Tetrys, an On-the-Fly Network Coding protocol
draft-detchart-nwcrg-tetrys-05

Abstract

This document describes Tetrys, an On-The-Fly Network Coding (NC) protocol that can be used to transport delay and loss sensitive data over a lossy network. Tetrys can recover from erasures within a RTT-independent delay, thanks to the transmission of coded packets. It can be used for both unicast, multicast and anycast communications.

Status of This Memo

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Table of Contents

• 1. Introduction
• 1.1. Requirements Notation
• 2. Definitions, Notations and Abbreviations
• 3. Architecture
• 3.1. Use Cases
• 3.2. Overview
• 4. Packet Format
• 4.1. Common Header Format
• 4.1.1. Header Extensions
• 4.2. Source Packet Format
• 4.3. Coded Packet Format
• 4.4. Acknowledgement Packet Format
• 5. The Coding Coefficient Generator Identifiers
• 5.1. Definition
• 5.2. Table of Identifiers
• 6. Tetrys Basic Functions
• 6.1. Encoding
• 6.1.1. Encoding Vector Formats
• 6.2. The Elastic Encoding Window
• 6.3. Recoding
• 6.3.1. Principle
• 6.3.2. Generating a coded symbol at an intermediate node
• 6.4. Decoding
• 7. Security Considerations
• 8. Privacy Considerations
• 9. IANA Considerations
• 10. Acknowledgments
• 11. References
• 11.1. Normative References
• 11.2. Informative References
• Authors' Addresses

1. Introduction

This document describes Tetrys, a novel network 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 the use of network codes is fairly recent in the Internet community, the use of application layer erasure codes in the IETF has already been standardized in the RMT [RMT] and the FECFRAME [FECFRAME] working groups. The protocol presented here can be seen as a network coding extension to standards solutions. The current proposal can be considered as a combination of network erasure coding and feedback mechanisms [Tetrys].

The main innovation of the Tetrys protocol is in the generation of coded packets from an elastic encoding window periodically updated with the receiver's feedbacks. This update is done in such a way that any source packets coming from an input flow is included in the encoding window as long as it is not acknowledged or the encoding window did not reach a size limit. This mechanism allows for losses on both the forward and return paths and in particular is resilient to acknowledgement losses.

With Tetrys, a coded packet is a linear combination over a finite field of the data source packets belonging to the coding window. The choice of the finite field of the coefficients is a trade-off between the best performance (with non-binary coefficients) and the system constraints (binary codes in an energy constrained environment) and is driven by the application.

Thanks to the elastic encoding window, the coded packets are built on-the-fly, by using an algorithm or a function to choose the coefficients. The redundancy ratio can be dynamically adjusted, and the coefficients can be generated in different ways along a transmission. Compared to FEC block codes, this allows to reduce the bandwidth use and the decoding delay.

1.1. Requirements Notation

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119].

2. Definitions, Notations and Abbreviations

The terminology used in this document is presented below. It is aligned with the FECFRAME terminology as well as with recent activities in the Network Coding Research Group.

• Source symbol: a symbol that has to be 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 a coded symbols.
• Encoding vector: set of the encoding 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.
• Input symbol: a symbol at the input of the Tetrys Encoding Building Block.
• Output symbol: a symbol generated by the Tetrys Encoding Building Block. For a non systematic mode, all output symbols are coded symbols. For a systematic mode, output symbols can 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 can also bring 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 that are involved in the coding process.
• Coding Coefficient Generator Identifier: a unique identifier that define 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

• -- Editor's note: The architecture used in this document should be aligned with the future NC Architecture document [NWCRG-ARCH]. --

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 that takes place at a single encoding node. Note that the input stream can be a multiplex of several upper layer streams. Transmission can be over a single path or multiple paths. In addition, the flow can be sent in unicast, multicast, or anycast mode. This is the simplest use-case, that is very much inline with currently proposed scenarios for end-to-end streaming.

