Internet DRAFT - draft-irtf-nwcrg-tetrys
draft-irtf-nwcrg-tetrys
NWCRG J. Detchart
Internet-Draft ISAE-SUPAERO
Intended status: Experimental E. Lochin
Expires: 21 May 2023 ENAC
J. Lacan
ISAE-SUPAERO
V. Roca
INRIA
17 November 2022
Tetrys, an On-the-Fly Network Coding Protocol
draft-irtf-nwcrg-tetrys-04
Abstract
This document describes Tetrys, an On-The-Fly Network Coding (NC)
protocol that can be used to transport delay-sensitive and loss-
sensitive data over a lossy network. Tetrys may recover from
erasures within an RTT-independent delay, thanks to the transmission
of Coded Packets. This document is a record of the experience gained
by the authors while developing and testing the Tetrys protocol in
real conditions.
This document is a product of the Coding for Efficient Network
Communications Research Group (NWCRG). It conforms to the NWCRG
taxonomy[RFC8406].
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
working documents as Internet-Drafts. The list of current Internet-
Drafts is at https://datatracker.ietf.org/drafts/current/.
Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "work in progress."
This Internet-Draft will expire on 21 May 2023.
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Copyright Notice
Copyright (c) 2022 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
extracted from this document must include Revised BSD License text as
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provided without warranty as described in the Revised BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements Notation . . . . . . . . . . . . . . . . . . 4
2. Definitions, Notations and Abbreviations . . . . . . . . . . 4
3. Architecture . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1. Use Cases . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2. Overview . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Tetrys Basic Functions . . . . . . . . . . . . . . . . . . . 7
4.1. Encoding . . . . . . . . . . . . . . . . . . . . . . . . 7
4.2. The Elastic Encoding Window . . . . . . . . . . . . . . . 8
4.3. Decoding . . . . . . . . . . . . . . . . . . . . . . . . 8
5. Packet Format . . . . . . . . . . . . . . . . . . . . . . . . 8
5.1. Common Header Format . . . . . . . . . . . . . . . . . . 8
5.1.1. Header Extensions . . . . . . . . . . . . . . . . . . 10
5.2. Source Packet Format . . . . . . . . . . . . . . . . . . 11
5.3. Coded Packet Format . . . . . . . . . . . . . . . . . . . 12
5.3.1. The Encoding Vector . . . . . . . . . . . . . . . . . 13
5.4. Window Update Packet Format . . . . . . . . . . . . . . . 17
6. Research Issues . . . . . . . . . . . . . . . . . . . . . . . 18
6.1. Interaction with Congestion Control . . . . . . . . . . . 18
6.2. Adaptive Coding Rate . . . . . . . . . . . . . . . . . . 19
6.3. Using Tetrys Below The IP Layer For Tunneling . . . . . . 21
7. Security Considerations . . . . . . . . . . . . . . . . . . . 21
7.1. Problem Statement . . . . . . . . . . . . . . . . . . . . 21
7.2. Attacks against the Data Flow . . . . . . . . . . . . . . 21
7.3. Attacks against Signaling . . . . . . . . . . . . . . . . 22
7.4. Attacks against the Network . . . . . . . . . . . . . . . 22
7.5. Baseline Security Operation . . . . . . . . . . . . . . . 23
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 23
9. Implementation Status . . . . . . . . . . . . . . . . . . . . 23
10. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 23
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 24
11.1. Normative References . . . . . . . . . . . . . . . . . . 24
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11.2. Informative References . . . . . . . . . . . . . . . . . 25
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 26
1. Introduction
This document is a product of and represents the collaborative work
and consensus of the Coding for Efficient Network Communications
Research Group (NWCRG). It is not an IETF product and is not an IETF
standard.
This document describes Tetrys, a novel erasure coding protocol.
Network codes were introduced in the early 2000s [AHL-00] to address
the limitations of transmission over the Internet (delay, capacity
and packet loss). While network codes have seen some deployment
fairly recently in the Internet community, the use of application
layer erasure codes in the IETF has already been standardized in the
RMT [RFC3452] and the FECFRAME [RFC8680] working groups. The
protocol presented here may be seen as a network coding extension to
standard unicast transport protocols (or even multicast or anycast
with a few modifications). The current proposal may be considered a
combination of network erasure coding and feedback mechanisms
[Tetrys], [Tetrys-RT] .
The main innovation of the Tetrys protocol is in the generation of
Coded Packets from an Elastic Encoding Window. This window is filled
by any Source Packets coming from an input flow and is periodically
updated with the receiver feedback. These feedback messages provide
to the sender with information about the highest sequence number
received or rebuilt, which can enable flushing the corresponding
Source Packets stored in the encoding window. The size of this
window may be fixed or dynamically updated. If the window is full,
incoming Source Packets replace older sources packets which are
dropped. As a matter of fact, its limit should be correctly sized.
Finally, Tetrys allows to deal with losses on both the forward and
return paths and in particular, is resilient to acknowledgment
losses. All these operations are further detailed in Section 4.
With Tetrys, a Coded Packet is a linear combination over a finite
field of the data Source Packets belonging to the coding window. The
coefficients finite field's choice is a trade-off between the best
erasure recovery performance (finite fields of 256 elements) and the
system constraints (finite fields of 16 elements is preferred) and is
driven by the application.
