[ArtechHouse2010]APracticalGuidetoError-ControlCodingUsingMATLAB

书名：A Practical Guide to Error-Control Coding Using MATLAB
作者：Yuan Jiang
出版：Artech House， 2010
目录
Preface ix
1 Error Control in Digital Communications
and Storage 1
1.1 Error Control Coding at a Glance 1
1.1.1 Codes for Error Control 1
1.1.2 Important Concepts 5
1.2 Channel Capacity and Shannon’s Theorem 14
1.3 Considerations When Selecting
Coding Schemes 16
References 17
Selected Bibliography 17
2 Brief Introduction to Abstract Algebra 19
2.1 Elementary Algebraic Structures 19
2.1.1 Group 19
2.1.2 Field 22
2.2 Galois Field and Its Arithmetic 25
2.2.1 Galois Field 25
2.2.2 Arithmetic in GF (2m) 33
2.3 Implementation of GF (2m) Arithmetic 36
2.3.1 Arithmetic with Polynomial Representation 36
2.3.2 Arithmetic with Power Representation 39
2.3.3 A Special Case: Inversion 40
Problems 43
References 44
Selected Bibliography 44
3 Binary Block Codes 45
3.1 Linear Block Codes 45
3.1.1 Code Construction and Properties 45
3.1.2 Decoding Methods 51
3.1.3 Performance of Linear Block Codes 60
3.1.4 Encoder and Decoder Designs 65
3.1.5 Hamming Codes 66
3.2 Cyclic Codes 73
3.2.1 Basic Principles 74
3.2.2 Shift RegisterCBased Encoder and Decoder 81
3.2.3 Shortened Cyclic Codes and CRC 91
3.3 BCH Codes 95
3.3.1 Introduction 97
3.3.2 BCH Bound and Vandermonde Matrix 100
3.3.3 Decoding BCH Codes 101
Problems 110
References 111
Selected Bibliography 112
4 Reed-Solomon Codes 113
4.1 Introduction to RS Codes 113
4.1.1 Prelude: Nonbinary BCH Codes 113
4.1.2 Reed-Solomon Codes 117
4.2 Decoding of RS Codes 123
4.2.1 General Remarks 123
4.2.2 Determining the Error Location Polynomial 124
4.2.3 Frequency-Domain Decoding 135
4.2.4 Error and Erasure Decoding 140
4.3 RS Decoder: From Algorithm to
Architecture 143
4.3.1 Syndrome Computation Circuit 143
4.3.2 Architectures for Berlekamp-Massey
Algorithm 143
4.3.3 Circuit for Chien Search and Forney’s
Algorithm 149
4.4 Standardized RS Codes 149
Problems 150
References 151
5 Convolutional Codes 153
5.1 Fundamentals of Convolutional Codes 153
5.1.1 Code Generation and Representations 153
5.1.2 Additional Matters 161
5.2 Decoding of Convolutional Codes 165
5.2.1 Optimum Convolutional Decoding
and Viterbi Algorithm 166
5.2.2 Sequential Decoding 179
5.3 Designing Viterbi Decoders 189
5.3.1 Typical Design Issues 189
5.3.2 Design for High Performance 197
5.4 Good Convolutional Codes 201
5.4.1 Catastrophic Error Propagation 202
5.4.2 Some Known Good Convolutional Codes 202
5.5 Punctured Convolutional Codes 202
Problems 210
References 210
Selected Bibliography 212
6 Modern Codes 213
6.1 Turbo Codes 213
6.1.1 Code Concatenation 213
6.1.2 Concatenating Codes in Parallel: Turbo Code 218
6.1.3 Iterative Decoding of Turbo Codes 228
6.1.4 Implementing MAP 250
6.2 Low-Density Parity-Check Codes 252
6.2.1 Codes with Sparse Parity-Check Matrix 254
6.2.2 Decoding and Encoding Algorithms 259
6.2.3 High-Level Architecture Design for
LDPC Decoders 270
Problems 272
References 274
Selected Bibliography 276
About the Author 277
Index 279