Channel Coding for Telecommunications

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ISBN: 9780471982777 | 0471982776
Cover: Hardcover
Copyright: 10/29/1999

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This book clearly describes the leading techniques for channel coding. An advanced tutorial greatly improves the reader's understanding of the material. Rigorous analytical and theoretical examples are provided along with sample problems and solutions. The latest research findings on new techniques in channel coding are also included.

Preface

Introduction

xiii

Fundamentals

(24)

Weight, distance

(4)

Minimum distance, and error correction

(2)

Hamming bound

(1)

Parity check matrix and syndrome

(1)

Decoding principles

(3)

Error probability

(2)

Hamming codes

(2)

Generator matrix

(1)

Code, encoding and and equivalent codes

(1)

Cyclic codes

(1)

Dual codes

(1)

Shortening and extension of codes

(2)

Channel capacity and the coding theorem

(2)

Summary

(1)

Problems

(3)

Galois fields

(20)

Groups

(1)

Rings, fields

(1)

Prime fields

(7)

Primitive elements

(1)

Euclidean algorithm

(3)

Gaussian integers

(2)

Extension fields

(6)

Irreducible polynomials

(2)

Primitive polynomials and roots of polynomials

(2)

Properties of extension fields

(2)

Cyclotomic cosets

(1)

Quadratic residues

(1)

Summary

(1)

Problems

(3)

Reed--Solomon codes

(36)

Definition of RS codes

(10)

Discrete Fourier transform (DFT)

(1)

Generator polynomial

(1)

Parity check polynomial

(1)

Encoding

(1)

General definition of RS codes

(1)

Generalized RS codes and extended RS codes

(4)

Algebraic decoding

(21)

Key equation

(5)

Berlekamp--Massey algorithm

(1)

Euclidean algorithm

(7)

Calculation of the error values

(3)

Equivalence of the Euclidean and Berlekamp--Massey algorithms

(1)

Erasure correction

(2)

Summary

(1)

Problems

(4)

BCH codes

(14)

Primitive BCH codes

(7)

Definition based on cyclotomic cosets

(2)

Designed distance

(1)

Definition by the DFT

(1)

Properties of primitive BCH codes

(1)

Calculation of the generator polynomial

(2)

Non-primitive BCH codes

(1)

Shortening and extending BCH codes

(1)

Non-binary BCH codes

(1)

Relationship between BCH and RS codes

(1)

Asymptotic behavior of BCH codes

(1)

Decoding of BCH codes

(1)

Summary

(1)

Problems

(2)

Other classes of codes

(22)

First-order Reed--Muller codes, simplex codes and Walsh sequences

(9)

Reed--Muller and Hamming codes

(1)

Hamming and simplex codes

(1)

Simplex codes and binary pseudonoise (PN) sequences

(3)

Reed--Muller and simplex codes

102

(2)

Reed--Muller codes of higher order

104

(3)

q-ary Hamming codes

107

(2)

Quadratic residue codes

109

(1)

Consta- and negacyclic codes

110

(2)

Binary interpretation of codes over GF(q = 2m) and Z4

112

(1)

Summary

113

(1)

Problems

114

(3)

The trellis representation and properties of block codes

117

(26)

Cyclic dual codes

117

(3)

MacWilliams identity

120

(2)

Automorphism

122

(1)

Gilbert--Varshamov bound

123

(1)

Singleton bound (MDS)

124

(1)

Reiger bound (burst error correction)

125

(1)

Asymptotic bounds

126

(1)

Minimal trellis of linear block codes

127

(13)

Construction with the aid of the parity check matrix

129

(2)

Construction with the aid of the generator matrix

131

(5)

Properties of a minimal trellis

136

(4)

Summary

140

(2)

Problems

142

(1)

Decoding of block codes

143

(58)

Channel models and metrics

144

(6)

q-ary symmetric channel

145

(1)

Additive white Gaussian noise (AWGN)

146

(1)

Time-variant channels

147

(2)

Hamming and Euclidean metrics

149

(1)

Decoder principles, reliability, complexity and coding gain

150

(10)

Decoding principles

150

(1)

Reliability and decoding principles for binary transmission

151

(6)

Decoding complexity and Evseev's lemma

157

(1)

Coding gain

158

(2)

Decoding methods without reliability information

160

(10)

Permutation decoding

160

(3)

Majority logic decoding

163

(2)

DA algorithm

165

(3)

Hard-decision maximum-likelihood decoding: Viterbi algorithm

168

(2)

Decoding methods using reliability information

170

(25)

Symbolwise soft-decision decoding

170

(7)

List decoding using code trellises: Viterbi algorithm

177

(3)