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Thanks to the Elastic Encoding Window, the Coded Packets are built
on-the-fly, by using a predefined method to choose the coefficients.
The redundancy ratio may be dynamically adjusted, and the
coefficients may be generated in different ways, during the
transmission. Compared to FEC block codes, this allows reducing the
bandwidth use and the decoding delay.
The description of the design of the Tetrys protocol in this document
is complemented by a record of the experience gained by the authors
while developing and testing the Tetrys protocol in realistic
conditions. In particular, several research issues are discussed in
Section 6 following our own experience and observations.
1.1. Requirements Notation
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
BCP14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
2. Definitions, Notations and Abbreviations
The notation used in this document is based on the NWCRG taxonomy
[RFC8406] .
Source Symbol: a symbol that is transmitted between the ingress
and egress of the network.
Coded Symbol: a linear combination over a finite field of a set of
Source Symbols.
Source Symbol ID: a sequence number to identify the Source
Symbols.
Coded Symbol ID: a sequence number to identify the Coded Symbols.
Encoding Coefficients: elements of the finite field characterizing
the linear combination used to generate Coded Symbols.
Encoding Vector: a set of the coding coefficients and input Source
Symbol IDs.
Source Packet: a Source Packet contains a Source Symbol with its
associated IDs.
Coded Packet: a Coded Packet contains a Coded Symbol, the Coded
Symbol's ID, and Encoding Vector.
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Input Symbol: a symbol at the input of the Tetrys Encoder.
Output Symbol: a symbol generated by the Tetrys Encoder. For a
non-systematic mode, all Output Symbols are Coded Symbols. For a
systematic mode, Output Symbols MAY be the Input Symbols and a
number of Coded Symbols that are linear combinations of the Input
Symbols + the Encoding Vectors.
Feedback Packet: a Feedback Packet is a packet containing
information about the decoded or received Source Symbols. It MAY
also contain additional information about the Packet Error Rate or
the number of various packets in the receiver decoding window.
Elastic Encoding Window: an encoder-side buffer that stores all
the non-acknowledged Source Packets of the input flow involved in
the coding process.
Coding Coefficient Generator Identifier: a unique identifier that
defines a function or an algorithm allowing to generate the
Encoding Vector.
Code Rate: Define the rate between the number of Input Symbols and
the number of Output Symbols.
3. Architecture
3.1. Use Cases
Tetrys is well suited, but not limited to, the use case where there
is a single flow originated by a single source, with intra stream
coding at a single encoding node. Note that the input stream MAY be
a multiplex of several upper layer streams. Transmission MAY be over
a single path or multiple paths. This is the simplest use-case, that
is very much aligned with currently proposed scenarios for end-to-end
streaming.
3.2. Overview
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+----------+ +----------+
| | | |
| App | | App |
| | | |
+----------+ +----------+
| ^
| Source Source |
| Symbols Symbols |
| |
v |
+----------+ +----------+
| | output packets | |
| Tetrys |--------------->| Tetrys |
| Encoder |Feedback Packets| Decoder |
| |<---------------| |
+----------+ +----------+
Figure 1: Tetrys Architecture
The Tetrys protocol features several key functionalities. The
mandatory features are:
* on-the-fly encoding;
* decoding;
* signaling, to carry in particular the symbol identifiers in the
encoding window and the associated coding coefficients when
meaningful;
* feedback management;
* elastic window management;
* Tetrys packet header creation and processing;
and the optional features are :
* channel estimation;
* dynamic adjustment of the Code Rate and flow control;
* congestion control management (if appropriate). See Section 6.1
for further details;
Several building blocks provide these functionalities:
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* The Tetrys Building Block: this BB embeds both the Tetrys Decoder
and Tetrys Encoder and thus, is used during encoding, and decoding
processes. It must be noted that Tetrys does not mandate a
specific building block. Instead, any building block compatible
with the Elastic Encoding Window feature of Tetrys may be used.
* The Window Management Building Block: this building block is in
charge of managing the encoding window at a Tetrys sender.
To ease the addition of future components and services, Tetrys adds a
header extension mechanism, compatible with that of LCT [RFC5651],
NORM [RFC5740], FECFRAME [RFC8680].
4. Tetrys Basic Functions
4.1. Encoding
At the beginning of a transmission, a Tetrys Encoder MUST choose an
initial Code Rate (added redundancy) as it doesn't know the packet
loss rate of the channel. In the steady state, depending on the Code
Rate, the Tetrys Encoder MAY generate Coded Symbols when it receives
a Source Symbol from the application or some feedback from the
decoding blocks.
When a Tetrys Encoder needs to generate a Coded Symbol, it considers
the set of Source Symbols stored in the Elastic Encoding Window and
generates an Encoding Vector with the Coded Symbol. These Source
Symbols are the set of Source Symbols that are not yet acknowledged
by the receiver. For each Source Symbol, a finite field coefficient
is determined using a Coding Coefficient Generator. This generator
MAY take as input the Source Symbol IDs and the Coded Symbol ID and
MAY determine a coefficient in a deterministic way as presented in
Section 5.3. Finally, the Coded Symbol is the sum of the Source
Symbols multiplied by their corresponding coefficients.
A Tetrys Encoder SHOULD set a limit to the Elastic Encoding Window
maximum size. This controls the algorithmic complexity at the
encoder and decoder by limiting the size of linear combinations. It
is also needed in situations where window update packets are all lost
or absent.
