encoding windows, an alternative can be to use RLC over GF(2) and a
density threshold equal to 7 (i.e., an average density equal to 1/2)
or smaller.
Note that using a density threshold equal to 15 with RLC over GF(2)
is equivalent to using an XOR code that compute the XOR sum of all
the source symbols in the encoding window. In that case: (1) a
single repair symbol can be produced for any encoding window, and (2)
the repair_key parameter becomes useless (the coding coefficients
generation function does not rely on the PRNG).
10. IANA Considerations
This document registers two values in the "FEC Framework (FECFRAME)
FEC Encoding IDs" registry [RFC6363] as follows:
o YYYY refers to the Sliding Window Random Linear Codes (RLC) over
GF(2) FEC Scheme for Arbitrary Packet Flows, as defined in
Section 5 of this document.
o XXXX refers to the Sliding Window Random Linear Codes (RLC) over
GF(2^^8) FEC Scheme for Arbitrary Packet Flows, as defined in
Section 4 of this document.
11. Acknowledgments
The authors would like to thank Marie-Jose Montpetit for her valuable
feedbacks on this document.
12. References
12.1. Normative References
[fecframe-ext]
Roca, V. and A. Begen, "Forward Error Correction (FEC)
Framework Extension to Sliding Window Codes", Transport
Area Working Group (TSVWG) draft-ietf-tsvwg-fecframe-ext
(Work in Progress), March 2018,
<https://tools.ietf.org/html/
draft-ietf-tsvwg-fecframe-ext>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
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[RFC6363] Watson, M., Begen, A., and V. Roca, "Forward Error
Correction (FEC) Framework", RFC 6363,
DOI 10.17487/RFC6363, October 2011,
<https://www.rfc-editor.org/info/rfc6363>.
[RFC6364] Begen, A., "Session Description Protocol Elements for the
Forward Error Correction (FEC) Framework", RFC 6364,
DOI 10.17487/RFC6364, October 2011,
<https://www.rfc-editor.org/info/rfc6364>.
12.2. Informative References
[CA90] Carta, D., "Two Fast Implementations of the Minimal
Standard Random Number Generator", Communications of the
ACM, Vol. 33, No. 1, pp.87-88, January 1990.
[PGM13] Plank, J., Greenan, K., and E. Miller, "A Complete
Treatment of Software Implementations of Finite Field
Arithmetic for Erasure Coding Applications", University of
Tennessee Technical Report UT-CS-13-717,
http://web.eecs.utk.edu/~plank/plank/papers/
UT-CS-13-717.html, October 2013,
<http://web.eecs.utk.edu/~plank/plank/papers/
UT-CS-13-717.html>.
[PM88] Park, S. and K. Miller, "Random Number Generators: Good
Ones are Hard to Find", Communications of the ACM, Vol.
31, No. 10, pp.1192-1201, 1988.
[PTVF92] Press, W., Teukolsky, S., Vetterling, W., and B. Flannery,
"Numerical Recipies in C; Second Edition", Cambridge
University Press, ISBN: 0-521-43108-5, 1992.
[rand31pmc]
Whittle, R., "31 bit pseudo-random number generator",
September 2005, <http://www.firstpr.com.au/dsp/rand31/
rand31-park-miller-carta.cc.txt>.
[RFC5170] Roca, V., Neumann, C., and D. Furodet, "Low Density Parity
Check (LDPC) Staircase and Triangle Forward Error
Correction (FEC) Schemes", RFC 5170, DOI 10.17487/RFC5170,
June 2008, <https://www.rfc-editor.org/info/rfc5170>.
[RFC6726] Paila, T., Walsh, R., Luby, M., Roca, V., and R. Lehtonen,
"FLUTE - File Delivery over Unidirectional Transport",
RFC 6726, DOI 10.17487/RFC6726, November 2012,
<https://www.rfc-editor.org/info/rfc6726>.
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[RFC6816] Roca, V., Cunche, M., and J. Lacan, "Simple Low-Density
Parity Check (LDPC) Staircase Forward Error Correction
(FEC) Scheme for FECFRAME", RFC 6816,
DOI 10.17487/RFC6816, December 2012,
<https://www.rfc-editor.org/info/rfc6816>.
[RFC6865] Roca, V., Cunche, M., Lacan, J., Bouabdallah, A., and K.
Matsuzono, "Simple Reed-Solomon Forward Error Correction
(FEC) Scheme for FECFRAME", RFC 6865,
DOI 10.17487/RFC6865, February 2013,
<https://www.rfc-editor.org/info/rfc6865>.
[Roca16] Roca, V., Teibi, B., Burdinat, C., Tran, T., and C.
Thienot, "Block or Convolutional AL-FEC Codes? A
Performance Comparison for Robust Low-Latency
Communications", HAL open-archive document,hal-01395937
https://hal.inria.fr/hal-01395937/en/, November 2016,
<https://hal.inria.fr/hal-01395937/en/>.
[Roca17] Roca, V., Teibi, B., Burdinat, C., Tran, T., and C.
Thienot, "Less Latency and Better Protection with AL-FEC
Sliding Window Codes: a Robust Multimedia CBR Broadcast
Case Study", 13th IEEE International Conference on
Wireless and Mobile Computing, Networking and
Communications (WiMob17), October
2017 https://hal.inria.fr/hal-01571609v1/en/, October
2017, <https://hal.inria.fr/hal-01571609v1/en/>.
[WI08] Whittle, R., "Park-Miller-Carta Pseudo-Random Number
Generator", http://www.firstpr.com.au/dsp/rand31/,
January 2008, <http://www.firstpr.com.au/dsp/rand31/>.
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Appendix A. Decoding Beyond Maximum Latency Optimization
This annex introduces non normative considerations. They are
provided as suggestions, without any impact on interoperability. For
more information see [Roca16].
It is possible to improve the decoding performance of sliding window
codes without impacting maximum latency, at the cost of extra CPU
overhead. The optimization consists, for a receiver, to extend the
linear system beyond the decoding window, by keeping a certain number
of old source symbols.
ls_max_size > dw_max_size
Usually the following choice is a good trade-off between decoding
performance and extra CPU overhead:
ls_max_size = 2 * dw_max_size
When the dw_max_size is very small, it may be preferable to keep a
minimum ls_max_size value (e.g., LS_MIN_SIZE_DEFAULT = 40 symbols).
Going below this threshold will not save a significant amount of
memory nor CPU cycles. Therefore:
ls_max_size = max(2 * dw_max_size, LS_MIN_SIZE_DEFAULT)
Finally, it is worth noting that a good receiver, i.e., a receiver
that benefits from a protection that is significantly sufficient to
recover from the packet losses, can choose to reduce its ls_max_size
significantly. In that case lost ADUs will be recovered rapidly,
without relying on this optimization.
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
Figure 8: Relationship between parameters to decode beyond maximum
latency.
It means that source symbols, and therefore ADUs, may be decoded even
if the added latency exceeds the maximum value permitted by the
application. It follows that the corresponding ADUs will not be
useful to the application. However, decoding these "late symbols"
significantly improves the global robustness in bad reception
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conditions and is therefore recommended for receivers experiencing
bad communication conditions [Roca16]. In any case whether or not to
use this optimization and what exact value to use for the ls_max_size
parameter are decisions made by each receiver independently, without
any impact on the other receivers nor on the source.
Authors' Addresses
Vincent Roca
INRIA
Grenoble
France
EMail: vincent.roca@inria.fr
Belkacem Teibi
INRIA
Grenoble
France
EMail: belkacem.teibi@inria.fr
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