Internet DRAFT - draft-adjih-dragoncast
draft-adjih-dragoncast
Network Coding Research Group (NCWCRG) C. Adjih
Internet-Draft Inria
Intended status: Informational SY. Cho
Expires: January 16, 2014 Samsung Electronics Co.,LTD.(*)
E. Baccelli
Inria
July 15, 2013
Broadcast With Network Coding: DRAGONCAST
draft-adjih-dragoncast-00
Abstract
This document describes a Network Coding (NC) based broadcast
protocol suitable mainly for wireless networks, including mobile ad
hoc networks (MANET). It provides data dissemination from a single
source, based on intra-flow network coding and for Internet Protocol
(IP). It is designed to minimize the assumptions over the working
environment and thus may operates over dynamically evolving
environments.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on January 16, 2014.
Copyright Notice
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carefully, as they describe your rights and restrictions with respect
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Terminology . . . . . . . . . . . . . . . . . . . . . . . . . 4
3. Protocol Overview . . . . . . . . . . . . . . . . . . . . . . 5
3.1. General Functioning . . . . . . . . . . . . . . . . . . . 6
3.2. Protocol Principles and Definitions . . . . . . . . . . . 7
4. DRAS: DRAGONCAST Signaling . . . . . . . . . . . . . . . . . . 8
5. DRALIB: DRAGONCAST Local Information Base . . . . . . . . . . 11
6. DRAGONCAST Protocol Functioning . . . . . . . . . . . . . . . 13
6.1. Source Packet Generation . . . . . . . . . . . . . . . . . 14
6.2. Packet Processing . . . . . . . . . . . . . . . . . . . . 14
6.3. Packet Generation . . . . . . . . . . . . . . . . . . . . 14
7. DRAGON: Packet Rate Selection . . . . . . . . . . . . . . . . 14
7.1. DRAGON Rationale . . . . . . . . . . . . . . . . . . . . . 14
7.2. DRAGON (Dynamic Rate Adaptation from Gap with Other
Nodes) . . . . . . . . . . . . . . . . . . . . . . . . . . 15
8. Real-time Decoding: Sliding Encoding Window (SEW) . . . . . . 16
9. Security Considerations . . . . . . . . . . . . . . . . . . . 18
10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 18
11. Informative References . . . . . . . . . . . . . . . . . . . . 18
Appendix A. Network Coding Fundamentals . . . . . . . . . . . . . 19
A.1. Linear Coding . . . . . . . . . . . . . . . . . . . . . . 19
A.2. Random Linear Coding . . . . . . . . . . . . . . . . . . . 20
A.3. Decoding, Vector Space, and Rank . . . . . . . . . . . . . 20
Appendix B. Acknowledgements . . . . . . . . . . . . . . . . . . 21
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1. Introduction
The goal of this document is to describe a protocol for broadcast in
wireless networks with network coding.
It is best suited to multi-hop wireless networks. Compared to wired
networks, they have specific properties, see for instance
[I-D.baccelli-multihop], including:
- Wireless 'neighborcast': one wireless transmission by a node may
reach several receivers. This property may be used to optimize
broadcast.
- Time-variation: the visibility between two nodes may evolves
with time, due to node mobility, physical changes in the
propagation environment or other reasons.
- Unreliability of wireless communications: due to wireless
channel conditions or properties, transmissions losses (packet
erasures) potentially occur.
In wireless networks, applications sometimes require the
communication primitive of broadcasting information to the entire
network. As an example, in the context of MANETs, the Simplified
Multicast Forwarding (SMF) [RFC6621] has been proposed for this
purpose.
For applications where a single source sends a large volume of
information to the entire network, it will be split in several
packets, which will then be broadcast to the entire network. In this
case, network coding can provide two features: natural error
correction, and efficiency (in terms of the number of transmissions).
A large literature on this topic has evidenced the benefits of
network coding and explored design and implementation aspects.
In this document, we present DRAGONCAST (D.R.A.G.O.N., "Dynamic Rate
Adaptation from Gap with Other Nodes"), one such protocol for
broadcasting with network coding.