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4.2. The Elastic Encoding Window
When an input Source Symbol is passed to a Tetrys Encoder, it is
added to the Elastic Encoding Window. This window MUST have a limit
set by the encoding building Block. If the Elastic Encoding Window
reached its limit, the window slides over the symbols: the first
(oldest) symbol is removed, and the newest symbol is added. As an
element of the coding window, this symbol is included in the next
linear combinations created to generate the Coded Symbols.
As explained below, the Tetrys Decoder sends periodic feedback
indicating the received or decoded Source Symbols. When the sender
receives the information that a Source Symbol was received or decoded
by the receiver, it removes this symbol from the coding window.
4.3. Decoding
A standard Gaussian elimination is sufficient to recover the erased
Source Symbols, when the matrix rank enables it.
5. Packet Format
5.1. Common Header Format
All types of Tetrys packets share the same common header format (see
Figure 2).
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| V | C |S| Reserved | HDR_LEN | PKT_TYPE |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Congestion Control Information (CCI, length = 32*C bits) |
| ... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Transport Session Identifier (TSI, length = 32*S bits) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Header Extensions (if applicable) |
| ... |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2: Common Header Format
As already noted above in the document, this format is inspired and
inherits from the LCT header format [RFC5651] with slight
modifications.
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* Tetrys version number (V): 4 bits. Indicates the Tetrys version
number. The Tetrys version number for this specification is 1.
* Congestion control flag (C): 2 bits. C=0 indicates the Congestion
Control Information (CCI) field is 0 bits in length. C=1
indicates the CCI field is 32 bits in length. C=2 indicates the
CCI field is 64 bits in length. C=3 indicates the CCI field is 96
bits in length.
* Transport Session Identifier flag (S): 1 bit. This is the number
of full 32-bit words in the TSI field. The TSI field is 32*S bits
in length, i.e., the length is either 0 bits or 32 bits.
* Reserved (Resv): 9 bits. These bits are reserved. In this
version of the specification, they MUST be set to zero by senders
and MUST be ignored by receivers.
* Header length (HDR_LEN): 8 bits. The total length of the Tetrys
header in units of 32-bit words. The length of the Tetrys header
MUST be a multiple of 32 bits. This field may be used to directly
access the portion of the packet beyond the Tetrys header, i.e.,
to the first next header if it exists, or to the packet payload if
it exists and there is no other header, or to the end of the
packet if there are no others headers or packet payload.
* PKT_TYPE: Tetrys packet type, 8 bits. Type of packet. There is 3
types of packets: the PKT_TYPE_SOURCE (0) defined in Section 5.2,
the PKT_TYPE_CODED (1) defined in Section 5.3 and the
PKT_TYPE_WND_UPT (3), for window update packets defined in
Section 5.4.
* Congestion Control Information (CCI): 0, 32, 64, or 96 bits Used
to carry congestion control information. For example, the
congestion control information could include layer numbers,
logical channel numbers, and sequence numbers. This field is
opaque for this specification. This field MUST be 0 bits (absent)
if C=0. This field MUST be 32 bits if C=1. This field MUST be 64
bits if C=2. This field MUST be 96 bits if C=3.
* Transport Session Identifier (TSI): 0 or 32 bits The TSI uniquely
identifies a session among all sessions from a particular Tetrys
encoder. The TSI is scoped by the IP address of the sender, and
thus the IP address of the sender and the TSI together uniquely
identify the session. Although a TSI, conjointly with the IP
address of the sender, always uniquely identifies a session,
whether the TSI is included in the Tetrys header depends on what
is used as the TSI value. If the underlying transport is UDP,
then the 16-bit UDP source port number MAY serve as the TSI for
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the session. If there is no underlying TSI provided by the
network, transport or any other layer, then the TSI MUST be
included in the Tetrys header.
5.1.1. Header Extensions
Header Extensions are used in Tetrys to accommodate optional header
fields that are not always used or have variable size. The presence
of Header Extensions MAY be inferred by the Tetrys header length
(HDR_LEN). If HDR_LEN is larger than the length of the standard
header, then the remaining header space is taken by Header
Extensions.
If present, Header Extensions MUST be processed to ensure that they
are recognized before performing any congestion control procedure or
otherwise accepting a packet. The default action for unrecognized
Header Extensions is to ignore them. This allows the future
introduction of backward-compatible enhancements to Tetrys without
changing the Tetrys version number. Non-backward-compatible Header
Extensions CANNOT be introduced without changing the Tetrys version
number.
There are two formats for Header Extensions as depicted in Figure 3 :
* The first format is used for variable-length extensions, with
Header Extension Type (HET) values between 0 and 127.
* The second format is used for fixed-length (one 32-bit word)
extensions, using HET values from 128 to 255.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| HET (<=127) | HEL | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
. .
. Header Extension Content (HEC) .
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| HET (>=128) | Header Extension Content (HEC) |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: Header Extension Format
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* Header Extension Type (HET): 8 bits
The type of the Header Extension. This document defines several
possible types. Additional types may be defined in future
versions of this specification. HET values from 0 to 127 are used
for variable-length Header Extensions. HET values from 128 to 255
are used for fixed-length 32-bit Header Extensions.
* Header Extension Length (HEL): 8 bits
The length of the whole Header Extension field, expressed in
multiples of 32-bit words. This field MUST be present for
variable-length extensions (HETs between 0 and 127) and MUST NOT
be present for fixed-length extensions (HETs between 128 and 255).
