Essentials of Error-Control Coding
Autor Jorge Castiñeira Moreira, Patrick Guy Farrellen Limba Engleză Hardback – oct 2006
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Specificații
ISBN-13: 9780470029206
ISBN-10: 047002920X
Pagini: 388
Dimensiuni: 174 x 246 x 27 mm
Greutate: 0.87 kg
Editura: Wiley
Locul publicării:Chichester, United Kingdom
ISBN-10: 047002920X
Pagini: 388
Dimensiuni: 174 x 246 x 27 mm
Greutate: 0.87 kg
Editura: Wiley
Locul publicării:Chichester, United Kingdom
Public țintă
Postgraduate and undergraduate students on courses such as telecommunications engineering,communication networks, electronic engineering, computer science, information systems and technology, digital signal processing, applied mathematics. Engineers and researchers working in any of the areas above, advanced students in related subjects.Cuprins
Preface xiii
Acknowledgements xv
List of Symbols xvii
Abbreviations xxv
1 Information and Coding Theory 1
1.1 Information 3
1.2 Entropy and Information Rate 4
1.3 Extended DMSs 9
1.4 Channels and Mutual Information 10
1.5 Channel Probability Relationships 13
1.6 The A Priori and A Posteriori Entropies 15
1.7 Mutual Information 16
1.8 Capacity of a Discrete Channel 21
1.9 The Shannon Theorems 22
1.10 Signal Spaces and the Channel Coding Theorem 27
1.11 Error-Control Coding 32
1.12 Limits to Communication and their Consequences 34
2 Block Codes 41
2.1 Error-Control Coding 41
2.2 Error Detection and Correction 41
2.3 Block Codes: Introduction and Parameters 43
2.4 The Vector Space over the Binary Field 44
2.5 Linear Block Codes 50
2.6 Syndrome Error Detection 55
2.7 Minimum Distance of a Block Code 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
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
4 BCH Codes 97
4.1 Introduction: The Minimal Polynomial 97
4.2 Description of BCH Cyclic Codes 99
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
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
5.7 Decoding of RS and BCH Codes Using the Berlekamp-Massey Algorithm 128
5.8 A Practical Application: Error-Control Coding for the Compact Disk 136
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
5.11 Importance of Interleaving 148
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
6.5 Convolutional Codes in Systematic Form 168
6.6 General Structure of Finite Impulse Response and Infinite Impulse Response FSSMs 170
6.7 State Transfer Function Matrix: Calculation of the Transfer Function 172
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
6.16 Punctured Convolutional Codes and Rate-Compatible Schemes 200
7 Turbo Codes 209
7.1 A Turbo Encoder 210
7.2 Decoding of Turbo Codes 211
7.3 Markov Sources and Discrete Channels 215
7.4 The BCJR Algorithm: Trellis Coding and Discrete Memoryless Channels 218
7.5 Iterative Coefficient Calculation 221
7.6 The BCJR MAP Algorithm and the LLR 234
7.7 Turbo Decoding 239
7.8 Construction Methods for Turbo Codes 249
7.9 Other Decoding Algorithms for Turbo Codes 257
7.10 EXIT Charts for Turbo Codes 257
8 Low-Density Parity Check Codes 277
8.1 Different Systematic Forms of a Block Code 278
8.2 Description of LDPC Codes 279
8.3 Construction of LDPC Codes 280
8.4 The Sum-Product Algorithm 282
8.5 Sum-Product Algorithm for LDPC Codes: An Example 284
8.6 Simplifications of the Sum-Product Algorithm 297
8.7 A Logarithmic LDPC Decoder 302
8.8 Extrinsic Information Transfer Charts for LDPC Codes 306
8.9 Fountain and LT Codes 317
8.10 LDPC and Turbo Codes 322
Bibliography and References 323
Problems 324
Appendix A: Error Probability in the Transmission of Digital Signals 327
Appendix B: Galois Fields GF(q) 339
Answers to Problems 351
Index 357
Acknowledgements xv
List of Symbols xvii
Abbreviations xxv
1 Information and Coding Theory 1
1.1 Information 3
1.2 Entropy and Information Rate 4
1.3 Extended DMSs 9
1.4 Channels and Mutual Information 10
1.5 Channel Probability Relationships 13
1.6 The A Priori and A Posteriori Entropies 15
1.7 Mutual Information 16
1.8 Capacity of a Discrete Channel 21
1.9 The Shannon Theorems 22
1.10 Signal Spaces and the Channel Coding Theorem 27
1.11 Error-Control Coding 32
1.12 Limits to Communication and their Consequences 34
2 Block Codes 41
2.1 Error-Control Coding 41
2.2 Error Detection and Correction 41
2.3 Block Codes: Introduction and Parameters 43
2.4 The Vector Space over the Binary Field 44
2.5 Linear Block Codes 50
2.6 Syndrome Error Detection 55
2.7 Minimum Distance of a Block Code 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
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
4 BCH Codes 97
4.1 Introduction: The Minimal Polynomial 97
4.2 Description of BCH Cyclic Codes 99
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
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
5.7 Decoding of RS and BCH Codes Using the Berlekamp-Massey Algorithm 128
5.8 A Practical Application: Error-Control Coding for the Compact Disk 136
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
5.11 Importance of Interleaving 148
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
6.5 Convolutional Codes in Systematic Form 168
6.6 General Structure of Finite Impulse Response and Infinite Impulse Response FSSMs 170
6.7 State Transfer Function Matrix: Calculation of the Transfer Function 172
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
6.16 Punctured Convolutional Codes and Rate-Compatible Schemes 200
7 Turbo Codes 209
7.1 A Turbo Encoder 210
7.2 Decoding of Turbo Codes 211
7.3 Markov Sources and Discrete Channels 215
7.4 The BCJR Algorithm: Trellis Coding and Discrete Memoryless Channels 218
7.5 Iterative Coefficient Calculation 221
7.6 The BCJR MAP Algorithm and the LLR 234
7.7 Turbo Decoding 239
7.8 Construction Methods for Turbo Codes 249
7.9 Other Decoding Algorithms for Turbo Codes 257
7.10 EXIT Charts for Turbo Codes 257
8 Low-Density Parity Check Codes 277
8.1 Different Systematic Forms of a Block Code 278
8.2 Description of LDPC Codes 279
8.3 Construction of LDPC Codes 280
8.4 The Sum-Product Algorithm 282
8.5 Sum-Product Algorithm for LDPC Codes: An Example 284
8.6 Simplifications of the Sum-Product Algorithm 297
8.7 A Logarithmic LDPC Decoder 302
8.8 Extrinsic Information Transfer Charts for LDPC Codes 306
8.9 Fountain and LT Codes 317
8.10 LDPC and Turbo Codes 322
Bibliography and References 323
Problems 324
Appendix A: Error Probability in the Transmission of Digital Signals 327
Appendix B: Galois Fields GF(q) 339
Answers to Problems 351
Index 357
Descriere
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.