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Iterative Error Correction : Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes - Sarah J. Johnson

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Iterative Error Correction

Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes

By: Sarah J. Johnson

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Hardcover | 8 February 2010

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Hardcover
356 Pages

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24.41 x 16.99 x 2.06

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Iterative error correction codes have found widespread application in cellular communications, digital video broadcasting and wireless LANs. This self-contained treatment of iterative error correction presents all the key ideas needed to understand, design, implement and analyse these powerful codes. Turbo, low-density parity-check, and repeat-accumulate codes are given equal, detailed coverage, with precise presentations of encoding and decoding procedures. Worked examples are integrated into the text to illuminate each new idea and pseudo-code is included for important algorithms to facilitate the reader''s development of the techniques described. For each subject, the treatment begins with the simplest case before generalizing. There is also coverage of advanced topics such as density-evolution and EXIT charts for those readers interested in gaining a deeper understanding of the field. This text is ideal for graduate students in electrical engineering and computer science departments, as well as practitioners in the communications industry.

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You Can Find This Book In

Non-Fiction Engineering & Technology Electronics & Communications Engineering Electronics Engineering Mathematics Applied Mathematics Energy Technology & Engineering Electrical Engineering Communications Engineering & Telecommunications Telephone Technology Mobile Phone Technology

Preface	p. xi
Notation	p. xv
Commonly used abbreviations	p. xix
Channels, codes and capacity	p. 1
Binary input memoryless channels	p. 2
Entropy, mutual information and capacity	p. 8
A measure of information	p. 8
Entropy	p. 10
Capacity	p. 13
Codes and decoding	p. 16
Decoding	p. 18
Performance measures	p. 24
Bibliographic notes	p. 29
Exercises	p. 30
Low-density parity-check codes	p. 34
Introduction	p. 34
Error correction using parity checks	p. 34
Low-density parity-check codes	p. 37
Encoding	p. 40
(Almost) linear-time encoding for LDPC codes	p. 44
Repeat-accumulate codes	p. 48
Decoding	p. 48
Message passing on the binary erasure channel	p. 50
Bit-flipping decoding	p. 54
Sum-product decoding	p. 61
Bibliographic notes	p. 71
Exercises	p. 72
Low-density parity-check codes: properties and constructions	p. 75
Introduction	p. 75
LDPC properties	p. 75
Choosing the degree distribution	p. 76
Girth and expansion	p. 82
Codeword and pseudo-codeword weights	p. 84
Cyclic and quasi-cyclic codes	p. 89
Implementation and complexity	p. 95
LDPC constructions	p. 97
Pseudo-random constructions	p. 97
Structured LDPC codes	p. 105
LDPC design rules	p. 114
Bibliographic notes	p. 117
Exercises	p. 118
Convolutional codes	p. 121
Introduction	p. 121
Convolutional encoders	p. 121
Memory order and impulse response	p. 125
Recursive convolutional encoders	p. 127
Puncturing	p. 131
Convolutional code trellises	p. 132
Minimum free distance	p. 135
Decoding convolutional codes	p. 136
Maximum a posteriori (BCJR) decoding	p. 136
Log MAP decoding	p. 148
Maximum likelihood (Viterbi) decoding	p. 156
Bibliographic notes	p. 160
Exercises	p. 161
Turbo codes	p. 165
Introduction	p. 165
Turbo encoders	p. 165
Iterative turbo decoding	p. 169
Turbo code design	p. 176
Interleaving gain	p. 176
Choosing the component codes	p. 178
Interleaver design	p. 182
Design rules	p. 188
Factor graphs and implementation	p. 190
Implementation and complexity	p. 191
Stopping criteria	p. 194
Bibliographic notes	p. 196
Exercises	p. 198
Serial concatenation and RA codes	p. 201
Serial concatenation	p. 201
Serially concatenated turbo codes	p. 203
Turbo decoding of SC codes	p. 203
Code design	p. 207
Repeat-accumulate codes	p. 209
Encoding RA codes	p. 211
Turbo decoding of RA codes	p. 212
Sum-product decoding of RA codes	p. 217
Irregular RA codes	p. 220
Weight-3 IRA codes	p. 224
Accumulate-repeat-accumulate codes	p. 226
Code design	p. 227
Bibliographic notes	p. 232
Exercises	p. 234
Density evolution and EXIT charts	p. 237
Introduction	p. 237
Density evolution	p. 238
Density evolution on the BEC	p. 239
Ensemble thresholds	p. 243
Density evolution and repeat-accumulate codes	p. 247
Density evolution on general binary input memoryless channels	p. 249
Density evolution and turbo codes	p. 254
Designing ensembles with good thresholds	p. 256
Approximations to density evolution	p. 260
EXIT charts	p. 261
Mutual information	p. 262
EXIT charts for turbo codes	p. 264
EXIT charts for RA codes	p. 273
EXIT charts for LDPC codes	p. 276
Code design and analysis using EXIT charts	p. 279
Bibliographic notes	p. 279
Exercises	p. 281
Error floor analysis	p. 283
Introduction	p. 283
Maximum likelihood analysis	p. 283
Input-output weight enumerating functions for convolutional codes	p. 285
Parallel concatenated code ensembles	p. 290
Serially concatenated code ensembles	p. 296
The error floor of irregular block codes	p. 301
Designing iterative codes to improve the interleaving gain and error floor	p. 305
Asymptotic (in the code length) performance of iterative ensembles	p. 306
Finite-length analysis	p. 309
Bibliographic notes	p. 318
Exercises	p. 320
References	p. 322
Index	p. 331
Table of Contents provided by Ingram. All Rights Reserved.

Iterative Error Correction

Turbo, Low-Density Parity-Check and Repeat-Accumulate Codes

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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