```
/*
* Fills in the table of coding coefficients (of the right size)
* provided with the appropriate number of coding coefficients to
* use for the repair symbol key provided.
*
* (in) repair_key key associated to this repair symbol. This
* parameter is ignored (useless) if m=2 and dt=15
* (in) cc_tab[] pointer to a table of the right size to store
* coding coefficients. All coefficients are
* stored as bytes, regardless of the m parameter,
* upon return of this function.
* (in) cc_nb number of entries in the table. This value is
* equal to the current encoding window size.
* (in) dt integer between 0 and 15 (inclusive) that
* controls the density. With value 15, all
* coefficients are guaranteed to be non zero
* (i.e. equal to 1 with GF(2) and equal to a
* value in {1,... 255} with GF(2^^8)), otherwise
* a fraction of them will be 0.
* (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_t repair_key,
uint8_t cc_tab[],
uint16_t cc_nb,
uint8_t dt,
uint8_t m)
{
uint32_t i;
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tinymt32_t s; /* PRNG internal state */
if (dt > 15) {
return SOMETHING_WENT_WRONG; /* bad dt 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 */
tinymt32_init(&s, repair_key);
for (i = 0 ; i < cc_nb ; i++) {
if (tinymt32_rand(&s, 16) <= dt) {
cc_tab[i] = (uint8_t) 1;
} else {
cc_tab[i] = (uint8_t) 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_rand(&s, 256);
} while (cc_tab[i] == 0);
}
} else {
/* here a certain fraction of coefficients should be 0 */
for (i = 0 ; i < cc_nb ; i++) {
if (tinymt32_rand(&s, 16) <= dt) {
do {
cc_tab[i] = (uint8_t) tinymt32_rand(&s, 256);
} while (cc_tab[i] == 0);
} else {
cc_tab[i] = 0;
}
}
}
break;
default:
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/* bad parameter m */
return SOMETHING_WENT_WRONG;
}
return EVERYTHING_IS_OKAY;
}
``````
Figure 2: Coding Coefficients Generation Function pseudo-code
3.6. Finite Fields Operations
3.6.1. 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.
3.6.2. 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] + cc_tab[1] * src_1[i] + ... +
cc_tab[ew_size - 1] * src_ew_size_1[i]
where * is the multiplication over GF(2^^8) and + is an XOR
operation. In practice various optimizations need to be used in
order to make this computation efficient (see in particular [PGM13]).
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With the RLC over GF(2) FEC Scheme (binary case), a linear
combination is computed as follows. The repair symbol is the XOR sum
of all the source symbols corresponding to a coding coefficient
cc_tab[j] equal to 1 (i.e., the source symbols corresponding to zero
coding coefficients are ignored). The XOR sum of the byte of
position i in each source is computed and stored in the corresponding
byte of the repair symbol, where i belongs to {0; E-1}. In practice,
the XOR sums will be computed several bytes at a time (e.g., on 64
bit words, or on arrays of 16 or more bytes when using SIMD CPU
extensions).
With both FEC Schemes, the details of how to optimize the computation
of these linear combinations are of high practical importance but out
of scope of this document.
4. Sliding Window RLC FEC Scheme over GF(2^^8) for Arbitrary 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;
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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
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
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source symbol, and after reaching the maximum value (2^32-1),
wrapping to zero occurs.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Symbol ID (ESI) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: Source FEC Payload ID Encoding Format
4.1.3. Repair FEC Payload ID
A FEC Repair Packet MAY contain one or more repair symbols. When
there are several repair symbols, all of them MUST have been
generated from the same encoding window, using Repair_Key values that
are managed as explained below. A receiver can easily deduce the
number of repair symbols within a FEC Repair Packet by comparing the
received FEC Repair Packet size (equal to the UDP payload size when
UDP is the underlying transport protocol) and the symbol size, E,
communicated in the FFCI.
A FEC Repair Packet MUST contain a Repair FEC Payload ID that is
prepended to the repair symbol as illustrated in Figure 6.
+--------------------------------+
| IP Header |
+--------------------------------+
| Transport Header |
+--------------------------------+
| Repair FEC Payload ID |
+--------------------------------+
| Repair Symbol |
+--------------------------------+
Figure 6: Structure of an FEC Repair Packet with the Repair FEC
Payload ID
More precisely, the Repair FEC Payload ID is composed of the
following fields (Figure 7):
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. 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.
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Density Threshold for the coding coefficients, DT (4-bit field):
this unsigned integer carries the Density Threshold (DT) used by
the coding coefficient generation function Section 3.5. More
precisely, it controls the probability of having a non zero coding
coefficient, which equals (DT+1) / 16. When a FEC Repair Packet
contains several repair symbols, the DT value applies to all of
them;
Number of Source Symbols in the encoding window, NSS (12-bit field):
this unsigned integer indicates the number of source symbols in
the encoding window when this repair symbol was generated. When a
FEC Repair Packet contains several repair symbols, this NSS value
applies to all of them;
ESI of First Source Symbol in the encoding window, FSS_ESI (32-bit
field):
this unsigned integer indicates the ESI of the first source symbol
in the encoding window when this repair symbol was generated.