* Header Extension Content (HEC): variable length
The content of the Header Extension. The format of this subfield
depends on the Header Extension Type. For fixed-length Header
Extensions, the HEC is 24 bits. For variable-length Header
Extensions, the HEC field has variable size, as specified by the
HEL field. Note that the length of each Header Extension MUST be
a multiple of 32 bits. Also, note that the total size of the
Tetrys header, including all Header Extensions and all optional
header fields, cannot exceed 255 32-bit words.
5.2. Source Packet Format
A Source Packet is a Common Packet Header encapsulation, a Source
Symbol ID and a Source Symbol (payload). The Source Symbols MAY have
variable sizes.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ Common Packet Header /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Symbol ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ Payload /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: Source Packet Format
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Common Packet Header: a common packet header (as common header
format) where Packet Type=0.
Source Symbol ID: the sequence number to identify a Source Symbol.
Payload: the payload (Source Symbol)
5.3. Coded Packet Format
A Coded Packet is the encapsulation of a Common Packet Header, a
Coded Symbol ID, the associated Encoding Vector, and a Coded Symbol
(payload). As the Source Symbols MAY have variable sizes, all the
Source Symbol sizes need to be encoded. To generate this encoded
payload size, as a 16-bit unsigned value, the linear combination uses
the same coefficients as the coded payload. The result MUST be
stored in the Coded Packet as the Encoded Payload Size (16 bits): as
it is an optional field, the Encoding Vector MUST signal the use of
variable Source Symbol sizes with the field V (see Section 5.3.1).
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ Common Packet Header /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Coded Symbol ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ Encoding Vector /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoded Payload Size | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| |
/ Payload /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: Coded Packet Format
Common Packet Header: a common packet header (as common header
format) where Packet Type=1.
Coded Symbol ID: the sequence number to identify a Coded Symbol.
Encoding Vector: an Encoding Vector to define the linear combination
used (coefficients and Source Symbols).
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Encoded Payload Size: the coded payload size used if the Source
Symbols have a variable size (optional,Section 5.3.1).
Payload: the Coded Symbol.
5.3.1. The Encoding Vector
An Encoding Vector contains all the information about the linear
combination used to generate a Coded Symbol. The information
includes the source identifiers and the coefficients used for each
Source Symbol. It MAY be stored in different ways depending on the
situation.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| EV_LEN | CCGI | I |C|V| NB_IDS | NB_COEFS |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| FIRST_SOURCE_ID |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| b_id | |
+-+-+-+-+-+-+-+-+ id_bit_vector +-+-+-+-+-+-+-+
| | Padding |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
+ coef_bit_vector +-+-+-+-+-+-+-+
| | Padding |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 6: Encoding Vector Format
* Encoding Vector Length (EV_LEN) (8-bits): size in units of 32-bit
words.
* Coding Coefficient Generator Identifier (CCGI): 4-bit ID to
identify the algorithm or the function used to generate the
coefficients. As a CCGI is included in each encoded vector, it
MAY dynamically change between the generation of 2 Coded Symbols.
The CCGI builds the coding coefficients used to generate the Coded
Symbols. They MUST be known by all the Tetrys encoders or
decoders. 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
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between two elements is the multiplication modulo a given
irreducible polynomial of degree 8. The following irreducible
polynomial is used for GF(2^(8)): x^(8) + x^(4) + x^(3) + x^(2) +
1 With GF(2^(4)), multiplication between two elements is the
multiplication modulo a given irreducible polynomial of degree 4.
The following irreducible polynomial is used for GF(2^(4)): x^(4)
+ x + 1
- 0: Vandermonde based coefficients over the finite field
GF(2^(4)), as defined below. Each coefficient is built as
alpha^( (source_symbol_id*coded-symbol_id) % 16), with alpha
the root of the primitive polynomial.
- 1: Vandermonde based coefficients over the finite field
GF(2^(8)), as defined below. Each coefficient is built as
alpha^( (source_symbol_id*coded-symbol_id) % 256), with alpha
the root of the primitive polynomial.
- Suppose we want to generate the Coded Symbol 2 as a linear
combination of the Source Symbols 1,2,4 using CCGI=1. The
coefficients will be alpha^( (1 * 1) % 256), alpha^( (1 * 2) %
256), alpha^( (1 * 4) % 256).
* Store the Source Symbol ID Format (I) (2 bits):
- 00 means there is no Source Symbol ID information.
- 01 means the Encoding Vector contains the edge blocks of the
Source Symbol IDs without compression.
- 10 means the Encoding Vector contains the compressed list of
the Source Symbol IDs.
- 11 means the Encoding Vector contains the compressed edge
blocks of the Source Symbol IDs.
* Store the Encoding Coefficients (C): 1 bit to indicate if an
Encoding Vector contains information about the coefficients used.
* Having Source Symbols with Variable Size Encoding (V): set V to 1
if the combination which refers to the Encoding Vector is a
combination of Source Symbols with variable sizes. In this case,
the Coded Packets MUST have the 'Encoded Payload Size' field.
* NB_IDS: the number of source IDs stored in the Encoding Vector
(depending on I).
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* Number of coefficients (NB_COEFS): The number of the coefficients
used to generate the associated Coded Symbol.
