网络编码：基础与应用

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"Network Coding: Fundamentals and Applications" 本书是一本专为对网络编码及其在通信网络各个领域应用感兴趣的科研人员和实践者编写的指南。它假设读者具有基本的网络知识，但对网络编码技术或应用没有先前的了解。这本书的目标是让网络专业人士能够掌握这一领域的基础知识，并学习如何运用这些技术。同时，对于想要在网络编码领域进行研究的研究生来说，本书也极具价值。它可以作为专注于网络编码或高级编码技术课程的教科书或参考书。网络编码是一种革命性的网络传输技术，它超越了传统的数据包转发策略，通过在网络节点上混合和编码数据来提高网络性能和效率。与传统的存储和转发方法不同，网络编码允许节点在转发数据时进行运算，从而可能实现更高的带宽利用率、更稳定的流媒体传输、增强的容错能力以及更安全的数据传输。本书由Muriel Médard和Alex Sprintson两位专家编辑，他们分别来自麻省理工学院和德州农工大学。书中涵盖了网络编码的基础理论，包括线性网络编码、非线性网络编码、分布式网络编码等核心概念。此外，还深入探讨了网络编码在无线网络、认知无线电、多播、内容分发网络、网络安全、错误校正等方面的应用。全书配有彩色可下载插图，以帮助读者更好地理解复杂的网络编码方案和设计。为了保护版权，未经出版商书面许可，任何部分不得以任何形式或任何方式复制或传播，包括电子或机械复制，录音，或任何信息存储和检索系统。有兴趣寻求许可的读者可以按照出版商提供的指引获取更多信息，如与版权清算中心等组织的安排。《网络编码：基础与应用》提供了一个全面的平台，让读者能够深入了解网络编码的基本原理并掌握其实际应用，无论是对于专业研究人员还是学生，都是一份宝贵的资源。通过学习本书，读者将能够理解网络编码如何改变网络通信的格局，并有能力将这些知识应用于实际的网络设计和优化中。

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MEDARD 07-lof-xxiii-xxx-9780123809186 2011/10/13 15:56 Page xxv #3

List of Figures

xxv

4.1 Video broadcasting from one device to multiple receivers. 89

4.2 Content distribution in a Multi-Hop Network. 90

4.3 Viral content spreading. 91

4.4 Mobile distributed storage. 92

4.5 Multi-path reception. 94

4.6 NC system components. 94

4.7 NC system with erasures. 97

4.8 Dilbert on randomness.

 United Feature Syndicate INC./Dist. by PIB

Copenhagen 2010. 98

4.9 Coding throughput on a Nokia N95 mobile phone, with look-up table

based implementation. Generation sizes between 10 and 400 and the block

size of 1.5 kB [17] are tested. 100

4.10 Decoding throughput on a powerful desktop PC ﬁtted with a Nvidia 260

GTX graphics card. Generation sizes of 128, 256, 512 are tested along with

block sizes between 1 kB and 32 kB [20]. 104

4.11 Decoding throughput on an OpenGL graphics card. Generation sizes

between 16 and 64 are tested at a block size of 1 kB [23]. 105

4.12 Decoding throughput on a Nokia N95-8GB. Generation sizes between 16

and 64 are tested at a block size of 1.5 kB [25]. 107

4.13 Pure NC: (a) Partially decoded data; (b) Image starting to appear as the

decoders rank increases; (c) The ﬁnal decoded image. Systematic NC:

(d) Received uncoded data; (e) Erasures corrected by coded packets;

(f) The ﬁnal decoded image. 108

4.14 Application throughput with and without NC. 109

4.15 Normalized energy consumption of the application with and without NC. 110

4.16 Trade-off between low and high ﬁeld size and generation size. 111

5.1 The network architecture of eMBMS. 117

5.2 The structure of the source block. 120

5.3 The framework of streaming and download services in eMBMS. 121

5.4 Cumulative Distribution Function of the actual packet error rate in each

block with a different source block length. 125

5.5 Network architecture of user cooperation. 127

5.6 Illustration of progressive recovery in user cooperation. 128

5.7 Overhead saving in the cellular link by user cooperation. 136

5.8 Cooperation cost saving by network coding over the short-range link. 137

5.9 Comparison of the number of the exchanged packets over the short-range

link with/without network coding. 138

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MEDARD 07-lof-xxiii-xxx-9780123809186 2011/10/13 15:56 Page xxvi #4

