Codes and turbo codes

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.