* The first source identifier (FIRST_SOURCE_ID): the first Source
Symbol ID used in the combination.
* Number of bits for each edge block (b_id): the number of bits
needed to store the edge.
* Information about the Source Symbol IDs (id_bit_vector): if I=01,
store the edge blocks as b_id * (NB_IDS * 2 - 1). If I=10, store
in a compressed way the edge blocks.
* The coefficients (coef_bit_vector): The coefficients stored
depending on the CCGI (4 or 8 bits for each coefficient).
* Padding: padding to have an Encoding Vector size multiple of
32-bit (for the id and coefficient part).
The Source Symbol IDs are organized as a sorted list of 32-bit
unsigned integers. Depending on the feedback, the Source Symbol IDs
MAY be successive or not in the list. If they are successive, the
boundaries are stored in the Encoding Vector: it just needs 2*32-bit
of information. If not, the full list or the edge blocks MAY be
stored, and a differential transform to reduce the number of bits
needed to represent an identifier MAY be used.
For the following subsections, let's take as an example the
generation of an encoding vector for a Coded Symbol which is a linear
combination of the Source Symbols with IDs 1,2,3,5,6,8,9 and 10 (or
as edge blocks: [1..3],[5..6],[8..10])
There are several ways to store the Source Symbols IDs into the
encoding vector:
* If no information about the Source Symbol IDs is needed, the field
I MUST be set to 0b00: no b_id and no id_bit_vector field
* If the edge blocks are stored without compression, the field I
MUST be set to 0b01. In this case, set b_id to 32 (as a symbol id
is 32 bits), and store into id_bit_vectors the list as 32 bits
unsigned integers: 1,3,5,6,8,10
* If the Source Symbols Ids are stored as a list with compression,
the field I MUST be set to 0b10. In this case, see
Section 5.3.1.1 but rather than compressing the edge blocks, we
compress the full list of the Source Symbol IDs.
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* If the edge blocks are stored with compression, the field I MUST
be set to 0b11. In this case, see Section 5.3.1.1.
5.3.1.1. Compressed list of Source Symbol IDs
Let's continue with our Coded Symbol defined in the previous section.
The Source Symbols IDs used in the linear combination are:
[1..3],[5..6],[8..10].
If we want to compress and store this list into the encoding vector,
we MUST follow this procedure:
1. Keep the first element in the packet as the first_source_id: 1.
2. Apply a differential transform to the other elements
([3,5,6,8,10]) which removes the element i-1 to the element i,
starting with the first_source_id as i0, and get the list L =
[2,2,1,2,2]
3. Compute b, the number of bits needed to store all the elements,
which is ceil(log2(max(L))), where max(L) represents the maximum
of the elements of the list L: here, 2 bits.
4. Write b in the corresponding field, and write all the b * [(2 *
NB blocks) - 1] elements in a bit vector, here: 10 10 01 10 10.
5.3.1.2. Decompressing the Source Symbol IDs
When a Tetrys Decoding Block wants to reverse the operations, this
algorithm is used:
1. Rebuild the list of the transmitted elements by reading the bit
vector and b: [10 10 01 10 10] => [2,2,1,2,2]
2. Apply the reverse transform by adding successively the elements,
starting with first_source_id: [1,1+2,(1+2)+2,(1+2+2)+1,...] =>
[1,3,5,6,8,10]
3. Rebuild the blocks using the list and first_source_id:
[1..3],[5..6],[8..10].
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5.4. Window Update Packet Format
A Tetrys Decoder MAY send back to another building block some Window
Update packets. They contain information about what the packets
received, decoded or dropped, and other information such as a packet
loss rate or the size of the decoding buffers. They are used to
optimize the content of the encoding window. The window update
packets are OPTIONAL, and hence they could be omitted or lost in
transmission without impacting the protocol behavior.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ Common Packet Header /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| nb_missing_src |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| nb_not_used_coded_symb |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| first_src_id |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| plr | sack_size | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| |
/ SACK Vector /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 7: Window Update Packet Format
Common Packet Header: a common packet header (as common header
format) where Packet Type=2.
nb_missing_src: the number of missing Source Symbols in the receiver
since the beginning of the session.
nb_not_used_coded_symb: the number of Coded Symbols at the receiver
that have not already been used for decoding (e.g., the linear
combinations contain at least 2 unknown Source Symbols).
first_src_id: ID of the first Source Symbol to consider in the SACK
vector.
plr: packet loss ratio expressed as a percentage normalized to a
8-bit unsigned integer. For example, 2.5 % will be stored as
floor(2.5 * 256/100) = 6. Conversely, if 6 is the stored value, the
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corresponding packet loss ratio expressed as a percentage is
6*100/256 = 2.34 %. This value is used in the case of dynamic Code
Rate or for statistical purpose. The choice of calculation is left
to the Tetrys Decoder, depending on a window observation, but should
be the PLR seen before decoding.
sack_size: the size of the SACK vector in 32-bit words. For
instance, with value 2, the SACK vector is 64 bits long.
SACK vector: bit vector indicating symbols that must be removed in
the encoding window from the first Source Symbol ID. In most cases,
these symbols were received by the receiver. The other cases concern
some events with non-recoverable packets (for example in the case of
a burst of losses) where it is better to drop and abandon some
packets, and thus to remove them from the encoding window, to allow
the recovery of the following packets. The "First Source Symbol" is
included in this bit vector. A bit equal to 1 at the i-th position
means that this window update packet removes the Source Symbol of ID
equal to "First Source Symbol ID" + i from the encoding window.
