Buch, Englisch, 360 Seiten, Format (B × H): 174 mm x 246 mm, Gewicht: 871 g
ISBN: 978-0-470-02920-6
Verlag: Wiley
Rapid advances in electronic and optical technology have enabled the implementation of powerful error-control codes, which are now used in almost the entire range of information systems with close to optimal performance. These codes and decoding methods are required for the detection and correction of the errors and erasures which inevitably occur in digital information during transmission, storage and processing because of noise, interference and other imperfections.
Error-control coding is a complex, novel and unfamiliar area, not yet widely understood and appreciated. This book sets out to provide a clear description of the essentials of the subject, with comprehensive and up-to-date coverage of the most useful codes and their decoding algorithms. A practical engineering and information technology emphasis, as well as relevant background material and fundamental theoretical aspects, provides an in-depth guide to the essentials of Error-Control Coding.
- Provides extensive and detailed coverage of Block, Cyclic, BCH, Reed-Solomon, Convolutional, Turbo, and Low Density Parity Check (LDPC) codes, together with relevant aspects of Information Theory
- EXIT chart performance analysis for iteratively decoded error-control techniques
- Heavily illustrated with tables, diagrams, graphs, worked examples, and exercises
- Invaluable companion website features slides of figures, algorithm software, updates and solutions to problems
Offering a complete overview of Error Control Coding, this book is an indispensable resource for students, engineers and researchers in the areas of telecommunications engineering, communication networks, electronic engineering, computer science, information systems and technology, digital signal processing and applied mathematics.
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
- Mathematik | Informatik EDV | Informatik Daten / Datenbanken Informationstheorie, Kodierungstheorie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
Preface xiii
Acknowledgements xv
List of Symbols xvii
Abbreviations xxv
1 Information and Coding Theory 1
1.1 Information 3
1.1.1 A Measure of Information 3
1.2 Entropy and Information Rate 4
1.3 Extended DMSs 9
1.4 Channels and Mutual Information 10
1.4.1 Information Transmission over Discrete Channels 10
1.4.2 Information Channels 10
1.5 Channel Probability Relationships 13
1.6 The A Priori and A Posteriori Entropies 15
1.7 Mutual Information 16
1.7.1 Mutual Information: Definition 16
1.7.2 Mutual Information: Properties 17
1.8 Capacity of a Discrete Channel 21
1.9 The Shannon Theorems 22
1.9.1 Source Coding Theorem 22
1.9.2 Channel Capacity and Coding 23
1.9.3 Channel Coding Theorem 25
1.10 Signal Spaces and the Channel Coding Theorem 27
1.10.1 Capacity of the Gaussian Channel 28
1.11 Error-Control Coding 32
1.12 Limits to Communication and their Consequences 34
Bibliography and References 38
Problems 38
2 Block Codes 41
2.1 Error-Control Coding 41
2.2 Error Detection and Correction 41
2.2.1 Simple Codes: The Repetition Code 42
2.3 Block Codes: Introduction and Parameters 43
2.4 The Vector Space over the Binary Field 44
2.4.1 Vector Subspaces 46
2.4.2 Dual Subspace 48
2.4.3 Matrix Form 48
2.4.4 Dual Subspace Matrix 49
2.5 Linear Block Codes 50
2.5.1 Generator Matrix G 51
2.5.2 Block Codes in Systematic Form 52
2.5.3 Parity Check Matrix H 54
2.6 Syndrome Error Detection 55
2.7 Minimum Distance of a Block Code 58
2.7.1 Minimum Distance and the Structure of the H Matrix 58
2.8 Error-Correction Capability of a Block Code 59
