Fundamentals of Convolutional Coding [Hardcover]

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

• Two new chapters on low-density parity-check (LDPC) convolutional codes and iterative coding
• Viterbi, BCJR, BEAST, list, and sequential decoding of convolutional codes
• Distance properties of convolutional codes
• Includes a downloadable solutions manual

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