6. Research Issues
The present document describes the baseline protocol, allowing
communications between a Tetrys encoder and a Tetrys decoder. In
practice, Tetrys can be used either as a standalone protocol or
embedded inside an existing protocol, and either above, within or
below the transport layer. There are different research questions
related to each of these scenarios that should be investigated for
future protocol improvements. We summarize them in the following
subsections.
6.1. Interaction with Congestion Control
The Tetrys and congestion control components generate two separate
channels (see [RFC9265], section 2.1):
* the Tetrys channel carries source and Coded Packets (from the
sender to the receiver) and information from the receiver to the
sender (e.g., signaling which symbols have been recovered, loss
rate prior and/or after decoding, etc.);
* the congestion control channel carries packets from a sender to a
receiver, and packets signaling information about the network
(e.g., number of packets received versus lost, Explicit Congestion
Notification (ECN) marks, etc.) from the receiver to the sender.
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In practice, depending on how Tetrys is deployed (i.e., above, within
or below the transport layer), [RFC9265] identifies and discusses
several topics. They are briefly listed below and adapted to the
particular case of Tetrys:
* congestion related losses may be hidden if Tetrys is deployed
below the transport layer without any precaution (i.e., Tetrys
recovering packets lost because of a congested router), which can
severely impact the the congestion control efficiency. An
approach is suggested to avoid hiding such signals in [RFC9265],
section 5;
* having Tetrys and non-Tetrys flows sharing the same network links
can raise fairness issues between these flows. The situation
depends in particular on whether some of these flows are
congestion controlled and not others, and which type of congestion
control is used. The details are out of scope of this document,
but may have major impacts in practice;
* coding rate adaptation within Tetrys can have major impacts on
congestion control if done inappropriately. This topic is
discussed more in detail in Section 6.2;
* Tetrys can leverage on multipath transmissions, the Tetrys packets
being sent to the same receiver through multiple paths. Since
paths can largely differ, a per-path flow control and congestion
control adaptation could be needed;
* protecting several application flows within a single Tetrys flow
raises additional questions. This topic is discussed more in
detail in Section 6.3.
6.2. Adaptive Coding Rate
When the network conditions (e.g., delay and loss rate) strongly vary
over time, an adaptive coding rate can be used to increase or reduce
the amount of Coded Packets among a transmission dynamically (i.e.,
the added redundancy), with the help of a dedicated algorithm,
similarly to [A-FEC]. Once again, the strategy differs, depending on
which layer Tetrys is deployed (i.e., above, within or below the
transport layer). Basically, we can slice these strategies in two
distinct classes: when Tetrys is deployed inside the transport layer,
versus outside (i.e., above or below). A deployment within the
transport layer obviously means that interactions between transport
protocol micro-mechanisms, such as the error recovery mechanism, the
congestion control, the flow control or both, are envisioned.
Otherwise, deploying Tetrys within a non congestion controlled
transport protocol, like UDP, would not bring out any other advantage
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than deploying it below or above the transport layer.
The impact deploying a FEC mechanism within the transport layer is
further discussed in [RFC9265], section 4, where considerations
concerning the interactions between congestion control and coding
rates, or the impact of fairness, are investigated. This adaptation
may be done jointly with the congestion control mechanism of a
transport layer protocol, as proposed by [CTCP]. This allows the use
of monitored congestion control metrics (e.g., RTT, congestion
events, or current congestion window size) to adapt the coding rate
conjointly with the computed transport sending rate. The rationale
is to compute an amount of repair traffic that does not lead to
congestion. This joint optimization is mandatory to prevent flows to
consume the whole available capacity as also discussed in
[I-D.singh-rmcat-adaptive-fec] where the authors point out that an
increase in the repair ratio should be done conjointly with a
decrease in the source sending rate.
Finally, adapting a coding rate can also be done outside the
transport layer and without considering transport layer metrics. In
particular, this adaptation may be done jointly with the network as
proposed in [RED-FEC]. In this paper, the authors propose a Random
Early Detection FEC mechanism in the context of video transmission
over wireless networks. Briefly, the idea is to add more redundancy
packets if the queue at the access point is less occupied and vice
versa. A first theoretical attempt for video delivery has been
proposed [THAI] with Tetrys. This approach is interesting as it
illustrates a joint collaboration between the application
requirements and the network conditions and combines both signals
coming from the application needs and the network state (i.e.,
signals below or above the transport layer).
To conclude, there are multiple ways to enable an adaptive coding
rate. However, all of them depend on:
* the signal metrics that can be monitored and used to adapt the
coding rate;
* the transport layer used, whether congestion controlled or not;
* the objective sought (e.g., to minimize congestion, or to fit
application requirements).
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6.3. Using Tetrys Below The IP Layer For Tunneling
The use of Tetrys to protect an aggregate of flows, typically when
Tetrys is used for tunneling, to recover from IP datagram losses,
raises research questions. When redundancy is applied without flow
differentiation, this may come in contradiction with the service
requirements of individual flows, some of them may be more penalized
by high latency and jitter than by partial reliability, while other
flows may have opposite requirements. In practice head-of-line
blocking will impact all flows in a similar manner despite their
different needs, which asks for more elaborate strategies inside
Tetrys.