xxvi

List of Figures

6.1 The CONCERTO architecture. Black lines indicate the processing ﬂow

for application packets generated at this node; Blue lines indicate the

processing ﬂow for network coded packets received from neighbors (for

forwarding and/or decoding); Red lines indicate repair request packets

received from neighbors; Orange lines indicate periodic neighbor discovery

packets; and Green dashed lines indicated intra-module control ﬂow. The

yellow modules are network coding speciﬁc and are discussed in more

detail in the remainder of this chapter. 147

6.2 A ﬁxed size vector in each network coded packet contains the linear

coefﬁcients associated with the source packets. These coefﬁcients are used

by the destination to decode a generation of packets. 150

6.3 Subgraph constructor system diagram. 153

6.4 A six-node network that shows the ﬂow of data and reliability control

information. 156

6.5 The Master/Slave forwarding architecture. 157

6.6 Algorithm used by the Master Forwarder to select the next packet to send. 157

6.7 The network coding problem formulation treats unicast and broadcast as

special cases of multicast. Here the light blue nodes are part of the subgraph

that forwards information from the source S to the destinations D

and D

. 161

6.8 Network coding is robust to routing “loops” since packets that are not

innovative (do not contain new information) do not trigger a transmission. 161

6.9 Network coding provides low-latency link layer encoding as part of its

normal operation. 162

6.10 Network coding naturally incorporates opportunistic receptions since

innovative packets are always stored upon reception. 164

6.11 Network coding subgraph construction takes into account link quality and

uses multiple low quality links if that is optimal. 165

6.12 Architecture of the baseline system. 167

6.13 Alpha/Bravo Phase includes 10 man-pack radios, two truck mounted

radios, and two aircraft mounted radios (not shown) as well as 21 stationary

radios. 171

6.14 MANET topology during the Bravo/Charlie phase in the ground scenario.

Note the large number of poor quality links. 171

6.15 Video ﬂows used to evaluate baseline and CONCERTO performance in

ground and air scenarios. Video Load 1 is “intra-squad” while Video Loads

2 and 3 add “inter-squad” multi-hop sessions (indicated in orange and

purple). 173

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use only by the author(s), editor(s), reviewer(s), Elsevier and typesetter diacriTech. It is not allowed to publish this proof online

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MEDARD 07-lof-xxiii-xxx-9780123809186 2011/10/13 15:56 Page xxvii #5

List of Figures

xxvii

6.16 Video performance comparison CONCERTO vs. Baseline in the Ground

scenario. 174

6.17 CONCERTO and baseline latency for the air scenario. 175

6.18 Comparison of total network transmission. 175

6.19 Performance over distance. 176

6.20 Distance-utility comparison. 177

6.21 Subgraph consists of green (source) node, blue (forwarder) nodes, yellow

(forwarder-destination) nodes and orange (destination) nodes. Size of node

indicates forwarding rate. 178

6.22 Video performance in air scenario. 179

8.1 Example networks where the separation between source and network

coding fails. (a) An instance of the non-multicast example from [16]. In this

example, sources X

and X

are jointly distributed with individual

entropies H(X

) = H(X

) = 3 and joint entropy H(X

, X

) = 4. (b) The

two-transmitter, three-receiver multicast example from [17]. In this

example, sources X

and X

are jointly distributed with individual

entropies H(X

) = H(X

) = 2 and joint entropy H(X

, X

) = 3. In both

examples, each edge has capacity 1 +  for some  > 0. 220

8.2 The rate region for sources (X

, X

) and (

) may be different even

when the entropy vectors (H(X

), H(X

, X

)) and

(H(

), H(

)) are identical, as shown by the given example.

Sources X

and

are uniformly distributed on alphabet {0, 1, 2, 3}.

