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The art of error correcting coding - Moreloz R.H.

Moreloz R.H. The art of error correcting coding - Wiley publishing , 2002. - 232 p.
ISBN 0471-49581-6
Download (direct link): artoferrorcorrecting2002.pdf
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6.2.3 Products of codes.........................................................Ill
6.2.4 Concatenated codes........................................................117
6.2.5 Generalized concatenated codes............................................119
7 Soft-decision decoding................................................................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-decision decoding: The bit-flip algorithm..................163
8.3.3 Iterative probabilistic decoding: belief propagation......................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
viii 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. 1 Length 8...........................................................................207
A.2 Length 16..........................................................................207
A.3 Length 32 ........................................................................ 208
A.4 Length 64 ........................................................................ 209
A.5 Length 128 ........................................................................211
Index
219
Preface
This book is the result of hundreds of emails from all over the world with questions on theory and applications of error correcting coding (ECC), from colleagues from both academia and industry. Most of the questions have been from engineers and computer scientists needing to select, implement or simulate a particular coding scheme. The questions were sparked by an ECC web site that was initially set up at Imai Laboratory at the Institute of Industrial Science, University of Tokyo, at the beginning of 1995. The reader will notice the absence of theorems and proofs in this text. The approach is to teach basic concepts by using simple examples. References to theoretical developments are made when needed. This book is intended to be a reference guide to error correcting coding techniques for graduate students and professionals interested in learning the basic techniques and applications of ECC. Computer programs that implement the basic encoding and decoding algorithms of practical coding schemes are available on a companion web site at:
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