文件名称:
The Art of Error Correcting Coding
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文件大小: 5mb
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上传时间: 2009-09-21
详细说明： Preface .......................................... ix ......................................... Foreword xi ... .................................... The ECC web site xi11 ..................................... 1 Introduction .................... 1.1 Error correcting coding: Basic concepts 1.1.1 Block codes and convolutional codes ................. 1.1.2 Hamming distance, Hamming spheres and error correcting capability ............................... 1.2 Linear block codes .................. 1.2.1 Generator and parity-check matrices 1.2.2 The weight is the distance ....................... ................. 1.3 Encoding and decoding of linear block codes ........................ 1.3.1 EncodingwithGandH ........................ 1.3.2 Standard array decoding 1.3.3 Hamming spheres, decoding regions and the standard array ...... ................... 1.4 Weight distribution and error performance 1.4.1 Weight distribution and undetected error probability over a BSC ... 1.4.2 Performance bounds over BSC . AWGN and fading channels ..... .......... 1.5 General structureof a hard-decisiondecoder of linearcodes ..................... 2 Hamming. Golay and Reed-Muller codes 23 ................................. 2.1 Hamming codes 23 .................. 2.1.1 Encoding and decoding procedures 24 ............................. 2.2 The binary Golay code 25 ................................ 2.2.1 Encoding 25 ................................ 2.2.2 Decoding 26 ...... 2.2.3 Arithmetic decoding of the extended (24. 12. 8) Golay code 26 ........................... 2.3 Binary Reed-Muller codes 27 .................. 2.3.1 Boolean polynomials and RM codes 27 ............ 2.3.2 Finite geometries and majority-logic decoding 28 ........................ 3 Binary cyclic codes and BCH codes 33 ............................... 3.1 Binary cyclic codes 33 ................ 3.1.1 Generator and parity-check polynomials 33 CONTENTS ....................... 3.1.2 The generator polynomial 34 ............. 3.1.3 Encoding and decoding of binary cyclic codes 35 ...................... 3.1.4 The parity-check polynomial 36 ................ 3.1.5 Shortened cyclic codes and CRC codes 37 ........................ 3.2 General decoding of cyclic codes 39 ........................... 3.2.1 GF(2m) arithmetic 41 ............................... 3.3 Binary BCH codes 44 ................................ 3.4 Polynomial codes 45 ......................... 3.5 Decoding of binary BCH codes 46 .............. 3.5.1 General decoding algorithm for BCH codes 48 ............... 3.5.2 The Berlekamp-Massey algorithm (BMA) 49 .............................. 3.5.3 PGZ decoder 52 ....................... 3.5.4 Euclidean Algorithm (EA) 53 ................... 3.5.5 Chien search and error correction 55 ..................... 3.5.6 Errors-and-erasures decoding 55 .................. 3.6 Weight distribution and performance bounds 56 ..................... 3.6.1 Error performance evaluation 57 ................... 4 Non-binary BCH codes: Reed-Solomon codes 63 ......................... 4.1 RS codes as polynomial codes 63 ......................... 4.2 From binary BCH to RS codes 63 ............................... 4.3 Decoding RS codes 64 .................... 4.3.1 Remarks on decoding algorithms 69 ..................... 4.3.2 Errors-and-erasures decoding 69 ............................... 4.4 Weight distribution 73 5 Binaryconvolutionalcodes ............................. 75 ................................. 5.1 Basic structure 75 5.1.1 Recursive systematic convolutional codes ............... 80 .............................. 5.1.2 Free distance 81 ......................... 5.2 Connections with block codes 81 .......................... 5.2.1 Zero-tail construction 81 ..................... 5.2.2 Direct-truncation construction 82 ......................... 5.2.3 Tail-biting construction 82 5.2.4 Weight distributions .......................... 83 5.3 Weight enumeration and performance bounds ................. 84 5.4 Decoding: Viterbi algorithm with Hamming metrics .............. 86 5.4.1 Maximum likelihood decoding and metrics .............. 87 5.4.2 The Viterbi algorithm .......................... 