It is based on intra-flow coding. It attempts to maximize simplicity
and universality: it does not use explicitly or implicit knowledge
relative to the topology (such as the direction or distance to the
source, the loss rate of the links, ...), hence is perfectly suited
to the most dynamic wireless networks.
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2. Terminology
+--------------+---------------------------------------------------+
| Abbreviation | Definition |
+--------------+---------------------------------------------------+
| MANET | Mobile Ad Hoc Network |
| NHDP | Neighborhood Discovery Protocol |
| OLSR | Optimized Link State Routing |
| SMF | Simplified Multicast Forwarding |
| TLV | Type-Length-Value encoding |
| DRAGON | Dynamic Rate Adaptation from Gap with Other Nodes |
| SEW | Sliding Encoding Window |
| PME | Protocol Message Element |
| F-PME | Flow Protocol Message Element |
| S-PME | State Protocol Message Element |
| ED-PME | Encoded Data Protocol Message Element |
+--------------+---------------------------------------------------+
Table 1
The following table summarizes the definitions and notations related
to network coding in general and to DRAGONCAST. More details on
network coding can be found in Appendix A.
+----------------+--------------------------------------------------+
| Name | Definition |
+----------------+--------------------------------------------------+
| Coded Packet | Linear combination of source packets |
| Encoding | Coefficients in the linear combination of source |
| Vector | packets |
| Vector | abbrev. for "Information Vector", coded packet |
| Innovative | A coded packet that brings new information |
+----------------+--------------------------------------------------+
Table 2
+-----------------------------+-------------------------------------+
| Name | Notation |
+-----------------------------+-------------------------------------+
| Source packets | P(1), ..., P(k) |
| Linear combination of | a(1) P(1) + ... + a(k) P(k) |
| packets | |
| Set of coded packets at a | q(v,i) = a(v,i,1) P(1) + ... + |
| node v | a(v,i,M) P(M) |
+-----------------------------+-------------------------------------+
Table 3
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3. Protocol Overview
DRAGONCAST is a protocol for broadcasting a set of packets from one
source to a entire network with network coding (various parts are
described in [CA08a], [CA08b], [C08]). The protocol is distributed
and requires minimal coordination.
The base functioning is simple: the broadcast is initiated by
transmissions for the source. Every node in the network retransmits
coded packets with a changing interval between transmissions. At the
same time, every node collects received coded packets, and performs
decoding as they are received. Finally, termination is automatically
detected when all the nodes have successfully received all data.
DRAGONCAST is based on several building blocks that are in two
categories. The first category concerns the protocol aspects
themselves:
o DRAS (DRAgoncast Signaling): the signaling for the control plane
for DRAGONCAST. The signaling is mostly present on a header to
each coded packet (e.g piggybacking). It includes with
information relative to the state of the node, in addition to the
packet encoding information. This allows each node to maintains
information about the state of its neighbors.
o DRALIB (DRAgoncast Local Information Base): this information base
maintains information about the flows, the decoding process, and
the state of the neighbors
o DRAGONCAST: the protocol itself with message generation and
message processing
The second category is relative to policy, that is building blocks
that define high level protocol behavior:
o DRAGON: a dynamic packet rate adjustment policy. Every node is
retransmitting coded packets with a certain packet rate; this rate
is adjusted dynamically. Essentially, the rate of the node
increases if it detects some nodes in the current neighborhood are
"falling behind" in the decoding process. This is called a
"dimension gap", and the proposed adaptation algorithm is a
Dynamic Rate Adjustment from Gap with Other Nodes (DRAGON), a
heuristic.
o SEW: a real-time decoding method denoted SEW (Sliding Encoding
Window). It does not requires the concept of generation; instead,
the knowledge of the state of neighbors is used to constrain the
content of generated coded packets and allow real-time decoding.
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SEW maintains a buffer of the currently undecoded packets.
The Figure 1 represents the organization of the different building
blocks.
