Codes and turbo codes / edited by Claude Berrou.

Includes bibliographical references and index.

Cover -- Codes and Turbo Codes -- Foreword -- Table of Contents -- Chapter 1 Introduction -- 1.1 Digital Messages -- 1.2 A First Code -- 1.3 Hard Input Decoding and Soft Input Decoding -- 1.4 Hard Output Decoding and Soft Output Decoding -- 1.5 The Performance Measure -- 1.6 What Is a Good Code? -- 1.7 Families of Codes -- Chapter 2 Digital Communications -- 2.1 Digitalmodulations -- 2.1.1 Introduction -- 2.1.2 Linear Memoryless Modulations -- 2.1.3 Memoryless Modulation With M States (M-Fsk) -- 2.1.4 Modulations With Memory By Continuous Phase Frequency Shift Keying (Cpfsk) -- 2.2 Structure and Performance of the Optimal Receiver on a Gaussian Channel -- 2.2.1 Structure of the Coherent Receiver -- 2.2.2 Performance of the Coherent Receiver -- 2.3 Transmission on a Band-Limited Channel -- 2.3.1 Introduction -- 2.3.2 Intersymbol Interference -- 2.3.3 Condition of Absence of Isi: Nyquist Criterion -- 2.3.4 Expression of the Error Probability in Presence of Nyquist Filtering -- 2.4 Transmission on Fading Channels -- 2.4.1 Characterization of a Fading Channel -- 2.4.2 Transmission on Non-Frequency-Selective Slow-Fading Channels -- Performance on a Rayleigh Channel -- Performance on a Rayleigh Channel With Diversity -- Transmission on a Slow-Fading Frequency-Selective Channel -- Transmission With Equalization At Reception -- Chapter 3 Theoretical Limits -- 3.1 Information Theory -- 3.1.1 Transmission Channel -- 3.1.2 An Example: the Binary Symmetric Channel -- 3.1.3 Overview of the Fundamental Coding Theorem -- 3.1.4 Geometrical Interpretation -- 3.1.5 Random Coding -- 3.2 Theoretical Limits to Performance -- 3.2.1 Binary Input and Real Output Channel -- 3.2.2 Capacity of a Transmission Channel -- 3.3 Practical Limits to Performance -- 3.3.1 Gaussian Binary Input Channel -- 3.3.2 Gaussian Continuous Input Channel -- 3.3.3 Some Examples of Limits -- 3.4 Minimum Distances Required -- 3.4.1 Mhd Required With 4-Psk Modulation -- 3.4.2 Mhd Required With 8-Psk Modulation -- 3.4.3 Mhd Required With 16-Qam Modulation -- Bibliography -- Chapter 4 Block Codes -- 4.1 Block Codes With Binary Symbols -- 4.1.1 Generator Matrix of a Binary Block Code -- 4.1.2 Dual Code and Parity Check Matrix -- 4.1.3 Minimum Distance -- 4.1.4 Extended Codes and Shortened Codes -- 4.1.5 Product Codes -- 4.1.6 Examples of Binary Block Codes -- 4.1.7 Cyclic Codes -- 4.2 Block Codes With Non-Binary Symbols -- 4.2.1 Reed-Solomon Codes -- 4.2.2 Implementing the Encoder -- 4.3 Decoding and Performance of Codes With Binary Symbols -- 4.3.1 Error Detection -- 4.3.2 Error Correction -- 4.4 Decoding and Performance of Codes With Non-Binary Symbols . . -- 4.4.1 Hard Input Decoding of Reed-Solomon Codes -- 4.4.2 Petersons Directmethod -- 4.4.3 Iterativemethod -- 4.4.4 Hard Input Decoding Performance of Reed-Solomon Codes -- Bibliography -- Appendix: Notions About Galois Fields and Minimal Polynomials -- Definition -- Primitive Element of a Galois Field -- Minimal Polynomial With Coefficients in F2 Associated With An Element of a Galois Field Fq -- Mi.

This book is devoted to one of the essential functions of modern telecommunications systems: channel coding or error correction coding. At the crossroads of information theory, mathematics and electronics, channel coding has undergone many developments since Claude Shannon's founding work. From the simple Hamming code (1950) and LDPC codes (1962) to the more recent turbo codes (1993), channel coding has evolved considerably and has incorporated ever more sophisticated concepts, especially the probabilistic processing of information. The book's main topic is iteratively decoded algebraic codes, convolutional codes and concatenated codes, and it also presents digital modulation with which channel coding is closely associated to make up the heart of the physical layer of telecommunications systems. The most important theoretical aspects are given, and the building of codes is detailed and justified. Decoding algorithms are developed and, whenever possible, accompanied by simulation results characteristic of their correcting power. The authors are researchers and lecturers recognised for their expertise in the field of encoding and decoding algorithms and associated circuits. Codes and Turbo Codes is intended both as a means for discovering the domain, a valuable source of information about the many techniques imagined since the mid-twentieth century, and as a step towards addressing problems not yet entirely solved.