2.9 Syndrome Detection and the Standard Array 61
2.10 Hamming Codes 64
2.11 Forward Error Correction and Automatic Repeat ReQuest 65
2.11.1 Forward Error Correction 65
2.11.2 Automatic Repeat ReQuest 68
2.11.3 ARQ Schemes 69
2.11.4 ARQ Scheme Efficiencies 71
2.11.5 Hybrid-ARQ Schemes 72
Bibliography and References 76
Problems 77
3 Cyclic Codes 81
3.1 Description 81
3.2 Polynomial Representation of Codewords 81
3.3 Generator Polynomial of a Cyclic Code 83
3.4 Cyclic Codes in Systematic Form 85
3.5 Generator Matrix of a Cyclic Code 87
3.6 Syndrome Calculation and Error Detection 89
3.7 Decoding of Cyclic Codes 90
3.8 An Application Example: Cyclic Redundancy Check Code for the Ethernet Standard 92
Bibliography and References 93
Problems 94
4 BCH Codes 97
4.1 Introduction: The Minimal Polynomial 97
4.2 Description of BCH Cyclic Codes 99
4.2.1 Bounds on the Error-Correction Capability of a BCH Code: The Vandermonde Determinant 102
4.3 Decoding of BCH Codes 104
4.4 Error-Location and Error-Evaluation Polynomials 105
4.5 The Key Equation 107
4.6 Decoding of Binary BCH Codes Using the Euclidean Algorithm 108
4.6.1 The Euclidean Algorithm 108
Bibliography and References 112
Problems 112
5 Reed–Solomon Codes 115
5.1 Introduction 115
5.2 Error-Correction Capability of RS Codes: The Vandermonde Determinant 117
5.3 RS Codes in Systematic Form 119
5.4 Syndrome Decoding of RS Codes 120
5.5 The Euclidean Algorithm: Error-Location and Error-Evaluation Polynomials 122
5.6 Decoding of RS Codes Using the Euclidean Algorithm 125
5.6.1 Steps of the Euclidean Algorithm 127
5.7 Decoding of RS and BCH Codes Using the Berlekamp–Massey Algorithm 128
5.7.1 B–M Iterative Algorithm for Finding the Error-Location Polynomial 130
5.7.2 B–M Decoding of RS Codes 133
5.7.3 Relationship Between the Error-Location Polynomials of the Euclidean and B–M Algorithms 136
5.8 A Practical Application: Error-Control Coding for the Compact Disk 136
5.8.1 Compact Disk Characteristics 136
5.8.2 Channel Characteristics 138
5.8.3 Coding Procedure 138
5.9 Encoding for RS codes CRS(28, 24), CRS(32, 28) and CRS(255, 251) 139
5.10 Decoding of RS Codes CRS(28, 24) and CRS(32, 28) 142
5.10.1 B–M Decoding 142
5.10.2 Alternative Decoding Methods 145
5.10.3 Direct Solution of Syndrome Equations 146
5.11 Importance of Interleaving 148
Bibliography and References 152
Problems 153
6 Convolutional Codes 157
6.1 Linear Sequential Circuits 158
6.2 Convolutional Codes and Encoders 158
6.3 Description in the D-Transform Domain 161
6.4 Convolutional Encoder Representations 166
6.4.1 Representation of Connections 166
6.4.2 State Diagram Representation 166
6.4.3 Trellis Representation 168
6.5 Convolutional Codes in Systematic Form 168
6.6 General Structure of Finite Impulse Response and Infinite Impulse Response FSSMs 170
6.6.1 Finite Impulse Response FSSMs 170
6.6.2 Infinite Impulse Response FSSMs 171
6.7 State Transfer Function Matrix: Calculation of the Transfer Function 172
6.7.1 State Transfer Function for FIR FSSMs 172
6.7.2 State Transfer Function for IIR FSSMs 173
6.8 Relationship Between the Systematic and the Non-Systematic Forms 175
6.9 Distance Properties of Convolutional Codes 177
6.10 Minimum Free Distance of a Convolutional Code 180
6.11 Maximum Likelihood Detection 181
6.12 Decoding of Convolutional Codes: The Viterbi Algorithm 182
6.13 Extended and Modified State Diagram 185
6.14 Error Probability Analysis for Convolutional Codes 186
6.15 Hard and Soft Decisions 189
6.15.1 Maximum Likelihood Criterion for the Gaussian Channel 192
6.15.2 Bounds for Soft-Decision Detection 194
6.15.3 An Example of Soft-Decision Decoding of Convolutional Codes 196<
