```
/**
* This function outputs a pseudo-random integer in [0 .. 15] range.
*
* @param s pointer to tinymt internal state.
* @return unsigned integer between 0 and 15 inclusive.
*/
uint32_t tinymt32_rand16(tinymt32_t *s)
{
return (tinymt32_generate_uint32(s) & 0xF);
}
/**
* This function outputs a pseudo-random integer in [0 .. 255] range.
*
* @param s pointer to tinymt internal state.
* @return unsigned integer between 0 and 255 inclusive.
*/
uint32_t tinymt32_rand256(tinymt32_t *s)
{
return (tinymt32_generate_uint32(s) & 0xFF);
}
``````
Figure 2: 4-bit and 8-bit mapping functions for TinyMT32
Any implementation of this PRNG MUST fulfil three validation
criteria, the one described in [tinymt32] (for the TinyMT32 32-bit
unsigned integer generator) and the two ones detailed in Appendix A
(for the mapping to 4-bit and 8-bit intervals). Because of the way
the mapping functions work, it is unlikely that an implementation
that fulfils the first criteria fails to fulfil the two additional
ones.
3.6. 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. DT has values
between 0 (the minimum value) and 15 (the maximum value), and the
average probability of having a non zero coefficient equals (DT + 1)
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/ 16. In particular, when DT equals 15 the function guaranties that
all coefficients are non zero (i.e., maximum density).
These considerations apply to 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 is equal to 1.
With RLC over GF(2^^8) FEC Scheme (Section 4), m is equal to 8.
``````
/*
* 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=1 and dt=15
* (in/out) 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.
* (in) m Finite Field GF(2^^m) parameter. In this
* document only values 1 and 8 are considered.
* (out) returns 0 in case of success, an error code
* different than 0 otherwise.
*/
int generate_coding_coefficients (uint16_t repair_key,
uint8_t cc_tab[],
uint16_t cc_nb,
uint8_t dt,
uint8_t m)
{
uint32_t i;
tinymt32_t s; /* PRNG internal state */
if (dt > 15) {
return -1; /* error, bad dt parameter */
}
switch (m) {
case 1:
if (dt == 15) {
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/* all coefficients are 1 */
memset(cc_tab, 1, cc_nb);
} else {
/* here coefficients are either 0 or 1 */
tinymt32_init(&s, repair_key);
for (i = 0 ; i < cc_nb ; i++) {
cc_tab[i] = (tinymt32_rand16(&s) <= dt) ? 1 : 0;
}
}
break;
case 8:
tinymt32_init(&s, 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_t) tinymt32_rand256(&s);
} while (cc_tab[i] == 0);
}
} else {
/* here a certain number of coefficients should be 0 */
for (i = 0 ; i < cc_nb ; i++) {
if (tinymt32_rand16(&s) <= dt) {
do {
cc_tab[i] = (uint8_t) tinymt32_rand256(&s);
} while (cc_tab[i] == 0);
} else {
cc_tab[i] = 0;
}
}
}
break;
default:
return -2; /* error, bad parameter m */
}
return 0 /* success */
}
``````
Figure 3: Coding Coefficients Generation Function Reference
Implementation
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3.7. Finite Fields Operations
3.7.1. Finite Field Definitions
The two RLC FEC Schemes specified in this document reuse the Finite
Fields defined in [RFC5510], section 8.1. More specifically, the
elements of the field GF(2^^m) are represented by polynomials with
binary coefficients (i.e., over GF(2)) and degree lower or equal to
m-1. The addition between two elements is defined as the addition of
binary polynomials in GF(2), which is equivalent to a bitwise XOR
operation on the binary representation of these elements.
With GF(2^^8), multiplication between two elements is the
multiplication modulo a given irreducible polynomial of degree 8.
The following irreducible polynomial MUST be used for GF(2^^8):
x^^8 + x^^4 + x^^3 + x^^2 + 1
With GF(2), multiplication corresponds to a logical AND operation.
3.7.2. 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
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] XOR cc_tab[1] * src_1[i] XOR ...
XOR cc_tab[ew_size - 1] * src_ew_size_1[i]
where * is the multiplication over GF(2^^8). 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
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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 Packet
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.
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;
Window Size Ratio (WSR) parameter: a non-negative integer between 0
and 255 (both inclusive) used to initialize window sizes. A value
of 0 indicates this parameter is not considered (e.g., a fixed
encoding window size may be chosen). A value between 1 and 255
inclusive is required by certain of the parameter derivation
techniques described in Appendix C;
This element is required both by the sender (RLC encoder) and the
receiver(s) (RLC decoder).