Application (source)
................................................^..................
V
+---------------------------+ +---------------------------+
| | | |
| DRAGON | | SEW |
| | | |
| Packet Rate Selection | | Packet Encoding and |
| | | Real-time Packet Decoding |
+---------------------------+ +->| |
^ | +---------------------------+
Policy | +------+ ^
...............|.........|......................|..................
Protocol V v v
+---------------------------+ +---------------------------+
| | | |
| DRAGONCAST | | DRALIB |
| +<---> |
| Protocol | | Local Information Base |
| | | |
+---------------------------+ +---------------------------+
^
| .............................
v . Operating System
+--------------+------------+ .
| | . +--------------+
| DRAS | . | |
| +<----------->+ IP Stack |
| Signaling | . | |
| | . +--------------+
+---------------------------+ .
Figure 1: Organization of the DRAGONCAST Building Blocks
3.1. General Functioning
The source initiates broadcasting by sending its original data
packets with a format specified in Section 4.
When the source sends data packets, it produces packets of a
predefined, constant size, using padding if necessary. Other nodes
initiate transmission of encoded data upon receiving the first coded
packet, and stay in a transmission state where they will retransmit
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coded packets with an interval decided by packet rate selection
algorithms. Precisely, when intermediate nodes receive a data packet
that is a source packet or a coded packet, they start scheduling
encoded data transmission.
The scheduling interval is decided by the policy DRAGON from
Section 7. Transmitted packets by intermediate nodes are coded
packets generated using random linear coding with a header specified
in Section 4. Data transmission continues until nodes detect the
termination condition, i.e. that themselves and all their neighbors
have successfully decoded the data stream.
General operations of the protocol are described in the following
algorithm:
1. Source data transmission scheduling: the source transmits
sequentially D vectors (packets) of a generation with rate C
2. Nodes' data transmission start condition: the nodes start
transmitting a vector when they receive the first vector.
3. Nodes' data storing condition: the nodes store a received vector
in their local buffer only if the received vector has new and
different information from the vectors that the nodes already
have.
4. Nodes' termination conditions: the nodes continue transmitting
until themselves and their current known neighbors in their local
information base have enough vectors to recover the D source
packets.
5. Nodes' data transmission scheduling: every node retransmits
linear combinations of the vectors in its local buffer after
waiting for a delay computed from the rate selection.
6. Nodes' data transmission restart condition: When one node
receives a notification indicating that one neighboring node
requires more vectors to recover the D source packets and it has
already stopped data transmission, the node re-enters in a
transmission state.
3.2. Protocol Principles and Definitions
DRAGONCAST uses the following concepts and definitions:
o Source: a source is a node that will broadcast information to the
network. This information is called a "flow". A source may have
an arbitrary number of flows, however each flow will be coded
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independently (intra-flow coding).
o Flow: a flow is the unit of transmission of the protocol
DRAGONCAST. The flow represents a sequence of bytes at the source
that need to be broadcast. The source divides the flow in a
sequence of packets of equal size (padding may be used). The
packets are numbered, and can be identified by their packet index.
The packets of one flow may optionally divided in several
generations (one per default).
o Generation: a generation is a subset of a consecutive packets of
one flow.
4. DRAS: DRAGONCAST Signaling
DRAGONCAST uses one single packet format based on a sequence of Type-
Value including several protocol elements. The general packet format
is represented in 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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Packet size | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| |
| Protocol Message Element (PME) |
| +-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| |
: ... :
| |
| +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| |
| Protocol Message Element (PME) |
| +-+-+-+-+-+-+-+-+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 2
The following protocol elements are defined:
o The Flow Protocol Message Element (F-PME), Figure 3: it specifies
information identifying the flow and associated (constant)
parameters.
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o The State Protocol Message Element (S-PME), Figure 4: it specifies
information relative to the state of the sender with respect to
the decoding process.
o The Encoded Data Protocol Message Element (ED-PME), Figure 5: it
specifies parameters of the encoding, along with the coding vector
and include the coded packet data.
