Coding Theory Algorithms, Architectures and Applications

by Neubauer, Andre; Freudenberger, Jurgen; Kuhn, Volker

• ISBN13: 9780470028612
• ISBN10: 0470028610
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-11-12
• Publisher: Wiley-Interscience

Summary

One of the most important key technologies for digital communication systems as well as storage media is coding theory. It provides a means to transmit information across time and space over noisy and unreliable communication channels. Coding Theory: Algorithms, Architectures and Applications provides a concise overview of channel coding theory and practice, as well as the accompanying signal processing architectures. The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low density parity check codes and space-time codes. Coding Theory provides algorithms and architectures used for implementing coding and decoding strategies as well as coding schemes used in practice especially in communication systems. Feature of the book include: Unique presentation-like style for summarising main aspects Practical issues for implementation of coding techniques Sound theoretical approach to practical, relevant coding methodologies Covers standard coding schemes such as block and convolutional codes, coding schemes such as Turbo and LDPC codes, and space time codes currently in research, all covered in a common framework with respect to their applications. This book is ideal for postgraduate and undergraduate students of communication and information engineering, as well as computer science students. It will also be of use to engineers working in the industry who want to know more about the theoretical basics of coding theory and their application in currently relevant communication systems

Author Biography

Dr. Andre Neubauer, Münster University of Applied Sciences, Germany

Jürgen Freudenberger, HTWG Konstanz, University of Applied Sciences, Germany

Volker Kühn, University of Rostock, Germany

Table of Contents

Preface	p. ix
Introduction	p. 1
Communication Systems	p. 1
Information Theory	p. 3
Entropy	p. 3
Channel Capacity	p. 4
Binary Symmetric Channel	p. 5
AWGN Channel	p. 6
A Simple Channel Code	p. 8
Algebraic Coding Theory	p. 13
Fundamentals of Block Codes	p. 14
Code Parameters	p. 16
Maximum Likelihood Decoding	p. 19
Binary Symmetric Channel	p. 23
Error Detection and Error Correction	p. 25
Linear Block Codes	p. 27
Definition of Linear Block Codes	p. 27
Generator Matrix	p. 27
Parity-Check Matrix	p. 30
Syndrome and Cosets	p. 31
Dual Code	p. 36
Bounds for Linear Block Codes	p. 37
Code Constructions	p. 41
Examples of Linear Block Codes	p. 46
Cyclic Codes	p. 62
Definition of Cyclic Codes	p. 62
Generator Polynomial	p. 63
Parity-Check Polynomial	p. 67
Dual Codes	p. 70
Linear Feedback Shift Registers	p. 71
BCH Codes	p. 74
Reed-Solomon Codes	p. 81
Algebraic Decoding Algorithm	p. 84
Summary	p. 93
Convolutional Codes	p. 97
Encoding of Convolutional Codes	p. 98
Convolutional Encoder	p. 98
Generator Matrix in the Time Domain	p. 101
State Diagram of a Convolutional Encoder	p. 103
Code Termination	p. 104
Puncturing	p. 106
Generator Matrix in the D-Domain	p. 108
Encoder Properties	p. 110
Trellis Diagram and the Viterbi Algorithm	p. 112
Minimum Distance Decoding	p. 113
Trellises	p. 115
Viterbi Algorithm	p. 116
Distance Properties and Error Bounds	p. 121
Free Distance	p. 121
Active Distances	p. 122
Weight Enumerators for Terminated Codes	p. 126
Path Enumerators	p. 129
Pairwise Error Probability	p. 131
Viterbi Bound	p. 134
Soft-input Decoding	p. 136
Euclidean Metric	p. 136
Support of Punctured Codes	p. 137
Implementation Issues	p. 138
Soft-output Decoding	p. 140
Derivation of APP Decoding	p. 141
APP Decoding in the Log Domain	p. 145
Convolutional Coding in Mobile Communications	p. 147
Coding of Speech Data	p. 147
Hybrid ARQ	p. 150
EGPRS Modulation and Coding	p. 152
Retransmission Mechanism	p. 155
Link Adaptation	p. 156
Incremental Redundancy	p. 157
Summary	p. 160
Turbo Codes	p. 163
LDPC Codes	p. 165
Codes Based on Sparse Graphs	p. 165
Decoding for the Binary Erasure Channel	p. 168
Log-Likelihood Algebra	p. 169
Belief Propagation	p. 174
A First Encounter with Code Concatenation	p. 177
Product Codes	p. 177
Iterative Decoding of Product Codes	p. 180
Concatenated Convolutional Codes	p. 182
Parallel Concatenation	p. 182
The UMTS Turbo Code	p. 183
Serial Concatenation	p. 184
Partial Concatenation	p. 185
Turbo Decoding	p. 186
EXIT Charts	p. 188
Calculating an EXIT Chart	p. 189
Interpretation	p. 191
Weight Distribution	p. 196
Partial Weights	p. 196
Expected Weight Distribution	p. 197
Woven Convolutional Codes	p. 198
Encoding Schemes	p. 200
Distance Properties of Woven Codes	p. 202
Woven Turbo Codes	p. 205
Interleaver Design	p. 208
Summary	p. 212
Space-Time Codes	p. 215
Introduction	p. 215
Digital Modulation Schemes	p. 216
Diversity	p. 223
Spatial Channels	p. 229
Basic Description	p. 229
Spatial Channel Models	p. 234
Channel Estimation	p. 239
Performance Measures	p. 241
Channel Capacity	p. 241
Outage Probability and Outage Capacity	p. 250
Ergodic Error Probability	p. 252
Orthogonal Space-Time Block Codes	p. 257
Alamouti's Scheme	p. 257
Extension to More than Two Transmit Antennas	p. 260
Simulation Results	p. 263
Spatial Multiplexing	p. 265
General Concept	p. 265
Iterative APP Preprocessing and Per-layer Decoding	p. 267
Linear Multilayer Detection	p. 272
Original BLAST Detection	p. 275
QL Decomposition and Interference Cancellation	p. 278
Performance of Multi-Layer Detection Schemes	p. 287
Unified Description by Linear Dispersion Codes	p. 291
Summary	p. 294
Algebraic Structures	p. 295
Groups, Rings and Finite Fields	p. 295
Groups	p. 295
Rings	p. 296
Finite Fields	p. 298
Vector Spaces	p. 299
Polynomials and Extension Fields	p. 300
Discrete Fourier Transform	p. 305
Linear Algebra	p. 311
Acronyms	p. 319
Bibliography	p. 325
Index	p. 335
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