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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,WSR:191
In that case the name values "E" and "WSR" are used to convey the E
and WSR parameters respectively.
If another mechanism requires the FSSI to be carried as an opaque
octet string, the encoding format consists of the following three
octets, where the E field is carried in "big-endian" or "network
order" format, that is, most significant byte first:
Encoding symbol length (E): 16-bit field;
Window Size Ratio Parameter (WSR): 8-bit field.
These three octets can be communicated as such, or for instance, be
subject to an additional Base64 encoding.
0 1 2
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol Length (E) | WSR |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: 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 5.
+--------------------------------+
| IP Header |
+--------------------------------+
| Transport Header |
+--------------------------------+
| ADU |
+--------------------------------+
| Explicit Source FEC Payload ID |
+--------------------------------+
Figure 5: 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, carried in "big-endian" or "network order" format,
that is, most significant byte first (Figure 6):
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 6: 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 7.
+--------------------------------+
| IP Header |
+--------------------------------+
| Transport Header |
+--------------------------------+
| Repair FEC Payload ID |
+--------------------------------+
| Repair Symbol |
+--------------------------------+
Figure 7: 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 where all integer fields are carried in "big-endian"
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or "network order" format, that is, most significant byte first
(Figure 8):
Repair_Key (16-bit field): this unsigned integer is used as a seed
by the coefficient generation function (Section 3.6) in order to
generate the desired number of coding coefficients. This repair
key may be a monotonically increasing integer value that loops
back to 0 after reaching 65535 (see Section 6.1). 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 0.
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 3.6. 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 8: Repair FEC Payload ID Encoding Format
4.2. Procedures
All the procedures of Section 3 apply to this FEC Scheme.
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5. Sliding Window RLC FEC Scheme over GF(2) for Arbitrary Packet 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 4.1.2 apply here.
5.1.3. Repair FEC Payload ID
All the considerations of Section 4.1.3 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
the FECFRAME sender MUST set the Repair_Key field to zero on
transmission and a receiver MUST ignore it on receipt.
5.2. Procedures
All the procedures of Section 3 apply to this FEC Scheme.
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
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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 0. This repair key is
communicated to the coefficient generation function (Section 3.6) 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
(Section 3.7). 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 0 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 3.6), 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. Gaussian elimination is one possible
algorithm to solve this linear system. 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
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Source 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 D discusses a backward compatible
optimization whereby late source symbols MAY still be used within the
FECFRAME receiver in order to improve transmission 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 Licensing: proprietary.
o Contact: vincent.roca@inria.fr
8. Security Considerations
The FEC Framework document [RFC6363] provides a fairly 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 a receiver to
consider a different FEC Scheme. The consequences are severe, the
format of the Explicit Source FEC Payload ID and Repair FEC
Payload ID of received packets will probably differ, leading to
various malfunctions. Even if the original and modified FEC
Schemes share the same format, FEC decoding will either fail or
lead to corrupted decoded symbols. This will happen if an
attacker turns value YYYY (i.e., RLC over GF(2)) to value XXXX
(RLC over GF(2^^8)), an additional consequence being a higher
processing overhead at the receiver. In any case, the attack
results in a form of Denial of Service (DoS) or corrupted content.
o Encoding symbol length (E): setting this E parameter to a
different value will confuse a receiver. If the size of a
received FEC Repair Packet is no longer multiple of the modified E
value, a receiver quickly detects a problem and SHOULD reject the
packet. If the new E value is a sub-multiple of the original E
value (e.g., half the original value), then receivers may not
detect the problem immediately. For instance, a receiver may
think that a received FEC Repair Packet contains more repair
symbols (e.g., twice as many if E is reduced by half), leading to
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malfunctions whose nature depends on implementation details. Here
also, the attack always results in a form of DoS or corrupted
content.
It is therefore RECOMMENDED that security measures be taken to
guarantee the FFCI integrity, as specified in [RFC6363]. How to
achieve this depends on the way the FFCI is communicated from the
sender to the receiver, which is not specified in this document.
