TURBO CODING

Le Monde En Tique

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Ouvrage 0-7923-8378-8 : TURBO CODING
Turbo Coding presents a unified view of the revolutionary field of turbo error control coding, summarizing recent results in
the areas of encoder structure and performance analysis. The book also introduces new material, including a general theory
for the analysis and design of interleavers, and a unified framework for the analysis and design of decoding algorithms.
Turbo Coding explains the basics of turbo error control coding in a straightforward manner, while making its potential impact
on the design of digital communication systems as clear as possible. Chapters have been provided on the structure and performance of convolutional codes, interleaver design, and the structure and function of iterative decoders. The book also
provides insight into the theory that underlies turbo error control, and briefly summarizes some of the ongoing research efforts. Recent efforts to develop a general theory that unites the Viterbi and BCJR algorithms are discussed in detail. A chapter is provided on the newly discovered connection between iterative decoding and belief propagation in graphs, showing that this leads to parallel algorithms that outperform currently used turbo decoding algorithms.
Turbo Coding is a primary resource for both researchers and teachers in the field of error control coding.
Table of Contents
List of Acronyms xi
List of Tables xv
List of Figures xvii
Preface xxi
1 Introduction 1
1.1 Coding Gain 2
1.2 The Shannon Limit on Performance 5
1.3 Turbo Coding 6
Bibliography 10
2 Binary Codes, Graphs, and Trellises 11
2.1 Basic Definitions for BCE's 11
2.2 Graphs and Trellises 15
2.3 Labeled Trellises 19
2.4 Finite State Machines and BCE's 20
2.4.1 Minimal Convolutional Encoders 24
2.4.2 Systematic Encoders for 27
Convolutional Codes 2.4.3 The Number of Minimal Encoders 28
2.5 Trellis Description of a Linear Block 29
Code
Bibliography 33
3 Interleaving 35
3.1 A Framework for Interleaving 36
3.2 Block Interleavers 37
3.2.1 Classical Block Interleavers 38
3.3 Multiplex Interleavers 39
3.3.1 Classical Convolutional 40
Interleavers
3.4 Representations and Equivalence 40
3.4.1 Decomposition of Interleavers 41
3.4.2 Interleaver Generator Matrices 42
3.4.3 Causal Interleavers 42
3.5 The Shuffle Interleaver 44
3.6 Interleaver Parameters 47
3.6.1 The Delay of an Interleaver 47
3.6.2 The Memory of an Interleaver 48
3.6.3 The Spreading Factors of an 50
Interleaver
3.6.4 The Dispersion of an Interleaver 52
3.7 Some Specific Block Interleavers 53
3.7.1 Co-Prime Interleavers 53
3.7.2 Welch-Costas Interleavers 54
3.7.3 Other Algebraic Interleavers 55
3.7.4 PN, Random and s-Random 58
Interleavers
3.8 Simulation Results 59
Bibliography 62
4 Concatenated Codes 65
4.1 Serial Concatenated Encoders 65
4.1.1 The CCSDS Deep Space Telemetry 66
Standard
4.2 Parallel Concatenated Encoders 77
4.3 Generic Description for Concatenated 78
Codes
Bibliography 85
5 BCE and PCE Performance 89
5.1 Weight Enumerators for Component Codes 89
5.2 Weight Enumerators and Performance 96
Bounds
5.3 BCE Information Weight Distribution 102
5.4 PCE Information Weight Distribution 106
5.5 Summary 117
Bibliography 118
6 Turbo Decoding 121
6.1 Probabilities, Measures and Metrics 121
6.2 Symbol Detection 124
6.2.1 Detection by Partitions 126
6.2.2 Channels and Sources 130
6.3 Soft Symbol Detection -- A DMS over a 133
DMC
6.3.1 Derivations of Recursions for DMS 135
over DMC
6.3.2 Soft Symbol Detection -- FSM 138
Encoder over a DMC 6.4 The Generalized VA and the BCJR 140
6.4.1 A Trellis Labeled by a Semiring 141
6.4.2 The Generalized Viterbi Algorithm 144
6.4.3 The Equivalence of the BCJR and 147
the VA
6.5 Turbo Decoding 149
6.5.1 Basic Computation 150
6.5.2 Turbo Decoding Procedure 156
6.6 Imperfectly Known Channels 157
Bibliography 162
7 Belief Propagation and Parallel Decoding 165
7.1 Reasoning and Probabilistic Networks 166
7.2 Beliefs and Belief Propagation 173
7.2.1 Belief Propagation on Loopless 173
Graphs
7.2.2 Belief Propagation on Loopy Graphs 179
7.3 Parallel Turbo Decoding 182
7.3.1 The Basic Algorithm 184
7.4 Variations on a Parallel Theme 188
7.4.1 Detailed Descriptions of EP1 and 190
EP2
7.5 Final Thoughts 195
Bibliography 196
Index 199

Auteur : HEEGARD
Editeur : KLUWER
Nombre de pages : 206
Date de publication : 01 1999

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