Ieee series on digital & mobile communication : fundamentals of convolutional coding (2nd edition).

Fundamentals of Convolutional Coding, Second Edition, regarded as a bible of convolutional coding brings you a clear and comprehensive discussion of the basic principles of this field. This edition has been expanded to reflect the developments in modern coding theory, including new chapters on low-d...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Johannesson, Rolf; Zigangirov, Kamil Sh
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Hoboken : John Wiley, 2015.
Temas:
Coding theory.
Convolutions (Mathematics)
Error-correcting codes (Information theory)
Convolutions (Mathématiques)
Codes correcteurs d'erreurs (Théorie de l'information)
Coding theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface xi
  • Acknowledgement xiv
  • 1 Introduction 1
  • 1.1 Why error control? 1
  • 1.2 Block codes-a primer 8
  • 1.3 Codes on graphs 21
  • 1.4 A first encounter with convolutional codes 28
  • 1.5 Block codes versus convolutional codes 35
  • 1.6 Capacity limits and potential coding gain revisited 36
  • 1.7 Comments 39
  • Problems 41
  • 2 Convolutional encoders-Structural properties 49
  • 2.1 Convolutional codes and their encoders 49
  • 2.2 The Smith form of polynomial convolutional generator matrices 58
  • 2.3 Encoder inverses 67
  • 2.4 Encoder and code equivalences 76
  • 2.5 Basic encoding matrices 79
  • 2.6 Minimalbasic encoding matrices 82
  • 2.7 Minimal encoding matrices and minimal encoders 90
  • 2.8 Canonical encoding matrices* 109
  • 2.9 Minimality via the invariantfactor theorem* 127
  • 2.10 Syndrome formers and dual encoders 131
  • 2.11 Systematic convolutional encoders 139
  • 2.12 Some properties of generator matrices-an overview 150
  • 2.13 Comments 150
  • Problems 152
  • 3 Distance properties of convolutional codes 161
  • 3.1 Distance measures-a first encounter 161
  • 3.2 Active distances 171
  • 3.3 Properties of convolutional codes via the active distances 179
  • 3.4 Lower bound on the distance profile 181
  • 3.5 Upper bounds on the free distance 186
  • 3.6 Timevarying convolutional codes 191
  • 3.7 Lower bound on the free distance 195
  • 3.8 Lower bounds on the active distances* 200
  • 3.9 Distances of cascaded concatenated codes* 207
  • 3.10 Path enumerators 213
  • 3.11 Comments 220
  • Problems 221
  • 4 Decoding of convolutional codes 225
  • 4.1 The Viterbi algorithm revisited 226
  • 4.2 Error bounds for timeinvariant convolutional codes 235
  • 4.3 Tighter error bounds for timeinvariant convolutional codes 250
  • 4.4 Exact bit error probability for Viterbi decoding 255
  • 4.5 The BCJR algorithm for APP decoding 271
  • 4.6 The oneway algorithm for APP decoding 283
  • 4.7 A simple upper bound on the bit error probability for extremely noisy channels 288.
  • 4.8 Tailbiting trellises 293
  • 4.9 Decoding of tailbiting codes 302
  • 4.10 BEAST decoding of tailbiting codes 308
  • 4.11 Comments 323
  • Problems 324
  • 5 Random ensemble bounds for decoding error probability 333
  • 5.1 Upper bounds on the output error burst lengths 333
  • 5.2 Bounds for periodically timevarying convolutional codes 345
  • 5.3 Lower error probability bounds for convolutional codes 355
  • 5.4 General bounds for timevarying convolutional codes 363
  • 5.5 Bounds for finite backsearch limits 375
  • 5.6 Quantization of channel outputs 379
  • 5.7 Comments 384
  • Problems 384
  • 6 List decoding 387
  • 6.1 List decoding algorithms 388
  • 6.2 List decoding-performance 391
  • 6.3 The list minimum weight 397
  • 6.4 Upper bounds on the probability of correct path loss 407
  • 6.5 Lower bound on the probability of correct path loss 416
  • 6.6 Correct path loss for timeinvariant convolutional codes 418
  • 6.7 Comments 422
  • Problems 423
  • 7 Sequential decoding 425
  • 7.1 The Fano metric 426
  • 7.2 The stack algorithm 431
  • 7.3 The Fano algorithm 433
  • 7.4 The Creeper algorithm* 436
  • 7.5 Simulations 448
  • 7.6 Computational analysis of the stack algorithm 450
  • 7.7 Error probability analysis of the stack algorithm 460
  • 7.8 Analysis of the Fano algorithm 471
  • 7.9 Analysis of Creeper* 477
  • 7.10 Comments 480
  • Problems 481
  • 8 Lowdensity paritycheck codes 485
  • 8.1 LDPC block codes 486
  • 8.2 LDPC convolutional codes 496
  • 8.3 Block and convolutional permutors 508
  • 8.4 Lower bounds on distances of LDPC codes 517
  • 8.5 Iterative decoding of LDPC codes 529
  • 8.6 Iterative limits and thresholds 538
  • 8.7 Braided block codes* 553
  • 8.8 Comments 562
  • Problems 562
  • 9 Turbo coding 567
  • 9.1 Parallel concatenation of two convolutional codes 567
  • 9.2 Distance bounds of turbo codes 570
  • 9.3 Parallel concatenation of three and more convolution codes 573
  • 9.4 Iterative decoding of turbo codes 582
  • 9.5 Braided convolutional codes* 586
  • 9.6 Comments 591.
  • Problems 591
  • 10 Convolutional codes with good distance properties 593
  • 10.1 Computing the Viterbi spectrum using FAST 594
  • 10.2 The magnificient BEAST 598
  • 10.3 Some classes of rate R = 1=2 convolutional codes 604
  • 10.4 Low rate convolutional codes 608
  • 10.5 High rate convolutional codes 621
  • 10.6 Tailbiting trellis encoders 622
  • 10.7 Comments 622
  • Appendix A: Minimal encoders 627
  • Appendix B: Wald's identity 635
  • References 647
  • Index 659.

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