They are used as the basis for DRAGONCAST Packets. Control
information is sent in-band, prepended to encoded packets. In the
normal flow of the protocol, the majority of transmitted packets are
"Data Packets". In the current version of the specification, the
packet MUST respect exactly one of the following formats:
o A regular data packet (with coded content): it MUST include the
three following elements, in this order exactly: F-PME, S-PME, ED-
PME
o A termination control packet (e.g. without coded content): it MUST
first include the two following elements, in this order exactly:
F-PME, S-PME.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type: FLOW | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +
| Flow Identifier (64 bits) |
| +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | Generation Identifier |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Source Packet Rate | Generation Number of Packets |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Sliding Encoding Window Size |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 3: Format of the Flow PME
The Flow PME includes the following fields:
o Flow Identifier (Flow-ID): an identifier of size 8 bytes for the
flow. Its semantics is opaque to DRAGONCAST.
o Generation Identifier: DRAGONCAST includes support for splitting a
flow (with a given Flow-ID), which allows flows with more than
65535 packets, and also allows to optionally operate with
generations.
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o Source Packet Rate: expressed as the average inter-departure of
the coded packets in milliseconds (e.g. "10 packets per second"
yields the value 100).
o Generation Number of Packets: total number of packets in the
Generation with the given Generation ID.
o Sliding Encoding Window Size: the size of the encoding window,
when generating coded packets.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type: STATE | Rank of Transmitter |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Lifetime | Number of Neighbors |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| High Index | Low Index |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
| Transmitter Address |
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 4: Format of the State PME
The State PME specifies state information of transmitter with respect
to the generation identified by a preceding F-PME and includes:
o Rank of Transmitter: denotes the current amount of innovative data
of the transmitter for the generation.
o Lifetime: denotes duration during which the information in this
packet (that is, the rank and the fact that transmitter is a
neighbor of a node receiving this packet) is considered valid
(after this it will expire).
o Number of neighbors: denotes the number of neighbors heard, that
are not yet expired.
o High Index: specifies the highest index present in a undecoded
linear combination in the decoding table.
o Low Index: specifies the lowest index present in a undecoded
linear combination in the decoding table. Hence all source
packets with lower indices have been decoded.
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o Transmitter Address: the IP address of the transmitter of the
message.
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
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|Type: ENCODED_DATA | Encoding Type and Parameters |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Vector Data Size | Coded Packet Data Size |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Encoding Vector Index Offset | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ |
| Encoding Vector Data |
: ... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Coded Packet Data |
: ... :
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Figure 5: Format of the Encoded Data PME
The Encoded Data PME holds actual coded packet content:
o Encoding Type and Parameters: in this version of the
specification, the fields contains one of the constants
ENCODING_GF_2, ENCODING_GF_4, ENCODING_GF_16 ENCODING_GF_256.
This represents the fact that the fields GF(2), GF(4), GF(16), or
GF(256) respectively are used as basis for the linear combination.
As a result, the coefficients are respectively coded on 1, 2, 4 or
8 bits.
o Encoding Vector Data Size: the size of the information
representing the encoding vector, in bytes. As indicated above,
one byte will hold an integral number of vector coefficients.
o Coded Packet Data Size: the size of data packets.
Constants: ENCODING_GF_2 = 0 ENCODING_GF_4 = 1 ENCODING_GF_16 = 2
ENCODING_GF_256 = 3
5. DRALIB: DRAGONCAST Local Information Base
A node maintains a Local Information Base that records information
about its decoding process, and the state of the neighbors.
The protocol state is maintained per flow: a flow is uniquely
identified by a flow identifier. In addition, DRAGONCAST supports
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the concept of partitioning a flow into generations. In this version
of the specification, each generation is considered as an independent
"flow".
The different information bases of DRALIB are structured
hierarchically as follows:
o Flow Information Set. Each flow is independently associated a Flow
Information Tuple, which contains one or several generations.