7. Security Considerations
First of all, it must be clear that the use of FEC protection to a
data stream does not provide, per se, any kind of security, but, on
the contrary, raises security risks. The situation with Tetrys is
mostly similar to that of other content delivery protocols making use
of FEC protection, and this is well described in FECFRAME [RFC6363].
This section leverages on this reference, adding new considerations
to comply with Tetrys specificities when meaningful.
7.1. Problem Statement
An attacker can either target the content, the protocol, or the
network. The consequences will largely differ, reflecting various
types of goals, like gaining access to confidential content,
corrupting the content, compromizing the Tetrys Encoder and/or Tetrys
Decoder, or compromizing the network behavior. In particular,
several of these attacks aim at creating a Denial-of-Service (DoS),
with consequences that may be limited to a single node (e.g., the
Tetrys Decoder), or that may impact all the nodes attached to the
targeted network (e.g., by making flows non-responsive to congestion
signals).
In the following sections, we discuss these attacks, according to the
component targeted by the attacker.
7.2. Attacks against the Data Flow
An attacker may want to access a confidential content, by
eavesdropping the traffic between the Tetrys Encoder/Decoder.
Traffic encryption is the usual approach to mitigate this risk, and
this encryption can be done either on the source flow, above Tetrys,
or below Tetrys, on the output packets, both Source and Coded
Packets. The choice on where to apply encryption depends on various
criteria, in particular the attacker model (e.g., when encryption
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happens below Tetrys, the security risk is assumed to be on the
interconnection network).
An attacker may also want to corrupt the content (e.g., by injecting
forged or modified Source and Coded Packets to prevent the Tetrys
Decoder to recover the original source flow). Content integrity and
source authentication services at the packet level are then needed to
mitigate this risk. Here, these services need to be provided below
Tetrys in order to enable the receiver to drop undesired packets and
only transfer legitimate packets to the Tetrys Decoder. It should be
noted that forging or modifying Feedback Packets will not corrupt the
content, although it will certainly compromize Tetrys operation (see
next section).
7.3. Attacks against Signaling
Attacks on signaling information (e.g., by forging or modifying
Feedback Packets to pretend the good reception or recovery of source
content) can easily prevent the Tetrys Decoder to recover the source
flow, thereby creating a DoS. In order to prevent this type of
attack, content integrity and source authentication services at the
packet level are needed for the feedback flow, from the Tetrys
Decoder to the Tetrys Encoder, as well. These services need to be
provided below Tetrys, in order to drop undesired packets and only
transfer legitimate Feedback Packets to the Tetrys Encoder.
On the opposite, an attacker in position to selectively drop Feedback
Packets (instead of modifying them) will not severily impact Tetrys
functionning, since Tetrys is naturally robust in front of such
losses. However it will have side impacts, like the use of bigger
linear systems (since the Tetrys Encoder cannot remove well received
or decoded source packets from its linear system), which mechanically
increases computational costs on both sides, encoder and decoder.
7.4. Attacks against the Network
Tetrys can react to congestion signals (Section 6.1) in order to
provide a certain level of fairness with other flows on a shared
network. This ability could be exploited by an attacker to create or
reinforce congestion events (e.g., by forging or modifying Feedback
Packets), which can potentially impact a significant number of nodes
attached to the network. Here also, in order to mitigate the risk,
content integrity and source authentication services at the packet
level are needed to enable the receiver to drop undesired packets and
only transfer legitimate packets to the Tetrys Encoder and Decoder.
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7.5. Baseline Security Operation
Tetrys can benefit from an IPsec/Encapsulating Security Payload
(IPsec/ESP) [RFC4303], that provides in particular confidentiality,
origin authentication, integrity, and anti-replay services. IPsec/
ESP can be useful to protect the Tetrys data flows (both directions)
against attackers located within the interconnection network, in
position to eavesdrop traffic, or inject forged traffic, or replay
legitimate traffic.
8. IANA Considerations
This document does not ask for any IANA registration.
9. Implementation Status
Editor's notes: RFC Editor, please remove this section motivated by
RFC 7942 before publishing the RFC. Thanks!
An implementation of Tetrys exists:
organization: ISAE-SUPAERO
Description: This is a proprietary implementation made by ISAE-
SUPAERO
Maturity: "production"
Coverage: this software implements TETRYS with some modifications
Licensing: proprietary
Implementation experience: maximum
Information update date: January 2022
Contact: jonathan.detchart@isae-supaero.fr
10. Acknowledgments
First, the authors want sincerely to thank Marie-Jose Montpetit for
continuous help and support on Tetrys. Marie-Jo, many thanks!
The authors also wish to thank NWCRG group members for numerous
discussions on on-the-fly coding that helped finalize this document.
Finally, the authors would like to thank Colin Perkins for providing
comments and feedback on the document.
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11. References
11.1. Normative References
[RFC2119] Bradner, S., "Keywords 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>.
[RFC3452] Luby, M., Vicisano, L., Gemmell, J., Rizzo, L., Handley,
M., Crowcroft, J., and RFC Publisher, "Forward Error
Correction (FEC) Building Block", RFC 3452,
DOI 10.17487/RFC3452, December 2002,
<https://www.rfc-editor.org/info/rfc3452>.
