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Full Description
The communication chain is constituted by a source and a recipient, separated by a transmission channel which may represent a portion of cable, an optical fiber, a radio channel, or a satellite link. Whatever the channel, the processing blocks implemented in the communication chain have the same foundation. This book aims to itemize.
In this first volume, after having presented the base of the information theory, we will study the source coding techniques with and without loss. Then we analyze the correcting codes for block errors, convutional and concatenated used in current systems.
Contents
Preface xiii List of Acronyms xv
Notations xix
Introduction xxiii
Chapter 1 Introduction to Information Theory 1
1.1 Introduction 1
1.2 Review of probabilities 2
1.3 Entropy and mutual information 7
1.4 Lossless source coding theorems 20
1.5 Theorem for lossy source coding 30
1.6 Transmission channel models 34
1.7 Capacity of a transmission channel 40
1.8 Exercises 54
Chapter 2 Source Coding 57
2.1 Introduction 57
2.2 Algorithms for lossless source coding 58
2.3 Sampling and quantization 69
2.4 Coding techniques for analog sources with memory 87
2.5 Application to the image and sound compression 101
2.6 Exercises 116
Chapter 3 Linear Block Codes 121
3.1 Introduction 121
3.2 Finite fields 122
3.3 Linear block codes 127
3.4 Decoding of binary linear block codes 152
3.5 Performance of linear block codes 172
3.6 Cyclic codes 182
3.7 Applications 214
3.8 Exercises 216
Chapter 4 Convolutional Codes 229
4.1 Introduction 229
4.2 Mathematical representations and hardware structures 229
4.3 Graphical representation of the convolutional codes 238
4.4 Free distance and transfer function of convolutional codes 242
4.5 Viterbi's algorithm for the decoding of convolutional codes 246
4.6 Punctured convolutional codes 249
4.7 Applications 249
4.8 Exercises 250
Chapter 5 Concatenated Codes and Iterative Decoding 253
5.1 Introduction 253
5.2 Soft input soft output decoding 254
5.3 LDPC codes 288
5.4 Parallel concatenated convolutional codes or turbo codes 306
5.5 Other classes of concatenated codes 330
5.6 Exercises 335
Appendices 339
Appendix A 341
Appendix B 343
Bibliography 345
Index 353
Summary of Volume 2 355
