Error correcting coding is often analyzed in terms of its application to the separate levels within the data network in isolation from each other. In this fresh approach, the authors consider the data network as a superchannel (a multi-layered entity) which allows error correcting coding to be evaluated as it is applied to a number of network layers as a whole. By exposing the problems of applying error correcting coding in data networks, and by discussing coding theory and its applications, this original technique shows how to correct errors in the network through joint coding at different network layers.Discusses the problem of reconciling coding applied to different layers using a superchannel approachIncludes thorough coverage of all the key codes: linear block codes, Hamming, BCH and Reed-Solomon codes, LDPC codes decoding, as well as convolutional, turbo and iterative codingConsiders new areas of application of error correcting codes such as transport coding, code-based cryptosystems and coding for image compressionDemonstrates how to use error correcting coding to control such important data characteristics as mean message delayProvides theoretical explanations backed up by numerous real-world examples and practical recommendationsFeatures a companion website containing additional research results including new constructions of LDPC codes, joint error-control coding and synchronization, Reed-Muller codes and their list decodingBy progressing from theory through to practical problem solving, this resource contains invaluable advice for researchers, postgraduate students, engineers and computer scientists interested in data communications and applications of coding theory.
Author(s): Grigorii Kabatiansky
Edition: 1
Year: 2005
Language: English
Pages: 288
Error Correcting Coding and Security for Data Networks......Page 4
Contents......Page 8
Preface......Page 10
ACKNOWLEDGMENTS......Page 12
1.1 International Recommendations on Using Error Control Coding at Different Network Layers......Page 14
1.2 Classification of Problems on Coding in Networks......Page 17
2.1 Main Definitions......Page 20
2.2 Algebraic Structures......Page 24
2.3 Linear Block Codes......Page 33
2.4 Cyclic Codes......Page 38
2.5 Bounds on Minimum Distance......Page 58
3.1 Minimum Distance Decoding......Page 64
3.2 Information Set Decoding......Page 65
3.3 A Supercode Decoding Algorithm......Page 74
3.4 The Complexity of Decoding in the Channel with Independent Errors......Page 78
4.1 Hamming Codes......Page 90
4.2 Reed-Solomon Codes......Page 94
4.3 BCH Codes......Page 97
4.4 Decoding of BCH Codes......Page 99
4.5 The Sudan Algorithm and its Extensions......Page 104
5.1 Low-Density Parity-Check Codes......Page 116
5.2 LDPC Constructions......Page 119
5.3 Estimating the Minimum Distance of EG-LDPC Codes......Page 126
5.4 Burst-Error-Correcting LDPC Codes......Page 129
5.5 Decoding Schemes of LDPC Codes......Page 131
5.6 Simulation Results in AWGN......Page 143
Appendix 5.A Euclidean Geometries......Page 151
6.1 Convolutional Codes Representation and Encoding......Page 154
6.2 Viterbi Decoding Algorithm......Page 163
6.3 List Decoding......Page 173
6.4 Sequential Decoding......Page 175
6.5 Parallel-Concatenated Convolutional Codes and Soft Input Soft Output Decoding......Page 183
6.6 SISO Decoding Algorithms......Page 189
7.1 Decreasing the Message Delay with the help of Transport Coding......Page 204
7.2 Transmission of Message during Limited Time......Page 210
7.3 Transmission of Priority Messages without using Priority Packets......Page 213
7.4 Estimation of the Effectiveness of Transport Coding for the Nonexponential Model of Packet Delay......Page 216
8.1 Public-Key Cryptography......Page 226
8.2 Codebased Cryptosystems: McEliece and Niederreiter......Page 232
8.3 Cryptosystems Based on Full Decoding......Page 241
8.4 Further Development of Codebased Cryptosystems......Page 246
8.5 Codebased Cryptosystems and RSA: Comparison and Perspectives......Page 250
8.6 Codebased Signature......Page 252
9.1 Transport Coding in a Network with Unreliable Channels......Page 260
9.2 Reconciliation of Channel and Transport Coding......Page 262
9.3 Use of Tornado Codes for Reconciliation of Channel and Transport Coding......Page 266
9.4 Development of Coding Methods at the Presentation Layer......Page 271
9.5 Reconciliation of Coding at Neighbour Layers of a Network......Page 278
Index......Page 288