Sources X

and

are drawn according to distributions Q(x

) and

Q(ˆx

|ˆx

), respectively, as deﬁned above. The rate regions for the coded

side information problem differ for these two sources. For example, when

p = 0.5 and each link has capacity 1 + , the given demands can be met

for source (X

, X

) but not for source (

). 223

9.1 Rateless broadcast over N independent erasure channels, where C

[t] is

Bernoulli distributed with mean c

. 238

9.2 Extension of the setup of Fig. 9.1 to a full tree of depth h, where each

erasure link fades independently with the uniform mean of c. 243

9.3 A multicast setting in a general network topology. 244

9.4 Extension of the setup to streaming ﬂows, where HOL stands for

Head-of-Line. 245

9.5 Extension of the setup to streaming ﬂows with delay sensitivities. 246

9.6 Optimum revenue performance of RNC for varying N and K. 247

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xxviii

List of Figures

9.7 Optimum revenue performance comparison of RNC versus Scheduling

for varying K with N = 50. 247

9.8 Fraction of receivers that have successfully decoded a single packet in a

block of K packets in s time slots, r

[s] as a function of s for c = 1/2. 250

9.9 Mean throughput behavior under different scalings of K with N. 251

9.10 Comparing actual throughput to upper and lower bounds for c = 0.9 and

K = 50 ln(N). 252

9.11 Comparing actual throughput to upper and lower bounds for c = 0.9 and

K = N . 252

9.12 The three phases of a typical delivery under the two-hop transmission

scheme, in which the dotted line indicates the movement of the relay node

over one or multiple time slots. 255

9.13 The virtual channel representation. 257

9.14 Delay-throughput trade-offs with coding and without coding. 259

9.15 The virtual channel representation of a multicast session. 260

10.1 Temporal network representing the contacts between nodes. 272

10.2 Ratios of transmissions required by simple ﬂooding and an RLC broadcast

scheme under a uniform at random mobility model and Random Waypoint

Mobility (RWP, with different average velocity) (Fig. 10.8 in [11]). 282

10.3 Packet delivery ratio under varying forwarding factors in sparse networks

(Fig. 10.4 in [49]). 283

10.4 Event-driven graph for calculating minimum block delivery delay for block

(1, 4, 0, 2) under the contact trace shown in Fig. 10.1, assuming each node

can store at most B relay packets. Links over which random linear

combinations are transmitted are drawn in thick lines (there are η = 4 such

links), e.g., over link (1, 1.2) → (2, 1.2), node 1 transmits a random linear

combination of the two packets to node 2. Over link (3, 23) → (4, 23),

node 3 does not perform RLC as it has only one encoded packet in its

buffer. 285

10.5 DTN with N = 101 nodes, homogeneous exponential inter-meeting time

with rate β = 0.0049, bandwidth constraint of b = 1 packet per contact,

and unlimited buffer space. 290

10.6 CDF of different delay metrics of 100 simulation runs, under the same

network setting as that of Fig. 10.5. 291

10.7 Block delivery delay vs transmission number trade-off under the same

network setting as Fig. 10.5 except for the bandwidth and buffer

constraints. 293

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网络编码：基础与应用

Network Coding Fundamentals

读取process.bmp或者process.raw，产生1组二进制序列（长度为16），通过‘异或’操作，完成图像的编码，另存为coding.bmp或者coding.raw；

读取coding.bmp或者coding.raw，利用之前(1)的1组二进制序列（长度为16），通过‘异或’操作，完成图像的解码，另存为decoding.bmp或者decoding.raw；

用matlab读取coding.bmp或者coding.raw，利用之前(1)的1组二进制序列（长度为16），通过‘异或’操作，完成图像的解码，另存为decoding.bmp或者decoding.raw；

用matlab读取process.bmp或者process.raw，产生1组二进制序列（长度为16），通过‘异或’操作，完成图像的编码，另存为coding.bmp或者coding.raw；

读取 coding.bmp 或者 coding.raw，利用之前的 1 组二进制序列（长度为 16），通过‘异或’操作，完成图像的解码

有关 线性码 的 参考文献

用matlab编写：读取process.bmp，产生1组二进制序列（长度为16），通过‘异或’操作，完成图像的编码，另存为coding.bmp

PIP 21.1.1 setuptools56.0.0 警告：您使用的是pip版本21.1.1，但是可以使用版本23.1.2。您应该考虑通过'/d ata/user/0/coding.- yu.pythoncompiler.new/files/PYR00T3/bin/pytho- n3-mpip 安装进行升级 -升级pip 命令。

用matlab编写：读取coding.bmp，用上次的1组二进制序列（长度为16），通过‘异或’操作，完成图像的解码，另存为decoding.bmp

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有关线性码的参考文献