88 ......................... 5.4.3 Implementation issues 90 ......................... 5.5 Punctured convolutional codes 96 5.5.1 Implementation issues related to punctured convolutional codes ... 99 .............................. 5.5.2 RCPC codes 100 .......................... 6 Modifying and combining codes 103 ................................ 6.1 Modifying codes 103 ............................... 6.1.1 Shortening 103 CONTENTS vii ................................ 6.1.2 Extending 105 ............................... 6.1.3 Puncturing 105 ...................... 6.1.4 Augmenting and expurgating 106 ................................ 6.2 Combining codes 108 ......................... 6.2.1 Time-sharing of codes 108 .......................... 6.2.2 Direct-sums of codes 109 ............................ 6.2.3 Products of codes 111 ........................... 6.2.4 Concatenated codes 117 .................... 6.2.5 Generalized concatenated codes 119 ................................ 7 Soft-decisiondecoding 123 ................... 7.1 Binary transmission over AWGN channels 124 .................... 7.2 Viterbi algorithm with Euclidean metric 124 ............... 7.3 Decoding binary linear block codes with a trellis 130 .............................. 7.4 The Chase algorithm 131 ........................... 7.5 Ordered statistics decoding 133 .................... 7.6 Generalized minimum distance decoding 134 .................. 7.6.1 Sufficient conditions for optimality 135 .................................. 7.7 List decoding 136 ............................. 7.8 Soft-output algorithms 136 ...................... 7.8.1 Soft-output Viterbi algorithm 136 ............... 7.8.2 Maximum-a-posteriori (MAP) algorithm 139 .......................... 7.8.3 Log-MAP algorithm 141 ....................... 7.8.4 Max-Log-MAP algorithm 142 ....................... 7.8.5 Soft-output OSD algorithm 142 ............................. 8 Iteratively decodable codes 145 ................................ 8.1 Iterative decoding 147 .................................. 8.2 Product codes 149 .................. 8.2.1 Parallel concatenation: turbo codes 149 .......................... 8.2.2 Serial concatenation 155 .......................... 8.2.3 Block product codes 157 ........................ 8.3 Low-density parity-check codes 161 .............................. 8.3.1 Tanner graphs 161 8.3.2 Iterative hard-decisiondecoding: The bit-flip algorithm ........ 163 .......... 8.3.3 Iterative probabilistic decoding: beliefpropagation 164 ..................... 9 Combining codes and digital modulation 171 .................................... 9.1 Motivation 171 ......................... 9.1.1 Examples of signal sets 172 ........................... 9.1.2 Coded modulation 174 ........................ 9.1.3 Distance considerations 175 ........................ 9.2 Trellis-coded modulation (TCM) 176 .................. 9.2.1 Set partitioning and trellis mapping 176 ..................... 9.2.2 Maximum-likelihood decoding 177 ............ 9.2.3 Distance considerations and error performance 177 ................ 9.2.4 Pragmatic TCM and two-stage decoding 178 ... vlll CONTENTS 9.3 Multilevel coded modulation (MCM) ...................... 182 9.3.1 Constructions and multi-stage decoding ................ 183 9.3.2 Unequal-error-protection with MCM ................. 185 9.4 Bit-interleaved coded modulation (BICM) ................... 191 9.4.1 Gray mapping .............................. 191 9.4.2 Metric generation: De-mapping .................... 192 ............................... 9.4.3 Interleaving 193 9.5 Turbo trellis-coded modulation (TTCM) .................... 194 9.5.1 Pragmatic turbo TCM ......................... 194 9.5.2 Turbo TCM with symbol interleaving ................. 194 9.5.3 Turbo TCM with bit interleaving .................... 194 References ........................................ 197 Appendix A Weight distributions of extended BCH codes .............. 207 A.l Length8 .................................. 207 A.2 Length16 .................................... 207 A.3 Length32 .................................... 208 A.4 Length 64 .................................... 209 A.5 Length 128 ................................... 211 Index ........................................... 219 ...展开收缩
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