Their state is maintained in a:
* Generation Information Set. Each generation contains the state
of the neighbors with respect to the propagation and the
decoding of the generation, stored in a:
+ Neighbor Information Set, describing the neighbors. Such
information may also be provided by another protocol, such
as OLSR [RFC3626] or NHDP [RFC6130]
In addition, for decoding purposes, it includes the:
+ Decoding Information Base
Each node maintains a Flow Information Set, which contains collected
information about current flows. Specifically, the Flow Information
Set consists of Flow Information Tuples each which records:
o Flow Information Tuple
o F_flow_identifier: the identifier of the flow
o F_source_rate: the packet rate of the source
o F_generation_set: the Generation Information Set associated to the
flow
Each node maintains, for each of its Flow Information Tuple, a
Generation Information Set, which contains information specific to a
generation:
o Generation Information Tuple
o G_generation_identifier: an integer (generations are numbered from
0)
o G_generation_size: number of coded packets in the generation
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o G_encoding_window_size: the size of the sliding encoding window
(for SEW)
o G_decoding: the Decoding Information Base associated to this
generation
o G_neighbor_set: the Neighbor Information Set associated to this
generation
For each generation, a node maintains a Neighbor Information Set,
which contains its known neighbors (with an expiration time), and
information related to their state.
Specifically, the Neighbor Information Set consists of Neighbor
Tuples, each of which contain information about a single neighbor,
for a given flow and for a given generation, as follows:
o Neighbor Tuple
o N_neighbor_address: address of the neighbor (heard) node
o N_neighbor_rank: the rank of the neighbor
o N_high_index: high index of the neighbor
o N_low_index: low index of the neighbor
o N_validity_time: the validity time of the tuple (after which it
expires)
For each generation, a node maintains a Decoding Information Base
with the following content:
o D_coded_packet_set: a set of coded packets. For each, the node
maintains:
* Encoding vector
* Coded packet content
During the decoding process, the decoding module (SEW) performs real-
time decoding by performing Gaussian elimination on the list of coded
packets.
6. DRAGONCAST Protocol Functioning
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6.1. Source Packet Generation
A node that acts as a data source for a flow, also runs a instance of
the DRAGONCAST protocol for that flow (e.g. has a Flow Tuple with all
associated information).
In addition, it adds periodically source packets in the associated
Flow Information Base respecting the source rate.
6.2. Packet Processing
Whenever a node receives an encoded packet:
o It updates its Flow Information Base related to the associated
flow. This includes rank and expiration time.
o It notifies SEW for real-time decoding. In turn, SEW will forward
any decoded packets to the application.
o It notifies DRAGON which may update the transmission packet rate
of the flow.
6.3. Packet Generation
For every "active" flow in its Flow Information Base, a node will
generate coded packets, with an interval between packets defined by
DRAGON (from the computed packet rate).
If for a given flow and generation, in the associated neighbor set,
no neighbor is known to require coded packets, the packet is
generated without encoded packet (without Encoded Data PME).
From information in its Local Information Base, every node is able to
determines if it needs to sends packets, as described in [C08].
7. DRAGON: Packet Rate Selection
In this section, we describe one packet rate selection algorithms,
proposed for DRAGONCAST.
7.1. DRAGON Rationale
The heuristic DRAGON has been proposed and analyzed in [CA08a], and
is inspired by Fragouli et al. [FWB06]. We briefly summarize it in
this section for completeness. The starting point of our heuristic
DRAGON, is that the observation that, for real-time decoding, the
rank of nodes inside the network should be close to the index of the
last source packet, and that in any case, they should at least evolve
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in parallel.
Thus, one would expect the rank of a node to grow at the same pace as
the source transmission, as in the example of optimal rate selections
for static networks. Decreasing the rates of intermediate nodes by a
too large factor, would not permit the proper propagation of source
packets in real time. On the contrary, increasing excessively their
rates, would not increase the rate of the decoded packets (naturally
bounded by the source rate) while it would decrease energy-efficiency
(by increasing the amount of redundant transmissions).
