TSVWG V. Roca
Internet-Draft B. Teibi
Intended status: Standards Track INRIA
Expires: September 5, 2018 March 4, 2018
Sliding Window Random Linear Code (RLC) Forward Erasure Correction (FEC)
Schemes for FECFRAME
draft-ietf-tsvwg-rlc-fec-scheme-02
Abstract
This document describes two fully-specified 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 are meant to
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 erasure recovery capabilities.
Status of This Memo
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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 . . . . . . . . . . . . . . . . . . 5
2. Definitions and Abbreviations . . . . . . . . . . . . . . . . 6
3. Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1. Parameters Derivation . . . . . . . . . . . . . . . . . . 7
3.2. ADU, ADUI and Source Symbols Mappings . . . . . . . . . . 9
3.3. Encoding Window Management . . . . . . . . . . . . . . . 10
3.4. Pseudo-Random Number Generator . . . . . . . . . . . . . 11
3.5. Coding Coefficients Generation Function . . . . . . . . . 12
4. Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary ADU
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 14
4.1.1. FEC Framework Configuration Information . . . . . . . 14
4.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 15
4.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 16
4.1.4. Additional Procedures . . . . . . . . . . . . . . . . 17
5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary ADU
Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1. Formats and Codes . . . . . . . . . . . . . . . . . . . . 18
5.1.1. FEC Framework Configuration Information . . . . . . . 18
5.1.2. Explicit Source FEC Payload ID . . . . . . . . . . . 18
5.1.3. Repair FEC Payload ID . . . . . . . . . . . . . . . . 18
5.1.4. Additional Procedures . . . . . . . . . . . . . . . . 18
6. FEC Code Specification . . . . . . . . . . . . . . . . . . . 18
6.1. Encoding Side . . . . . . . . . . . . . . . . . . . . . . 18
6.2. Decoding Side . . . . . . . . . . . . . . . . . . . . . . 19
7. Implementation Status . . . . . . . . . . . . . . . . . . . . 20
8. Security Considerations . . . . . . . . . . . . . . . . . . . 20
8.1. Attacks Against the Data Flow . . . . . . . . . . . . . . 20
8.1.1. Access to Confidential Content . . . . . . . . . . . 20
8.1.2. Content Corruption . . . . . . . . . . . . . . . . . 21
8.2. Attacks Against the FEC Parameters . . . . . . . . . . . 21
8.3. When Several Source Flows are to be Protected Together . 21
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8.4. Baseline Secure FEC Framework Operation . . . . . . . . . 21
9. Operations and Management Considerations . . . . . . . . . . 22
9.1. Operational Recommendations: Finite Field GF(2) Versus
GF(2^^8) . . . . . . . . . . . . . . . . . . . . . . . . 22
9.2. Operational Recommendations: Coding Coefficients Density
Threshold . . . . . . . . . . . . . . . . . . . . . . . . 22
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 23
11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 23
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 23
12.1. Normative References . . . . . . . . . . . . . . . . . . 23
12.2. Informative References . . . . . . . . . . . . . . . . . 24
Appendix A. Decoding Beyond Maximum Latency Optimization . . . . 26
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 26
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] in case of reliable file transfers over lossy networks, and
the FECFRAME protocol 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.
Defining this block size requires 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 an lost (erased) packet thanks to
FEC protection). Therefore, with a multicast/broadcast session where
different receivers experience different packet loss rates, the block
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size should be chosen by considering the worst communication
conditions one wants to support, but without exceeding the desired
maximum decoding latency. This choice will impact all receivers.
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 are extremely efficient for instance with media that
feature real-time constraints sent within a multicast/broadcast
session.
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 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 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.
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 FEC-related latency close
to zero [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 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), sliding window codes achieve more easily a target
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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 so as to reduce the
transmission 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 easily 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).
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;
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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
plr: packet loss rate on the packet 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_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
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 this FEC
Scheme.