3.2. Overview

+----------+                                            +----------+
|          |                                            |          |
|    App   |                                            |    App   |
|          |                                            |          |
+----------+                                            +----------+
     |                                                       ^
     |  source                                       source  |
     |  symbols                                      symbols |
     |                                                       |
     v                                                       |
+----------+                +----------+                +----------+
|          | output packets |          | output packets |          |
|  Tetrys  |--------------->|  Tetrys  |--------------->|  Tetrys  |
|  Encoder |feedback packets|  Recoder |feedback packets|  Decoder |
|          |<---------------|          |<---------------|          |
+----------+                +----------+                +----------+

Figure 1: Tetrys Architecture

The Tetrys protocol features several key functionalities:

• On-the-fly encoding;
• Recoding;
• Decoding;
• Signaling, to carry in particular the symbol identifiers in the encoding window and the associated coding coefficients when meaningful, in a manner that was previously used in FEC;
• Feedback management;
• Elastic window management;
• Channel estimation;
• Dynamic adjustment of the code rate and flow control;
• Congestion control management (if appropriate);
  • -- Editor's note: must be discussed --
• Tetrys packet header creation and processing;
• -- Editor's note: something else? --

These functionalities are provided by several building blocks:

• The Tetrys Building Block: this BB is used during encoding, recoding 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 can be used.
• The Window Management Building Block: this building block is in charge of managing the encoding encoding window at a Tetrys sender.
  • -- Editor's note: Is it worth moving it in a dedicated BB? To be discussed --

• Other ?

In order to enable future components and services to be added dynamically, Tetrys adds a header extension mechanism, compatible with that of LCT, NORM, FECFRAME [REFS].

4. Packet Format

4.1. Common Header Format

 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     |  Packet 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

All types of Tetrys packets share the same common header format (see Figure 2).

• -- Editor's note: this format inherits from the LCT header format (RFC 5651) with slight modifications. --

• 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.
  • -- Editor's note: version number and congestion control to be discussed --

• 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. 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 can be used to directly access the portion of the packet beyond the Tetrys header, i.e., to the first other 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 other headers or packet payload.
• Packet Type: 8 bits. Type of packet.
• 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 the purpose of 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 sender. 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 in conjunction with the IP address of the sender always uniquely identifies a session, whether or not 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 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.

4.1.1. 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 can 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

• Header Extension Type (HET): 8 bits The type of the Header Extension. This document defines a number of 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 sub-field 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.

4.2. Source Packet Format

A source packet is the encapsulation of a Common Packet Header, a Source Symbol ID and a source symbol (payload). The source symbols can 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

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)

4.3. 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 CAN have variable sizes, each source symbol size need to be encoded, and 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 6.1.1.2).

 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                                                               |
/                      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).

Encoded Payload Size: the coded payload size used if the source symbols have variable size (optional, Section 6.1.1.2)).

Payload: the coded symbol.

4.4. Acknowledgement Packet Format

A Tetrys Decoding Building Block or Tetrys Recoding Building Block MAY send back to another building block some Acknowledgement packets. They contain information about what it has received and/or decoded, and other information such as a packet loss rate or the size of the decoding buffers. The acknowledgement packets are OPTIONAL 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 of missing source symbols                 |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|              Nb of not already used coded symbols             |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|                    First Source Symbol ID                     |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|      PLR      |   SACK size   |                               |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               +
|                                                               |
/                          SACK Vector                          /
|                                                               |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

Figure 6: Acknowledgement Packet Format

Common Packet Header: a common packet header (as common header format) where Packet Type=2.

Nb missing source symbols: the number of missing source symbols in the receiver since the beginning of the session.

Nb of not already used coded symbols: the number coded symbols at the receiver that have not already been used for decoding (e.g., the linear combinations contains at least 2 unknown source symbols).

First Source Symbol ID: ID of the first source symbol to consider for acknowledgement.

PLR: packet loss ratio expressed as a percentage.

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 the acknowledged symbols from the first source symbol ID. The "First Source Symbol" is included in this bit vector. A bit equal to 1 at position i means that the source symbol of ID equal to "First Source Symbol ID" + i is acknowledged by this acknowledgment packet.