Similarly, attacks are possible against the Explicit Source FEC
Payload ID and Repair FEC Payload ID. More specifically, in case of
a FEC Source Packet, the following value can be modified by an
attacker who targets receivers:
o Encoding Symbol ID (ESI): changing the ESI leads a receiver to
consider a wrong ADU, resulting in severe consequences, including
corrupted content passed to the receiving application;
And in case of a FEC Repair Packet:
o Repair Key: changing this value leads a receiver to generate a
wrong coding coefficient sequence, and therefore any source symbol
decoded using the repair symbols contained in this packet will be
corrupted;
o DT: changing this value also leads a receiver to generate a wrong
coding coefficient sequence, and therefore any source symbol
decoded using the repair symbols contained in this packet will be
corrupted. In addition, if the DT value is significantly
increased, it will generate a higher processing overhead at a
receiver. In case of very large encoding windows, this may impact
the terminal performance;
o NSS: changing this value leads a receiver to consider a different
set of source symbols, and therefore any source symbol decoded
using the repair symbols contained in this packet will be
corrupted. In addition, if the NSS value is significantly
increased, it will generate a higher processing overhead at a
receiver, which may impact the terminal performance;
o FSS_ESI: changing this value also leads a receiver to consider a
different set of source symbols and therefore any source symbol
decoded using the repair symbols contained in this packet will be
corrupted.
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.
8.5. Additional Security Considerations for Numerical Computations
In addition to the above security considerations, inherited from
[RFC6363], the present document introduces several formulae, in
particular in Appendix C.1. It is RECOMMENDED to check that the
computed values stay within reasonable bounds since numerical
overflows, caused by an erroneous implementation or an erroneous
input value, may lead to hazardous behaviours. However, what
"reasonable bounds" means is use-case and implementation dependent
and is not detailed in this document.
Appendix C.2 also mentions the possibility of "using the timestamp
field of an RTP packet header" when applicable. A malicious attacker
may deliberately corrupt this header field in order to trigger
hazardous behaviours at a FECFRAME receiver. Protection against this
type of content corruption can be addressed with the above
recommendations on a baseline secure operation. In addition, it is
also RECOMMENDED to check that the timestamp value be within
reasonable bounds.
9. Operations and Management Considerations
The FEC Framework document [RFC6363] provides a fairly 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
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measured decoding speeds between 745 Mbps and 2.8 Gbps on an ARM
Cortex-A15 embedded board in [Roca17] for an encoding window of size
18 or 23 symbols). 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 computes the XOR sum of all
the source symbols in the encoding window. In that case: (1) only 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.
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11. Acknowledgments
The authors would like to thank the three TSVWG chairs, Wesley Eddy,
our shepherd, David Black and Gorry Fairhurst, as well as Spencer
Dawkins, our responsible AD, and all those who provided comments,
namely (alphabetical order) Alan DeKok, Jonathan Detchart, Russ
Housley, Emmanuel Lochin, and Marie-Jose Montpetit. Last but not
least, the authors are really grateful to the IESG members, in
particular Benjamin Kaduk, Mirja Kuhlewind, Eric Rescorla, and Adam
Roach for their highly valuable feedbacks that greatly contributed to
improve this specification.
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), January 2019,
```.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC6363] Watson, M., Begen, A., and V. Roca, "Forward Error
Correction (FEC) Framework", RFC 6363,
DOI 10.17487/RFC6363, October 2011,
.
[RFC6364] Begen, A., "Session Description Protocol Elements for the
Forward Error Correction (FEC) Framework", RFC 6364,
DOI 10.17487/RFC6364, October 2011,
.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, .
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[tinymt32]
Saito, M., Matsumoto, M., Roca, V., and E. Baccelli,
"TinyMT32 PRNG">TinyMT32 Pseudo Random Number Generator",
Transport Area Working Group (TSVWG) draft-roca-tsvwg-
tinymt32 (Work in Progress), February 2019,
.
12.2. Informative References
[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,
.
[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, .
[RFC5510] Lacan, J., Roca, V., Peltotalo, J., and S. Peltotalo,
"Reed-Solomon Forward Error Correction (FEC) Schemes",
RFC 5510, DOI 10.17487/RFC5510, April 2009,
.
[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,
.
[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,
.
[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,
.
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[RFC8406] Adamson, B., Adjih, C., Bilbao, J., Firoiu, V., Fitzek,
F., Ghanem, S., Lochin, E., Masucci, A., Montpetit, M-J.,
Pedersen, M., Peralta, G., Roca, V., Ed., Saxena, P., and
S. Sivakumar, "Taxonomy of Coding Techniques for Efficient
Network Communications", RFC 8406, DOI 10.17487/RFC8406,
June 2018, .
[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,
.
[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, .
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Appendix A. TinyMT32 Validation Criteria (Normative)
PRNG determinism, for a given seed, is a requirement. Consequently,
in order to validate an implementation of the TinyMT32 PRNG, the
following criterias MUST be met.