When a FEC Repair Packet contains several repair symbols, this
FSS_ESI value applies to all of them;
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Repair_Key | DT |NSS (# src symb in ew) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| FSS_ESI |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: Repair FEC Payload ID Encoding Format
4.1.4. Additional Procedures
The following procedure applies:
o The ESI of source symbols MUST start with value 0 for the first
source symbol and MUST be managed sequentially. Wrapping to zero
happens after reaching the maximum 32-bit value.
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
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5.1.1. FEC Framework Configuration Information
5.1.1.1. FEC Encoding ID
o FEC Encoding ID: the value assigned to this fully specified FEC
Scheme MUST be YYYY, as assigned by IANA (Section 10).
When SDP is used to communicate the FFCI, this FEC Encoding ID is
carried in the 'encoding-id' parameter.
5.1.1.2. FEC Scheme-Specific Information
All the considerations of Section 4.1.1.2 apply here.
5.1.2. Explicit Source FEC Payload ID
All the considerations of Section 4.1.1.2 apply here.
5.1.3. Repair FEC Payload ID
All the considerations of Section 4.1.1.2 apply here, with the only
exception that the Repair_Key field is useless if DT = 15 (indeed, in
that case all the coefficients are necessarily equal to 1 and the
coefficient generation function does not use any PRNG). When DT = 15
it is RECOMMENDED that the sender use value 0 for the Repair_Key
field, but a receiver SHALL ignore this field.
5.1.4. Additional Procedures
All the considerations of Section 4.1.1.2 apply here.
6. FEC Code Specification
6.1. Encoding Side
This section provides a high level description of a Sliding Window
RLC encoder.
Whenever a new FEC Repair Packet is needed, the RLC encoder instance
first gathers the ew_size source symbols currently in the sliding
encoding window. Then it chooses a repair key, which can be a
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 3.5) 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
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(Section 3.6). 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 3.5), 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
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
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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 B 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 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
before or after FEC protection, within the end-system or in a
middlebox), to the operational constraints (e.g., performing FEC
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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);
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
malfunctions whose nature depends on implementation details. Here
also, the attack always results in a form of DoS;
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
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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].
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.
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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 Section 3.1.1. It is RECOMMENDED to check that the
computed values stay within reasonnable bounds since numerical
overflows, caused by an erroneous implementation or an erroneous
input value, may lead to hazardous behaviours. However what
"reasonnable bounds" means is use-case and implementation dependent
and is not detailed in this document.
Section 3.1.2 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
reasonnable bounds.
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.
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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
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 Russ Housley, Alan DeKok, Spencer
Dawkins, Gorry Fairhurst, Jonathan Detchart, Emmanuel Lochin, and
Marie-Jose Montpetit for their valuable feedbacks on this document.
12. References
12.1. Normative References
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[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), September 2018,
```.
[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, .
12.2. Informative References
[KR12] Rikitake, K., "TinyMT Pseudo Random Number Generator for
Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
September 14, 2012, Copenhagen, Denmark, DOI:
http://dx.doi.org/10.1145/2364489.2364504, September 2012.
[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,
.
[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,
.
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[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,
.
[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 Pseudo-Random Number Generator
The TinyMT32 PRNG reference implementation is distributed under a BSD
license by the authors and excerpts of it are reproduced in Figure 8.
The differences with respect to the original source code are:
o the unused parts of the original source code have been removed;
o the appropriate parameter set has been added to the initialization
function;
o the tinymt32_rand() function has been added;
o the function order has been changed;
o certain internal variables have been renamed for compactness
purposes.
```
/**
* Tiny Mersenne Twister only 127 bit internal state
*
* Authors : Mutsuo Saito (Hiroshima University)
* Makoto Matsumoto (University of Tokyo)
*
* Copyright (c) 2011, 2013 Mutsuo Saito, Makoto Matsumoto,
* Hiroshima University and The University of Tokyo.
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials
* provided with the distribution.
* - Neither the name of the Hiroshima University nor the names of
* its contributors may be used to endorse or promote products
* derived from this software without specific prior written
* permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND
* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,
* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
* EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
* TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
* TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF
* THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include
```
/**
* tinymt32 internal state vector and parameters
*/
typedef struct {
uint32_t status[4];
uint32_t mat1;
uint32_t mat2;
uint32_t tmat;
} tinymt32_t;
static void tinymt32_next_state (tinymt32_t * s);
static uint32_t tinymt32_temper (tinymt32_t * s);
static double tinymt32_generate_32double (tinymt32_t * s);
/**
* Parameter set to use for the IETF RLC FEC Schemes specification.
* Do not change.
