Error Correction Capability of Random Network Error Correction Codes

Balli, H.; Yan, Xijin; Zhang, Zhen

doi:10.1109/isit.2007.4557447

Cited by 19 publications

(6 citation statements)

References 6 publications

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“…In various models and applications of random linear network coding [9], [14]- [17], H is assumed to be an invertible square matrix 1 . This assumption is based on the fact that when H is a square matrix, i.e., M = N , it is full rank with high probability if i) M is less than or equal to the maximum flow from the transmitter to the receiver, and ii) the field size for network coding is sufficiently large comparing with the number of network nodes [9], [18]. However, random linear network coding with small finite fields is attractive for low computing complexity.…”

Section: A Some Related Workmentioning

confidence: 99%

Coding for linear operator channels over finite fields

Yang¹,

Ho²,

Liu³

et al. 2010

2010 IEEE International Symposium on Information Theory

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Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver.There are NO constraints on the distribution of the transformation matrix and the field size.Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant.The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated.Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix.The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.

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Section: A Some Related Workmentioning

confidence: 99%

Coding for linear operator channels over finite fields

Yang¹,

Ho²,

Liu³

et al. 2010

2010 IEEE International Symposium on Information Theory

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show abstract

“…In the context of peer-to-peer content storage and distribution, random NC has been shown to be more robust against packet losses than traditional forward error correction [18]. In wireless networks, packet losses are usually due to transmission errors which corrupt the received packet.…”

Section: B Joint Source-network-channel Coding/decodingmentioning

confidence: 99%

Challenging issues in multimedia transmission over wireless networks based on network coding

Linh-Trung¹,

Bao²,

Duhamel

et al. 2012

2012 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT)

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Abstract-To meet increasing throughput, delay and reliability demands, future wireless networks will have to rely on increased cooperation both among nodes and among protocol layers in a node. This requires a wide variety of knowledge, from theoretical issues such as graph theory or information theory, to issues at the physical and network layers. A potential solution is the recently proposed network coding because it offers a number of desired properties such as resource efficiency, robustness and security. This paper focuses on two research directions for multimedia transmission over wireless networks based on network coding: (i) source-aware network coding and (ii) physical-layer network coding. These directions follow the cross-layer framework in designing the communication protocol stack. Challenging issues which are related to the practical design of network-coding enabled wireless networks are addressed and discussed.

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“…Ho et al [158] proved the optimality of random linear network coding and proposed the use of such codes on networks with unknown topology. A tight upper bound on the probability of decoding error for random linear network coding has recently been obtained by Balli et al [23].…”

Section: Appendix 14a: the Basic Inequalities And The Polymatroidal mentioning

confidence: 99%

Information theory and network coding

2009

Choice Reviews Online

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Part I of this book by itself may be regarded as a comprehensive textbook in information theory. The main reason why the book is in the present form is because in my opinion, the discussion of network coding in Part II is incomplete without Part I. Nevertheless, except for Chapter 21 on multi-source network coding, Part II by itself may be used satisfactorily as a textbook on single-source network coding.An elementary course on probability theory and an elementary course on linear algebra are prerequisites to Part I and Part II, respectively. For Chapter 11, some background knowledge on digital communication systems would be helpful, and for Chapter 20, some prior exposure to discrete-time linear systems is necessary. The reader is recommended to read the chapters according to the above chart. However, one will not have too much difficulty jumping around in the book because there should be sufficient references to the previous relevant sections.This book inherits the writing style from the previous book, namely that all the derivations are from the first principle. The book contains a large number of examples, where important points are very often made. To facilitate the use of the book, there is a summary at the end of each chapter.This book can be used as a textbook or a reference book. As a textbook, it is ideal for a two-semester course, with the first and second semesters covering selected topics from Part I and Part II, respectively. A comprehensive instructor's manual is available upon request.

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Error Correction Capability of Random Network Error Correction Codes

Cited by 19 publications

References 6 publications

Coding for linear operator channels over finite fields

Coding for linear operator channels over finite fields

Challenging issues in multimedia transmission over wireless networks based on network coding

Information theory and network coding

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