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3.1. Parameters Derivation
The Sliding Window RLC FEC Scheme relies on several key 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. In all situations, we MUST have:
ew_size <= ew_max_size
Decoding window maximum size, dw_max_size (in symbols): at a
receiver, this parameter determines the maximum size of the
decoding window. Said differently, this is the maximum number of
received or lost source symbols in the linear system (i.e., the
variables) that are still within their latency budget. In
situations where packets are sent with a fixed period, the
dw_max_size parameter directly determines the maximum decoding
latency experienced by the receiver, which necessarily needs to be
in line with the maximum FEC-related latency budget. Note also
that the optimization detailed in Appendix A can extend the linear
system with additional old source symbols (that timed-out) beyond
dw_max_size;
Symbol size, E (in bytes) and RLC code rate (cr): the E parameter
determines the (source or repair) symbol sizes. The cr parameter
determines the code rate, i.e., the amount of redundancy added to
the flow (it 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. In practice they
will usually be fixed, especially with multicast/broadcast
transmissions. In specific use-cases, in particular with unicast
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transmissions in presence of a feedback mechanism that estimates
the communication quality (out-of-scope of FECFRAME), the code
rate may be adjusted dynamically.
Let us assume that the encoding symbol size (E, in bytes) and code
rate (cr) are constant. Let us also assume a constant transmission
bitrate (br_out, in bits/s) at the output of the FECFRAME sender (as
in [Roca17]). It means that the source flow bitrate needs to be
adjusted according to the added repair flow overhead in order to keep
the total transmission bitrate fixed and equal to br_out. In order
to comply with the maximum FEC-related latency budget we need:
dw_max_size = (max_lat * br_out * cr) / (8 * E)
Sometimes the opposite can happen: the source 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 need:
dw_max_size = (max_lat * br_in) / (8 * E)
Finally, there are situations where no such assumption can be made
(e.g., with a variable bit rate input flow). In that case the
encoding and decoding window maximum sizes may be initialized, based
on the input flow features (e.g., the peak bitrate if it is known)
and great care must be taken on timing aspects at a sender (see
Section 3.3) and receiver. The details of how to manage these
situations are use-case dependent and out of scope of this document.
Then, once the dw_max_size has been determined, the ew_max_size can
be defined. For decoding to be possible, it is required that the
encoding window maximum size be at most equal to the decoding window
maximum size. It is often good practice to choose [Roca17]:
ew_max_size = dw_max_size * 0.75
However any value ew_max_size < dw_max_size can be used without
impact on the FEC-related latency budget. Finding the optimal value
will depend on the use-case details and should be determined after
simulations or field trials. This is of course out of scope of this
document.
Note that the decoding beyond maximum latency optimization
(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. In any case, the linear system maximum
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size is greater than (with the decoding optimization) or equal to
(without) the decoding window maximum size:
ls_max_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, a lost 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 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) 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]. Yet, any other
implementation of the PRNG algorithm that matches the above
validation criteria, like the ones detailed in [PM88], is
appropriate.
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.)
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In this document, pmms_rand(maxv) denotes the PRNG function that
implements the Park-Miller "minimal standard" algorithm, defined
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
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* value in {1,... 255} with GF(2^^8)), otherwise
* a fraction of them will be 0.
* (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);
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);
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
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
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.
4.1.1.1. Mandatory Information
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 can 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 carried 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. Mandatory Information
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. The only constraint is to increment by
1 the repair key for each of them, 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 sent. 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, can 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 should not be passed to
the application. Instead the associated source symbols should be
removed from the linear system maintained by the receiver(s).
Appendix A discusses a backward compatible optimization whereby those
late source symbols may still be used 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.
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
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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].
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
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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.
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
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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>.
[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>.
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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.
[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>.
[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/>.
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[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
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 SHOULD NOT be
delivered to the application and SHOULD be dropped once they are no
longer needed. However, decoding these "late symbols" significantly
improves the global robustness in bad reception 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
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Vincent Roca
INRIA
Grenoble
France
EMail: vincent.roca@inria.fr
Belkacem Teibi
INRIA
Grenoble
France
EMail: belkacem.teibi@inria.fr
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