5. The Coding Coefficient Generator Identifiers

5.1. Definition

The Coding Coefficient Generator Identifiers define a function or an algorithm to build the coding coefficients used to generate the coded symbols. They MUST be known by all the Tetrys encoders, recoders or decoders.

5.2. Table of Identifiers

0000: GF2 (or GF(2**1)) Vandermonde based coefficients. Each coefficient is built as alpha^( (source_symbol_id*coded-symbol_id) % 2).

0001: GF16 (or GF(2**4)) Vandermonde based coefficients. Each coefficient is built as alpha^( (source_symbol_id*coded-symbol_id) % 16).

0010: GF256 (or GF(2**8)) Vandermonde based coefficients. Each coefficient is built as alpha^( (source_symbol_id*coded_symbol_id) % 256).

0011: SRLC.

Others: To be discussed.

6. Tetrys Basic Functions

6.1. Encoding

At the beginning of a transmission, a Tetrys Encoding Building Block or MUST choose an initial code rate (added redundancy) as it doesn't know the packet loss rate of the channel. In steady state, depending on the code-rate, the Tetrys Encoding Building Block CAN generate coded symbols when it receives a source symbol from the application or some feedback from the decoding or recoding blocks.

When a Tetrys Encoding Building Block needs to generate a coded symbol, it considers the set of source symbols stored in the Elastic Encoding Window. These source symbols are the set of source symbols which are not yet acknowledged by the receiver.

A Tetrys Encoding Building Block SHOULD set a limit to the Elastic Encoding Window maximum size. This allows to control the algorithmic complexity at the encoder and decoder by limiting the size of linear combinations. It is also needed in situations where acknowledgment packets are all lost or absent.

At the generation of a coded symbol, the Tetrys Encoding Building Block generates an encoding vector containing the IDs of the source symbols stored in the Elastic Encoding Window. For each source symbol, a finite field coefficient is determined using a Coding Coefficient Generator. This generator CAN take as input the source symbol ID and the coded symbol ID and CAN determine a coefficient in a deterministic way. A classical example of such deterministic function is a generator matrix where the rows are indexed by the source symbol IDs and the columns by the coded symbol IDs. For example, the entries of this matrix can be built from a Vandermonde structure, like Reed-Solomon codes, or from a sparse binary matrix, like Low-Density Generator Matrix codes. Finally, the coded symbol is the sum of the source symbols multiplied by their corresponding coefficients.

6.1.1. Encoding Vector Formats

Each coded packet contains an encoding vector. The encoding vectors CAN contain the ID and/or coefficient of each source symbol contained in the coded symbol.

6.1.1.1. Transmitting the source symbol IDs

The source symbol IDs are organized as a sorted list of 32-bit unsigned integers. Depending on the feedback, the source symbol IDs can 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 edge blocks CAN be stored directly, or a differential transform to reduce the number of bits needed to represent an ID CAN be used.

6.1.1.1.1. Compressed list of Source symbol IDs

Assume the symbol IDs used in the combination are: [1..3],[5..6],[8..10].

1. Keep the first element in the packet as the first_source_id: 1.
2. Apply a differential transform to the others 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))): 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.

6.1.1.1.2. Decompressing the Source symbol IDs

When a Tetrys Decoding Building 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].

6.1.1.2. Encoding Vector Format

The encoding vector CAN be used to store the source symbol IDs included in the associated coded symbol, the coefficients used in the combination, or both. It CAN be used to send only the number of source symbols included in the coded symbol.

If the source IDs are stored, the number of blocks MUST be different from 0.

The encoding vector format uses a 4-bit Coding Coefficient Generator Identifier to identity the algorithm to generate the coefficients, and contains a set of blocks for the source symbol IDs used in the combination. In this format, the number of blocks is stored as a 8-bit unsigned integer. To reduce the overhead, a compressed way to store the symbol IDs is used: the IDs are not stored as themselves, but stored as the difference between the previous.