[RFC4303] Kent, S., "IP Encapsulating Security Payload (ESP)",
RFC 4303, DOI 10.17487/RFC4303, December 2005,
<https://www.rfc-editor.org/info/rfc4303>.
[RFC5510] Lacan, J., Roca, V., Peltotalo, J., Peltotalo, S., and RFC
Publisher, "Reed-Solomon Forward Error Correction (FEC)
Schemes", RFC 5510, DOI 10.17487/RFC5510, April 2009,
<https://www.rfc-editor.org/info/rfc5510>.
[RFC5651] Luby, M., Watson, M., Vicisano, L., and RFC Publisher,
"Layered Coding Transport (LCT) Building Block", RFC 5651,
DOI 10.17487/RFC5651, October 2009,
<https://www.rfc-editor.org/info/rfc5651>.
[RFC5740] Adamson, B., Bormann, C., Handley, M., Macker, J., and RFC
Publisher, "NACK-Oriented Reliable Multicast (NORM)
Transport Protocol", RFC 5740, DOI 10.17487/RFC5740,
November 2009, <https://www.rfc-editor.org/info/rfc5740>.
[RFC6363] Watson, M., Begen, A., Roca, V., and RFC Publisher,
"Forward Error Correction (FEC) Framework", RFC 6363,
DOI 10.17487/RFC6363, October 2011,
<https://www.rfc-editor.org/info/rfc6363>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
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[RFC8406] Adamson, B., Adjih, C., Bilbao, J., Firoiu, V., Fitzek,
F., Ghanem, S., Lochin, E., Masucci, A., Montpetit, M.,
Pedersen, M., Peralta, G., Roca, V., Ed., Saxena, P.,
Sivakumar, S., and RFC Publisher, "Taxonomy of Coding
Techniques for Efficient Network Communications",
RFC 8406, DOI 10.17487/RFC8406, June 2018,
<https://www.rfc-editor.org/info/rfc8406>.
[RFC8680] Roca, V., Begen, A., and RFC Publisher, "Forward Error
Correction (FEC) Framework Extension to Sliding Window
Codes", RFC 8680, DOI 10.17487/RFC8680, January 2020,
<https://www.rfc-editor.org/info/rfc8680>.
[RFC9265] Kuhn, N., Lochin, E., Michel, F., Welzl, M., and RFC
Publisher, "Forward Erasure Correction (FEC) Coding and
Congestion Control in Transport", RFC 9265,
DOI 10.17487/RFC9265, July 2022,
<https://www.rfc-editor.org/info/rfc9265>.
11.2. Informative References
[A-FEC] Bolot, J., Fosse-Parisis, S., and D. Towsley, "Adaptive
FEC-based error control for Internet telephony", IEEE
INFOCOM 99, pp. 1453-1460 vol. 3 DOI
10.1109/INFCOM.1999.752166, 1999.
[AHL-00] Ahlswede, R., Ning Cai, Li, S.-Y.R., and R.W. Yeung,
"Network information flow", IEEE Transactions on
Information Theory vol.46, no.4, pp.1204,1216, July 2000.
[CTCP] Kim (et al.), M., "Network Coded TCP (CTCP)",
arXiv 1212.2291v3, 2013.
[I-D.singh-rmcat-adaptive-fec]
Singh, V., Nagy, M., Ott, J., and L. Eggert, "Congestion
Control Using FEC for Conversational Media", Work in
Progress, Internet-Draft, draft-singh-rmcat-adaptive-fec-
03, 20 March 2016, <https://www.ietf.org/archive/id/draft-
singh-rmcat-adaptive-fec-03.txt>.
[RED-FEC] Lin, C., Shieh, C., Chilamkurti, N. K., Ke, C., and H. S.
Hwang, "A RED-FEC Mechanism for Video Transmission Over
WLANs", IEEE Transactions on Broadcasting, vol. 54, no. 3,
pp. 517-524 DOI 10.1109/TBC.2008.2001713, September 2008.
[Tetrys] Lacan, J. and E. Lochin, "Rethinking reliability for long-
delay networks", International Workshop on Satellite and
Space Communications 2008 (IWSSC08), October 2008.
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[Tetrys-RT]
Tournoux, P.U., Lochin, E., Lacan, J., Bouabdallah, A.,
and V. Roca, "On-the-fly erasure coding for real-time
video applications", IEEE Transactions on Multimedia, Vol
13, Issue 4, August 2011 (TMM.2011), August 2011.
[THAI] Tran-Thai, T., Lacan, J., and E. Lochin, "Joint on-the-fly
network coding/video quality adaptation for real-time
delivery", Signal Processing: Image Communication, vol. 29
(no. 4), pp. 449-461 ISSN 0923-5965, 2014.
Authors' Addresses
Jonathan Detchart
ISAE-SUPAERO
10, avenue Edouard Belin
BP 54032
31055 Toulouse CEDEX 4
France
Email: jonathan.detchart@isae-supaero.fr
Emmanuel Lochin
ENAC
7, avenue Edouard Belin
31400 Toulouse
France
Email: emmanuel.lochin@enac.fr
Jerome Lacan
ISAE-SUPAERO
10, avenue Edouard Belin
BP 54032
31055 Toulouse CEDEX 4
France
Email: jerome.lacan@isae-supaero.fr
Vincent Roca
INRIA
655, avenue de l'Europe
Inovallee; Montbonnot
38334 ST ISMIER cedex
France
Email: vincent.roca@inria.fr
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