The idea of the proposed rate selection is to find a balance between
these two inefficient states. As we have seen, ideally the rank of a
node would be comparable to the lastly sent source packet. Since we
wish to have a simple decentralized algorithm, instead of comparing
with the source, we compare indirectly the rank of a node with the
rank of all its perceived neighbors.
The key idea is to perform a control so that the rank of neighbor
nodes would tend to be equalized: if a node detects that one neighbor
had a rank which is too low in comparison with its own, it would tend
to increase its rate. Conversely, if all its neighbors have greater
ranks than itself, the node need not to send packets in fact.
7.2. DRAGON (Dynamic Rate Adaptation from Gap with Other Nodes)
In this section, we describe the proposed heuristic, DRAGON, as a
packet rate selection. It is based on the following definitions.
Precisely, let:
o D(v,t) denote the rank of a node v at time t
o N(v,t) denote the number of neighbors of one node
o g(v,t) denote the maximum gap of rank with its neighbors,
normalized by the number of neighbors
Then g(v,t) is evaluated as:
o g(v,t) = maximum, for all neighbors u, of { (D(v,t) - D(u,t)) /
N(u,t) }
We propose the following rate selection, DRAGON (Dynamic Rate
Adaptation from Gap with Other Nodes), which adjusts the rates
dynamically, based on that gap of rank between one node and its
neighbors as follows: The packet rate of node v is set to C(v,t) at
time t as:
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o if g(v,t) > 0 then: C(v,t) = A g(v,t) where A is some constant.
o Otherwise, the node stops sending encoded packets until g(v,t)
becomes larger than 0.
When computing the packet rate selection, DRAGONCAST Local
Information Base supplies the information necessary: for each
neighbor, the rank and the number of neighbors of the last packet
received, are maintained in the Neighbor Set. Although they might not
necessarily reflect the exact values at the computation time, they
are provide an estimate.
8. Real-time Decoding: Sliding Encoding Window (SEW)
In this section, we describe the method of DRAGONCAST for real-time
decoding, which allows recovery of some source packets without
requiring to decode all source packets at once. It is related to the
method from Sundararajan et al. [SSMMB09] described for TCP.
The real-time decoding method, Sliding Encoding Window (SEW) relies
on implicit cooperation between neighbor nodes, in order to ensure
the possibility of decoding. (Technically, as described in [CA08a],
it ensures the existence of a low triangle in global encoding vectors
saved in a node during the online Gauss elimination process).
The key of SEW, is to ensure the existence of an early decoding part;
to do so, every node in DRAGONCAST keeps track of the state of its
neighbors, in order to only send packets, The method SEW relies on
two principles:
o SEW coding rule: generates only coded packets that are linear
combinations of the first L source packets, where L is a quantity
that increases with time.
o SEW decoding rule: when decoding, performs a Gaussian elimination,
in such a way that one coded packet is only used to eliminate the
source packet with the highest possible index (i.e. the latest
source packet).
Before detailing the insights behind these rules, we first give
definition: the high index of a node, and the low index of a node.
As explained in Appendix A, a coded packet is a linear combination of
source packets. We define the highest and lowest index of a linear
combination, as the minimum and maximum of the coded packets
respectively. For instance, a packet Q = P(3) + P(5) + P(7) + P(8),
the highest index is 8 and the lowest index is 3.
Because all encoded packets have their own highest index and lowest
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index, we can also compute the maximum of the highest index of all
not-yet decoded packets in a node, as well as the minimum of the
lowest index. We refer to the maximum and the minimum as high index
of a node and low index of a node. Notice that a node will generally
have decoded the source packets from 1 up to its low index.
The intent of the SEW coding rule is to use knowledge about the state
of neighbors of one node, namely their high and low index. A node
restricts the generated packets to a subset of the packets of the
source, until it is confirmed that perceived neighbors of the node
are able to decode nearly all of them, up to a margin K. Notice that
once all its neighbors may decode up to the first L-K packets, it is
unnecessary for the node to include packets P(1), ... P(L) in its
generated combinations.