 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   |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|    b_coef     |                                               |
+-+-+-+-+-+-+-+-+          coef_bit_vector        +-+-+-+-+-+-+-+
|                                                 |   Padding   |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

Figure 7: 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 (see Section 5). As a CCGI is included in each encoded vector, it can dynamically change between the generation of 2 coded symbols.
• Store the Source symbol IDs (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 coefficients (C): 1 bit to know if an encoding vector contains information about the coefficients used.
• Having source symbols with variable size (V): set V to 1 if the combination which refers 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.
• Number of IDs used to store the source symbol IDs (NB_IDS): the number of IDs stored (depending on I).
• 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 (see Section 6.1.1.1).
• 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.
• Number of bits needed to store each coefficient (b_coef): the number of bits used to store the coefficients.
• The coefficients (coef_bit_vector): The coefficients stored (as a vector of b_coef * NB_COEFS).
• Padding: padding to have an Encoding Vector size multiple of 32-bit (for the id and coefficient part).

6.2. The Elastic Encoding Window

When an input source symbol is passed to a Tetrys Encoding Building Block, it is added to the Elastic Encoding Window. This window MUST have a limit set by the encoding building Block (depending of the use case: unicast, multicast, file transfer, real-time transfer, ...). If the Elastic Encoding Window reached its limit, the window slides over the symbols: the first (oldest) symbols are removed. Then, a packet containing this symbol can be sent onto the network. 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 receiver or the recoder sends periodic feedback indicating the received or decoded source symbols. In the case of a unicast transmission, when the sender receives the information that a source symbol was received and/or decoded by the receiver, it removes this symbol from the coding window.

In a multicast transmission:

• If the acknowledgement packets are not enabled, the coding window grows up to a limit. When the limit is reached, the oldest symbols are removed from the coding window.
• If the acknowledgement packets are enabled, a source symbol is removed from the coding window when all the receivers have received or decoded it or when the coding window reaches its limit.

6.3. Recoding

6.3.1. Principle

A Tetrys Recoding Block maintains a list of the ID of the source symbols included in the Elastic Coding Window of the sender. It also stores a set of received source and coded symbols able to regenerate the set or a subset of the symbols of the Elastic Coding Window. In other words, if R1, ..., Rt represent t received symbols and S1, ..., Sk represent the set or a subset of the source symbols of the Elastic Coding Window, there exists a t*k-matrix M such that (R1, ..., Rt).M = (S1, ..., Sk).

6.3.2. Generating a coded symbol at an intermediate node

At the generation of a coded symbol, the Tetrys Recoding Building Block generates an encoding vector containing the IDs of the source symbols stored in the Elastic Encoding Window or in the subset of the Elastic Encoding Window that it is able to regenerate. The Tetrys Recoding Building Block then generates a new coded symbol ID different from the received coded symbol IDs. From this coded symbol ID and the source symbol IDs of (S1, ..., Sk), a finite field coefficient is determined using a Coding Coefficient Generator. Let (a1, ...,ak) denote the obtained coefficients. To compute the linear combination (s1, ..., Sk).transpose(a1, ..., ak) the Tetrys Recoding Building block computes the vector v = (a1, ...,ak).transpose(M) and then computes the coded symbol R = (R1, ..., Rt).transpose(v). It can be verified that the new coded symbol is obtained without any decoding operation.

6.4. Decoding

A classical matrix inversion is sufficient to recover the source symbols.

7. Security Considerations

Tetrys inherits a subset of the security issues described as those described in FECFRAME [FECFRAME] and in particular in sections "9.2.2. Content Corruption" and "9.3. Attacks against the FEC Parameters". As an application layer end-to-end protocol, security considerations of Tetrys should also be comparable to those of HTTP/2 with TLS. ; the considerations from Section 10 of HTTP2 [HTTP2] apply in addition to those listed here.

8. Privacy Considerations

N/A

9. IANA Considerations

N/A

10. Acknowledgments

N/A

11. References

11.1. Normative References

11.2. Informative References

Authors' Addresses