The first criteria focusses on the tinymt32_rand256(), where the
32-bit integer of the core TinyMT32 PRNG is scaled down to an 8-bit
integer. Using a seed value of 1, the first 50 values returned by:
tinymt32_rand256() as 8-bit unsigned integers MUST be equal to values
provided in Figure 9.
37 225 177 176 21
246 54 139 168 237
211 187 62 190 104
135 210 99 176 11
207 35 40 113 179
214 254 101 212 211
226 41 234 232 203
29 194 211 112 107
217 104 197 135 23
89 210 252 109 166
Figure 9: First 50 decimal values returned by tinymt32_rand256() as
8-bit unsigned integers, with a seed value of 1.
The second criteria focusses on the tinymt32_rand16(), where the
32-bit integer of the core TinyMT32 PRNG is scaled down to a 4-bit
integer. Using a seed value of 1, the first 50 values returned by:
tinymt32_rand16() as 4-bit unsigned integers MUST be equal to values
provided in Figure 10.
5 1 1 0 5
6 6 11 8 13
3 11 14 14 8
7 2 3 0 11
15 3 8 1 3
6 14 5 4 3
2 9 10 8 11
13 2 3 0 11
9 8 5 7 7
9 2 12 13 6
Figure 10: First 50 decimal values returned by tinymt32_rand16() as
4-bit unsigned integers, with a seed value of 1.
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Appendix B. Assessing the PRNG Adequacy (Informational)
This annex discusses the adequacy of the TinyMT32 PRNG and the
tinymt32_rand16() and tinymt32_rand256() functions, to the RLC FEC
Schemes. The goal is to assess the adequacy of these two functions
in producing coding coefficients that are sufficiently different from
one another, across various repair symbols with repair key values in
sequence (we can expect this approach to be commonly used by
implementers Section 6.1). This section is purely informational and
does not claim to be a solid evaluation.
The two RLC FEC Schemes use the PRNG to produce pseudo-random coding
coefficients (Section 3.6), each time a new repair symbol is needed.
A different repair key is used for each repair symbol, usually by
incrementing the repair key value (Section 6.1). For each repair
symbol, a limited number of pseudo-random numbers is needed,
depending on the DT and encoding window size (Section 3.6), using
either tinymt32_rand16() or tinymt32_rand256(). Therefore we are
more interested in the randomness of small sequences of random
numbers mapped to 4-bit or 8-bit integers, than in the randomness of
a very large sequence of random numbers which is not representative
of the usage of the PRNG.
Evaluation of tinymt32_rand16(): We first generate a huge number
(1,000,000,000) of small sequences (20 pseudo-random numbers per
sequence), and perform statistics on the number of occurrences of
each of the 16 possible values across all sequences.
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value occurrences percentage (%) (total of 20000000000)
0 1250036799 6.2502
1 1249995831 6.2500
2 1250038674 6.2502
3 1250000881 6.2500
4 1250023929 6.2501
5 1249986320 6.2499
6 1249995587 6.2500
7 1250020363 6.2501
8 1249995276 6.2500
9 1249982856 6.2499
10 1249984111 6.2499
11 1250009551 6.2500
12 1249955768 6.2498
13 1249994654 6.2500
14 1250000569 6.2500
15 1249978831 6.2499
Figure 11: tinymt32_rand16(): occurrence statistics across a huge
number (1,000,000,000) of small sequences (20 pseudo-random numbers
per sequence), with 0 as the first PRNG seed.
The results (Figure 11) show that all possible values are almost
equally represented, or said differently, that the tinymt32_rand16()
output converges to a uniform distribution where each of the 16
possible value would appear exactly 1 / 16 * 100 = 6.25% of times.
Other types of biases may exist that may be visible with smaller
tests (e.g., to evaluation the convergence speed to a uniform
distribution). We therefore perform 200 tests, each of them
consisting in producing 200 sequences, keeping only the first value
of each sequence. We use non overlapping repair keys for each
sequence, starting with value 0 and increasing it after each use.
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value min occurrences max occurrences average occurrences
0 4 21 6.3675
1 4 22 6.0200
2 4 20 6.3125
3 5 23 6.1775
4 5 24 6.1000
5 4 21 6.5925
6 5 30 6.3075
7 6 22 6.2225
8 5 26 6.1750
9 3 21 5.9425
10 5 24 6.3175
11 4 22 6.4300
12 5 21 6.1600
13 5 22 6.3100
14 4 26 6.3950
15 4 21 6.1700
Figure 12: tinymt32_rand16(): occurrence statistics across 200 tests,
each of them consisting in 200 sequences of 1 pseudo-random number
each, with non overlapping PRNG seeds in sequence starting from 0.