Hence, the general idea of SEW is that it restricts the mixed
original packets within an encoded packet from a window of a fixed
size K. In other words, a node encodes only source packets inside a
fixed Encoding Window as:
i-th generated packet q(v,i) = a(v,i,k) P(k) + .... + a(v,i,k_K)
P(k+K)
where the { P(j) } is the set of packets generated by the source, The
sequence of coefficients for q(v,i) is the following global encoding
vector: [ 0, 0, ..., a(v,i,k), a(v,i,k+1), ..., a(v,i,k+K), ...,0,0].
A node will repeat transmissions of new random combinations within
the same window, until its neighbors have progressed in the decoding
process.
The intent of the SEW decoding rule, is to guarantee proper
functioning of the Gaussian elimination. An example of SEW decoding
rule is the following: assume that node v has received packets q(1)
and q(2), for instance q(1) = P(1) + P(9) and q(2) = P(1) + P(2) +
P(3). Then q(1) would be used to eliminate P(9) for newly incoming
packets (the highest possible index is 9), and q(2) would be used to
eliminate P(3) from further incoming packets. On the contrary, if
the SEW decoding rule was not applied and if q(1) were used to
eliminate P(1), then it would be used to eliminate it in q(2), and
would result into the computation of q(2) - q(1) = P(2) + P(3) -
P(9); this quantity now requires elimination of P(9), an higher index
than the initial one in q(2). In contrast the SEW decoding rule
guarantees the following invariant: during the Gaussian elimination
process, the highest index of every currently non-decoded packet will
always stay identical or decrease.
Provided that neighbor state is properly exchanged and known, as a
result, the combination of the SEW coding rule and the SEW decoding
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rule, guarantee that ultimately every node will be able to decode the
packets in the window starting from its lowest index; that is, they
guarantee early decoding.
Notice that improper knowledge of neighbor state might impact the
performance of the method but not its correctness: if a previously
unknown neighbor is detected (for instance due to mobility), the
receiving node will properly adjust its sending window. Conversely,
in DRAGONCAST, obsolete neighbor information, for instance about
disappeared neighbors, will ultimately expire.
9. Security Considerations
This document does not have any security considerations.
10. IANA Considerations
This document does not have any IANA actions.
11. Informative References
[RFC3626] Clausen, T. and P. Jacquet, "Optimized Link
State Routing Protocol (OLSR)", RFC 3626,
October 2003.
[RFC6130] Clausen, T., Dearlove, C., and J. Dean,
"Mobile Ad Hoc Network (MANET) Neighborhood
Discovery Protocol (NHDP)", RFC 6130,
April 2011.
[RFC6621] Macker, J., "Simplified Multicast
Forwarding", RFC 6621, May 2012.
[I-D.baccelli-multihop] Baccelli, E. and C. Perkins, "Multi-hop Ad
Hoc Wireless Communication", draft-baccelli-
manet-multihop-communication-02 (work in
progress), July 2013.
[CA08a] Cho, S-Y. and C. Adjih, "Wireless Broadcast
with Network Coding: Dynamic Rate
Selection", Conference MedHocNet 2008,
June 2008.
[CA08b] Cho, S-Y. and C. Adjih, "Wireless Broadcast
with Network Coding: DRAGONCAST", Inria
Research Report RR-6569, July 2008.
[C08] Cho, S-Y., "Efficient Information
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Dissemination in Wireless Multi-Hop
Networks", Ecole Polytechnique PhD thesis,
Sept 2008.
[HKMKE03] Ho, T., Koetter, R., Medard, M., Karger, D.,
and M. Effros, "The Benefits of Coding over
Routing in a Randomized Setting",
International Symposium on Information
Theory 2003, Jun 2003.
[CWJ03] Chou, P., Wu, Y., and K. Jain, "Practical
Network Coding", Forty-third Annual Allerton
Conference on Communication, Control, and
Computing 2003, Oct 2003.
[FWB06] Fragouli, C., Widmer, J., and J. Le Boudec,
"A Network Coding Approach to Energy
Efficient Broadcasting", INFOCOM 2006,
Apr 2006.