* This parameter set is the first entry of the precalculated parameter
* sets in file tinymt32dc.0.1048576.txt, by Kenji Rikitake, available
* at: https://github.com/jj1bdx/tinymtdc-longbatch/blob/master/
* tinymt32dc/tinymt32dc.0.1048576.txt
* It is also the parameter set used:
* Rikitake, K., "TinyMT Pseudo Random Number Generator for
* Erlang", ACM 11th SIGPLAN Erlang Workshop (Erlang'12),
* September, 2012.
*/
#define TINYMT32_MAT1_PARAM 0x8f7011ee
#define TINYMT32_MAT2_PARAM 0xfc78ff1f
#define TINYMT32_TMAT_PARAM 0x3793fdff
/**
* This function initializes the internal state array with a 32-bit
* unsigned integer seed.
* @param s pointer to tinymt internal state.
* @param seed a 32-bit unsigned integer used as a seed.
*/
void tinymt32_init (tinymt32_t * s, uint32_t seed)
{
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#define MIN_LOOP 8
#define PRE_LOOP 8
s->status[0] = seed;
s->status[1] = s->mat1 = TINYMT32_MAT1_PARAM;
s->status[2] = s->mat2 = TINYMT32_MAT2_PARAM;
s->status[3] = s->tmat = TINYMT32_TMAT_PARAM;
for (int i = 1; i < MIN_LOOP; i++) {
s->status[i & 3] ^= i + UINT32_C(1812433253)
* (s->status[(i - 1) & 3]
^ (s->status[(i - 1) & 3] >> 30));
}
for (int i = 0; i < PRE_LOOP; i++) {
tinymt32_next_state(s);
}
}
/**
* This function outputs an integer in the [0 .. maxv-1] range.
* @param s pointer to tinymt internal state.
* @return 32-bit unsigned integer between 0 and maxv-1 inclusive.
*/
uint32_t tinymt32_rand (tinymt32_t * s, uint32_t maxv)
{
return (uint32_t)(tinymt32_generate_32double(s) * (double)maxv);
}
/**
* Internal tinymt32 constants and functions.
* Users should not call these functions directly.
*/
#define TINYMT32_MEXP 127
#define TINYMT32_SH0 1
#define TINYMT32_SH1 10
#define TINYMT32_SH8 8
#define TINYMT32_MASK UINT32_C(0x7fffffff)
#define TINYMT32_MUL (1.0f / 16777216.0f)
/**
* This function changes internal state of tinymt32.
* @param s pointer to tinymt internal state.
*/
static void tinymt32_next_state (tinymt32_t * s)
{
uint32_t x;
uint32_t y;
y = s->status[3];
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x = (s->status[0] & TINYMT32_MASK)
^ s->status[1]
^ s->status[2];
x ^= (x << TINYMT32_SH0);
y ^= (y >> TINYMT32_SH0) ^ x;
s->status[0] = s->status[1];
s->status[1] = s->status[2];
s->status[2] = x ^ (y << TINYMT32_SH1);
s->status[3] = y;
s->status[1] ^= -((int32_t)(y & 1)) & s->mat1;
s->status[2] ^= -((int32_t)(y & 1)) & s->mat2;
}
/**
* This function outputs 32-bit unsigned integer from internal state.
* @param s pointer to tinymt internal state.
* @return 32-bit unsigned pseudos number
*/
static uint32_t tinymt32_temper (tinymt32_t * s)
{
uint32_t t0, t1;
t0 = s->status[3];
t1 = s->status[0] + (s->status[2] >> TINYMT32_SH8);
t0 ^= t1;
t0 ^= -((int32_t)(t1 & 1)) & s->tmat;
return t0;
}
/**
* This function outputs double precision floating point number from
* internal state. The returned value has 32-bit precision.
* In other words, this function makes one double precision floating
* point number from one 32-bit unsigned integer.
* @param s pointer to tinymt internal state.
* @return floating point number r (0.0 <= r < 1.0)
*/
static double tinymt32_generate_32double (tinymt32_t * s)
{
tinymt32_next_state(s);
return (double)tinymt32_temper(s) * (1.0 / 4294967296.0);
}
```
Figure 8: TinyMT32 pseudo-code
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Appendix B. Decoding Beyond Maximum Latency Optimization
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
Usually the following choice is a good trade-off between decoding
performance and extra CPU overhead:
ls_max_size = 2 * dw_max_size
When the dw_max_size is very small, it may be preferable to keep a
minimum ls_max_size value (e.g., LS_MIN_SIZE_DEFAULT = 40 symbols).
Going below this threshold will not save a significant amount of
memory nor CPU cycles. Therefore:
ls_max_size = max(2 * dw_max_size, LS_MIN_SIZE_DEFAULT)
Finally, it is worth noting that a good receiver, i.e., a receiver
that benefits from 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 9: 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 9). It follows that
the corresponding ADUs will not be useful to the application.
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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
Belkacem Teibi
INRIA
Univ. Grenoble Alpes
France
EMail: belkacem.teibi@inria.fr
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```