Figure 12 shows across all 200 tests, for each of the 16 possible
pseudo-random number values, the minimum (resp. maximum) number of
times it appeared in a tests, as well as the average number of
occurrences across the 200 tests. Although the distribution is not
perfect, there is no major bias. On the opposite, in the same
conditions, the Park Miller linear congruential PRNG of [RFC5170]
with a result scaled down to 4-bit values, using seeds in sequence
starting from 1, returns systematically 0 as the first value during
some time, then after a certain repair key value threshold, it
systematically returns 1, etc.
Evaluation of tinymt32_rand256(): The same approach is used here.
Results (not shown) are similar: occurrences vary between 7,810,3368
(i.e., 0.3905%) and 7,814,7952 (i.e., 0.3907%). Here also we see a
convergence to the theoretical uniform distribution where each of the
possible value would appear exactly 1 / 256 * 100 = 0.390625% of
times.
Appendix C. Possible Parameter Derivation (Informational)
Section 3.1 defines several parameters to control the encoder or
decoder. This annex proposes techniques to derive these parameters
according to the target use-case. This annex is informational, in
the sense that using a different derivation technique will not
prevent the encoder and decoder to interoperate: a decoder can still
recover an erased source symbol without any error. However, in case
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of a real-time flow, an inappropriate parameter derivation may lead
to the decoding of erased source packets after their validity period,
making them useless to the target application. This annex proposes
an approach to reduce this risk, among other things.
The FEC Schemes defined in this document can be used in various
manners, depending on the target use-case:
o the source ADU flow they protect may or may not have real-time
constraints;
o the source ADU flow may be a Constant Bitrate (CBR) or Variable
BitRate (VBR) flow;
o with a VBR source ADU flow, the flow's minimum and maximum
bitrates may or may not be known;
o and the communication path between encoder and decoder may be a
CBR communication path (e.g., as with certain LTE-based broadcast
channels) or not (general case, e.g., with Internet).
The parameter derivation technique should be suited to the use-case,
as described in the following sections.
C.1. Case of a CBR Real-Time Flow
In the following, we consider a real-time flow with max_lat latency
budget. The encoding symbol size, E, is constant. The code rate,
cr, is also constant, its value depending on the expected
communication loss model (this choice is out of scope of this
document).
In a first configuration, the source ADU flow bitrate at the input of
the FECFRAME sender is fixed and equal to br_in (in bits/s), and this
value is known by the FECFRAME sender. It follows 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)
assuming that the encoding and decoding times are negligible with
respect to the target max_lat. This is a reasonable assumption in
many situations (e.g., see Section 9.1 in case of small window
sizes). Otherwise the max_lat parameter should be adjusted in order
to avoid the problem. In any case, interoperability will never be
compromized by choosing a too large value.
In a second configuration, the FECFRAME sender generates a fixed
bitrate flow, equal to the CBR communication path bitrate equal to
br_out (in bits/s), and this value is known by the FECFRAME sender,
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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. We have:
dw_max_size = (max_lat * br_out * cr) / (8 * E)
assuming here also that the encoding and decoding times are
negligible with respect to the target max_lat.
For decoding to be possible within the latency budget, it is required
that the encoding window maximum size be smaller than or at most
equal to the decoding window maximum size. The ew_max_size is the
main parameter at a FECFRAME sender, but its exact value has no
impact on the the FEC-related latency budget. The ew_max_size
parameter is computed as follows:
ew_max_size = dw_max_size * WSR / 255
In line with [Roca17], WSR = 191 is considered as a reasonable value
(the resulting encoding to decoding window size ratio is then close
to 0.75), but other values between 1 and 255 inclusive are possible,
depending on the use-case.
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 * 255 / WSR
A receiver can then chose an appropriate linear system maximum size:
ls_max_size >= dw_max_size
It is good practice to use a larger value for ls_max_size as
explained in Appendix D, which does not impact maximum latency nor
interoperability.
In any case, for a given use-case (i.e., for target encoding and
decoding devices and desired protection levels in front of
communication impairments) and for the computed ew_max_size,
dw_max_size and ls_max_size values, it is RECOMMENDED to check that
the maximum encoding time and maximum memory requirements at a
FECFRAME sender, and maximum decoding time and maximum memory
requirements at a FECFRAME receiver, stay within reasonable bounds.