[SSMMB09] Sundararajan, J., Shah, D., Medard, M.,
Mitzenmacher, M., and J. Barros, "Network
Coding Meets TCP", INFOCOM 2009, Apr 2009.
Appendix A. Network Coding Fundamentals
This section introduces network coding concepts and terminology.
Network coding differs from classical routing by permitting coding at
intermediate nodes. One possible coding algorithm is linear coding
that performs only linear transformations through addition and
multiplication Precisely, linear coding assumes identically sized
packets and views the packets as vectors on a fixed Galois field. It
becomes then possible to perform linear combination of packets.
A.1. Linear Coding
In the case of single source broadcast, all packets initially
originate from one source: the source has k packets, which may be
seen equivalently as k vectors P(1), ..., P(k) from the vector space
over a Galois Field.
With network coding, any coded packet received by node, at any point
of time, is a linear combination of some source packets. The i-th
received coded packet at a node v is necessarily a linear combination
of the source packets P(1), .... P(k) and can be written as:
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q(v,i) = a(v,i,1) P(1) + ... + a(v,i,k) P(k)
The sequence of coefficients for a coded packet q(v,i) (denoted
"information vector", or simply "vector") is itself a vector
[a(v,i,1), a(v,i,2), ..., a(v,i,n)] (denoted "global encoding
vector").
With linear coding, when one node generates a coded packet, it
performs a linear combination of the packets that it possesses (the
set of received packets { q(v,i) }) with some set of coefficients
(g(1), ...., g(M)). It then transmits the result:
generated_coded_packet = g(1) q(v,1) + ... + g(M) q(v,M).
Since the vectors q(v,1), ... q(v,M) are in turn linear combinations
of the source packets P(1),... P(k), the generated coded packet, can
be expressed itself as a linear combination of these, yielding its
global encoding vector.
In practice, a special header containing the global coding vector of
the transmitted code packet may be added as proposed by Chou et al.
[CWJ03].
A.2. Random Linear Coding
As shown above, when a node generates a coded packet with linear
coding, an issue is how to select coefficients. Whereas centralized
deterministic methods exist, Ho and al. [HKMKE03] presented a novel
coding algorithm, which does not require any central coordination.
The coding algorithm is random linear coding: when a node transmits a
packet, it selects randomly the set of coefficients { g(i) }, which
will be used to perform a linear combination of the vectors q(v,M) as
indicated above.
A.3. Decoding, Vector Space, and Rank
A node v will recover the source packets P(1), ... P(k) its the
received packets q(v,1), ... q(v,M), considering the matrix of
coefficients a(v,i,j) for i=1,...M and j=1,..k from Appendix A.
Decoding amounts to inverting this matrix, for instance with Gaussian
elimination.
Thinking in terms of coding vectors, at any point of time, it is
possible to associate with one node v, the vector space, Q(v) spawned
by the coding vectors, and which is identified with the matrix. The
dimension of that vector space, denoted D(v), is also the rank of the
matrix. In the rest of this document, by abuse of language, we will
call "rank of a node", that rank and dimension.
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The rank of a node is a direct metric for the amount of useful
received packets, and a received packet is called innovative when it
increases the rank of the receiving node. Ultimately a node can
decode all source packets when its rank is equal to the the total
number of source packets.
Appendix B. Acknowledgements
This document also stems from contributions of and from discussions
with : Philippe Jacquet.
Authors' Addresses
Cedric Adjih
Inria
Phone: +33-136-635-215
EMail: Cedric.Adjih@inria.fr
Songyean Cho
Samsung Electronics Co.,LTD.(*)
(*) Author(Songyean Cho)'s contribution was done before
joining Samsung Electronics.
EMail: Songyean.Cho@gmail.com
Emmanuel Baccelli
Inria
Phone: +33-169-335-511
EMail: Emmanuel.Baccelli@inria.fr
URI: http://www.emmanuelbaccelli.org/
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