Bit–Interleaved Coded Modulation: Fundamentals, Analysis and Design

Presenting a thorough overview of bit–interleaved coded modulation (BICM), this book introduces the tools for the analysis and design of BICM transceivers. It explains in detail the functioning principles of BICM and proposes a refined probabilistic modeling of the reliability metrics the so–called L–values which are at the core of the BICM receivers. Alternatives for transceiver design based on these models are then studied.

Providing new insights into the analysis of BICM, this book is unique in its approach, providing a general framework for analysis and design, focusing on communication theoretic aspects of BICM transceivers. It adopts a tutorial approach, explains the problems in simple terms with the aid of multiple examples and case studies, and provides solutions using accessible mathematical tools.

The book will be an excellent resource for researchers in academia and industry: graduate students, academics, development engineers, and R & D managers.

Presents an introduction to BICM, placing it in the context of other coded modulation schemes

Offers explanations of the functioning principles and design alternatives

Provides a unique approach, focusing on communication theory aspects

Shows examples and case studies to illustrate analysis and design of BICM

Adopts a tutorial approach, explaining the problems in simple terms and presenting solutions using accessible mathematical tools

Dedication iii

Preface ix

Acknowledgements xi

Acronyms xvi

1 Introduction 1

1.1 Coded Modulation 1

1.2 The Road Towards BICM 4

1.3 Why Everybody Loves BICM 5

1.4 Outline of the Contents 8

References 9

2 Preliminaries 13

2.1 Notation Convention 13

2.2 Linear Modulation 16

2.3 Coded modulation 18

2.4 Channel Models 21

2.5 The Mapper 23

2.6 Codes and Encoding 34

2.7 The Interleaver 43

2.8 Bibliographical Notes 54

References 56

3 Decoding 61

3.1 Optimal Decoding 61

3.2 BICM Decoder 64

3.3 L–values 66

3.4 Hard–decision Decoding 78

3.5 Bibliographical Notes 80

References 81

4 Information–Theoretic Elements 83

4.1 Mutual Information and Channel Capacity 83

4.2 Coded Modulation 86

4.3 Bit–interleaved Coded Modulation 94

4.4 BICM, CM and MLC: A Comparison 111

4.5 Numerical Calculation of Mutual Information 117

4.6 Bibliographical Notes 121

References 122

5 Probability Density Functions of L–values 125

5.1 Introduction and Motivation 125

5.2 PDF of L–values for 1D Constellations 135

5.3 PDF of L–values for 2D Constellations 140

5.4 Fading Channels 155

5.5 Gaussian Approximations 160

5.6 Bibliographical Notes 172

References 174

6 Performance Evaluation 177

6.1 Uncoded Transmission 177

6.2 Coded Transmission 200

6.3 PEP Evaluation 225

6.4 Performance of BICM via Gaussian Approximations 238

6.5 Bibliographical Notes 247

References 249

7 Correction of L–values 253

7.1 Mismatched Decoding and L–values Correction 253

7.2 Optimal Correction of L–values 258

7.3 Suboptimal Correction of L–values 263

7.4 Bibliographical Notes 278

References 279

8 Interleaver Design 281

8.1 UEP in BICM and M–Interleavers 281

8.2 Exploiting UEP in MPAM Constellations 291

8.3 Bibliographical Notes 299

References 301

9 BICM Receivers for Trellis Codes 303

9.1 BICM with Trivial Interleavers 303

9.2 Code Design for BICM–T 312

9.3 Equivalent Labelings for Trellis Encoders 317

9.4 Bibliographical Notes 325

References 326

Index 328

Leszek Szczecinski University of Quebec, Canada

Alex Alvarado University College London, UK