List decoding in the code space C

180

(9)

List decoding based on ordered statistics

189

(3)

List decoding in code space C⊥

192

(3)

Decoding as an optimization problem

195

(3)

Summary

198

(1)

Problems

199

(2)

Convolutional codes

201

(86)

Fundamentals of convolutional codes

202

(28)

Encoding with sequential logic

202

(2)

Impulse response and convolution

204

(2)

Constraint length, memory and overall constraint length

206

(1)

Generator matrix in the time domain

207

(3)

State diagram, code tree and trellis

210

(3)

Free distance and path enumerators

213

(4)

Termination, truncation and tail-biting

217

(3)

Generator matrix in the Z domain

220

(4)

Systematic and catastrophic generator matrices

224

(2)

Punctured convolutional codes

226

(4)

Algebraic description

230

(14)

Code, generator matrix and encoder

230

(1)

Convolutional encoder in controller and observer canonical form

230

(3)

Equivalent generator matrices

233

(2)

Generator matrix in Smith form

235

(2)

Basic generator matrix

237

(2)

Catastrophic generator matrices

239

(1)

Systematic generator matrices

240

(2)

Parity check matrix and dual code

242

(2)

Distance measures

244

(7)

Row and column distance

244

(3)

Extended distance measures

247

(4)

Maximum-likelihood (Viterbi) decoding

251

(13)

Metrics

252

(2)

Viterbi algorithm

254

(3)

Bounds for decoding performance

257

(3)

Interleaving

260

(1)

Soft-output Viterbi algorithm (SOVA)

261

(3)

Maximum a posteriori decoding (MAP)

264

(4)

BCJR algorithm

264

(3)

Max log MAP algorithm

267

(1)

Sequential decoding

268

(4)

Fano metric

269

(2)

Zigangirov--Jelinek (ZJ) decoder

271

(1)

Fano decoder

271

(1)

(Partial) unit memory codes, (P)UM codes

272

(9)

Definition of (P)UM codes

273

(2)

Trellis of (P)UM codes

275

(1)

Distance measures for (P)UM codes

276

(1)

Construction of (P)UM codes

277

(2)

BMD decoding

279

(2)

Tables of good codes

281

(4)

Summary

285

(1)

Problems

286

(1)

Generalized code concatenation

287

(104)

Introductory examples

290

(5)

GC codes with block codes

295

(49)

Definition of GC codes

296

(2)

Partitioning of block codes

298

(7)

Code construction

305

(7)

Decoding of GC codes

312

(16)

Unequal error protection (UEP) codes

328

(1)

Cyclic codes as GC codes

329

(5)

Error locating codes

334

(6)

Error locating codes in two dimensions

340

(4)

GC codes with convolutional codes

344

(23)

Partitioning of (P)UM codes

345

(4)

Introductory example of trellis partitioning

349

(7)

Partitioning of convolutional codes

356

(5)

Construction and decoding of a GC code

361

(6)

GC codes with block and convolutional codes

367

(6)

Inner convolutional and outer block codes

367

(4)

Inner block and outer convolutional codes

371

(2)

Multiple concatenation and Reed--Muller codes

373

(14)

GMC decoding algorithm for RM codes

375

(5)

L-GMC, list decoding of RM codes

380

(3)

Simulation results and computational complexity

383

(4)

Summary

387

(4)

Coded modulation

391

(28)

Introductory examples

392

(1)

GC with block modulation

393

(14)

Partitioning of signals

394

(2)

Definition of coded modulation

396

(2)

Lattices and generalized multilevel concatenation

398

(4)

Decoding

402

(3)

Trellis-coded modulation systems

405

(2)

GC with convolutional modulation

407

(12)

Introductory example

408

(1)

Algebraic description of convolutional modulation

409

(3)

Partitioning of convolutional modulation

412

(1)

Outer convolutional codes

413

(3)

Outer block codes

416

(1)

Summary

417

(2)

A Serial and parallel concatenated codes and their iterative decoding: turbo codes

419

(18)

A.1 Serial code concatenation

420

(4)

A.2 Parallel code concatenation

424

(4)

A.3 Iterative decoding

428

(3)

A.4 Properties and performance aspects of serial and parallel concatenated codes

431

(6)

B Metrics

437

(8)

B.1 Lee metric

438

(2)

B.2 Manhattan and Mannheim metrics

440

(1)

B.3 Combinational metrics

441

(4)

C Log likelihood algebra

445

(2)

D Solutions

447

(28)

References

475

(14)

Index

489

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Channel Coding for Telecommunications

Summary

Author Biography

Table of Contents

Supplemental Materials