When assuming that the encoding and decoding times are negligible
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with respect to the target max_lat, this should be verified as well,
otherwise the max_lat SHOULD be adjusted accordingly.
The particular case of session start needs to be managed
appropriately since the ew_size, starting at zero, increases each
time a new source ADU is received by the FECFRAME sender, until it
reaches the ew_max_size value. Therefore 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 its ls_max_size accordingly if need be. With a CBR flow,
session start is expected to be the only moment when the encoding
window size will increase. Similarly, with a CBR real-time flow, the
session end is expected to be the only moment when the encoding
window size will progressively decrease. No adjustment of the
ls_max_size is required at the FECFRAME receiver in that case.
C.2. Other Types of Real-Time Flow
In the following, we consider a real-time source ADU flow with a
max_lat latency budget and a variable bitrate (VBR) measured at the
entry of the FECFRAME sender. A first approach consists in
considering the smallest instantaneous bitrate of the source ADU
flow, when this parameter is known, and to reuse the derivation of
Appendix C.1. Considering the smallest bitrate means that the
encoding and decoding window maximum size estimations are
pessimistic: these windows have the smallest size required to enable
on-time decoding at a FECFRAME receiver. If the instantaneous
bitrate is higher than this smallest bitrate, this approach leads to
an encoding window that is unnecessarily small, which reduces
robustness in front of long erasure bursts.
Another approach consists in using ADU timing information (e.g.,
using the timestamp field of an RTP packet header, or registering the
time upon receiving a new ADU). From the global FEC-related latency
budget, the FECFRAME sender can derive a practical maximum latency
budget for encoding operations, max_lat_for_encoding. For the FEC
Schemes specified in this document, this latency budget SHOULD be
computed with:
max_lat_for_encoding = max_lat * WSR / 255
It follows that any source symbols associated to an ADU that has
timed-out with respect to max_lat_for_encoding SHOULD be removed from
the encoding window. With this approach there is no pre-determined
ew_size value: this value fluctuates over the time according to the
instantaneous source ADU flow bitrate. For practical reasons, a
FECFRAME sender may still require that ew_size does not increase
beyond a maximum value (Appendix C.3).
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With both approaches, and 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 ls_max_size as explained in Appendix C.1.
When the observed NSS fluctuates significantly, a FECFRAME receiver
may want to adapt its ls_max_size accordingly. In particular when
the NSS is significantly reduced, a FECFRAME receiver may want to
reduce the ls_max_size too in order to limit computation complexity.
A balance must be found between using an ls_max_size "too large"
(which increases computation complexity and memory requirements) and
the opposite (which reduces recovery performance).
C.3. Case of a Non Real-Time Flow
Finally there are configurations where a source ADU flow has no 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. For instance, it
can derive from an estimation of the maximum memory amount that could
be dedicated to the linear system at a FECFRAME receiver, or the
maximum computation complexity at a FECFRAME receiver, both of them
depending on the ls_max_size parameter. The same considerations also
apply to the FECFRAME sender, where the maximum memory amount and
computation complexity depend on the ew_max_size parameter.
Here also, the NSS value contained in FEC Repair Packets is used by a
FECFRAME receiver to determine the current coding window size and
ew_max_size by observing its maximum value over the time.
Appendix D. Decoding Beyond Maximum Latency Optimization
(Informational)
This annex introduces non normative considerations. It is provided
as suggestions, without any impact on interoperability. For more
information see [Roca16].
With a real-time source ADU flow, it is possible to improve the
decoding performance of sliding window codes without impacting
maximum latency, at the cost of extra memory and CPU overhead. The
optimization consists, for a FECFRAME receiver, to extend the linear
system beyond the decoding window maximum size, by keeping a certain
number of old source symbols whereas their associated ADUs timed-out:
ls_max_size > dw_max_size
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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 receiver that benefits from an FEC
protection significantly higher than what is required to recover from
packet losses, can choose to reduce the ls_max_size. In that case
lost ADUs will be recovered 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 13: 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 (the "late source symbols" of Figure 13). 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 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 local
decisions made by each receiver independently, without any impact on
the other receivers nor on the source.
Authors' Addresses
Vincent Roca
INRIA
Univ. Grenoble Alpes
France
EMail: vincent.roca@inria.fr
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Belkacem Teibi
INRIA
Univ. Grenoble Alpes
France
EMail: belkacem.teibi@gmail.com
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