Error-control block codes for communications engineers

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Title:

Personal Author:

Lee, Charles, L. H., 1956-

Series:

Artech House telecommunications library

Publication Information:

Norwood, MA : Artech House, 2000

ISBN:

9781580530323

Subject Term:

Error-correcting codes (Information theory)

Telecommunication -- Mathematics

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000003589540	TK5102.96 L43 2000	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	30000003589508	TK5102.96 L43 2000	Open Access Book	Book	Searching... Unknown

A guide to error-control block codes for communications engineers. It examines linear block codes, cyclic codes, BCH codes, RS codes, and multilevel block-coded modulation, and provides valuable simulation results to save the reader time in understanding and using error-control block codes. Featuring real-world applications to such technologies as space and mobile communications and compact disks, as well as many illustrations of technique, this book offers itself as a tool for designing and engineering coded transmissions for reliable digital communications. Areas covered include: decoding on erasure channels with block codes or BCH and RS codes; designing efficient coded modulation schemes for bandwidth-constraint channels; decoding BCH and RS codes with Euclid's algorithm; and generating BCH and RS codes.

Author Notes

L.H. Charles Lee received his Ph.D. in Electrical Engineering from Manchester University (UK) and his B.Sc. in Electrical & Electronic Engineering from Loughborough University (UK).

Lee is a lecturer at MacQuarie University in Sydney, Australia. He is a member of the IEEE and the IEE.

050

Preface	p. xiii
1 Introduction of Coded Digital Communication Systems	p. 1
1.1 Introduction	p. 1
1.2 Elements of a Digital Communication System	p. 2
1.2.1 Data Source and Data Sink	p. 2
1.2.2 Channel Encoder and Channel Decoder	p. 3
1.2.3 Modulator, Transmission Path, and Demodulator	p. 3
1.2.4 Channel Models	p. 8
1.2.4.1 Discrete Memoryless Channel	p. 8
1.2.4.2 Binary Symmetric Channel	p. 8
1.2.4.3 Binary Symmetric Erasure Channel	p. 9
1.2.4.4 Burst Channel	p. 10
1.3 Types of Errors and Error-Control Codes	p. 11
References	p. 11
2 Introduction to Abstract Algebra	p. 13
2.1 Groups	p. 13
2.2 Rings	p. 16
2.2.1 Polynomial Rings	p. 19
2.3 Fields	p. 20
2.3.1 Polynomials over GF(2)	p. 23
2.3.2 Construction of Extension Field GF(2[superscript m]) from GF(2)	p. 24
2.3.3 Properties of Extension Field GF(2[superscript m])	p. 26
2.4 Implementation of Galois Field Arithmetic	p. 30
2.5 Vector Spaces	p. 32
2.6 Matrices	p. 36
References	p. 37
3 Linear Block Codes	p. 39
3.1 Basic Concepts and Definitions	p. 40
3.2 Matrix Description of Linear Block Codes	p. 42
3.3 Relationship of Minimum Distance to Error Detection and Correction	p. 45
3.4 Syndrome-Former Trellis Representation of Binary Linear Block Codes	p. 48
3.5 Examples of Binary Linear Block Codes	p. 51
3.5.1 Repetition Codes	p. 52
3.5.2 Single-Parity-Check Codes	p. 52
3.5.3 Single-Error-Correcting Hamming Codes	p. 53
3.5.4 Reed-Muller Codes	p. 54
3.6 Modifications of Linear Block Codes	p. 56
3.7 Decoding of Linear Block Codes	p. 58
3.7.1 Standard Array Decoding	p. 58
3.7.2 Syndrome Decoding	p. 61
3.7.3 Maximum-Likelihood Decoding	p. 63
3.7.3.1 Hard-Decision Decoding	p. 65
3.7.3.2 Soft-Decision Decoding	p. 68
3.7.4 Maximum-Likelihood Viterbi Algorithm Decoding	p. 70
3.7.4.1 Hard-Decision Decoding	p. 72
3.7.4.2 Soft-Decision Decoding	p. 73
3.8 Correction of Errors and Erasures	p. 76
3.9 Performance of Binary Block Codes	p. 79
3.10 Computer Simulation Results	p. 81
References	p. 83
4 Cyclic Codes	p. 85
4.1 Introduction	p. 85
4.2 Polynomial Description of Cyclic Codes	p. 85
4.3 Matrix Description of Cyclic Codes	p. 91
4.4 Encoding of Cyclic Codes	p. 94
4.5 Decoding of Cyclic Codes	p. 95
4.5.1 Syndrome Decoding	p. 95
4.5.2 Error-Trapping Decoding	p. 103
4.6 Golay Codes and Shortened Cyclic Codes	p. 107
4.7 Computer Simulation Results	p. 108
References	p. 110
5 Bose-Chaudhuri-Hocquenghem Codes	p. 111
5.1 Introduction	p. 111
5.2 General Description of BCH Codes	p. 111
5.3 Binary, Narrow-Sense, Primitive BCH Codes	p. 112
5.4 Parity-Check Matrix and BCH Bound on [superscript d]min	p. 116
5.5 Decoding of Binary BCH Codes	p. 119
5.5.1 Berlekamp-Massey Algorithm	p. 120
5.5.2 Euclid's Algorithm	p. 127
5.6 Correction of Errors and Erasures	p. 131
5.7 Computer Simulation Results	p. 136
References	p. 138
6 Reed-Solomon Codes	p. 139
6.1 Introduction	p. 139
6.2 Description of Reed-Solomon Codes	p. 139
6.3 Decoding of Reed-Solomon Codes	p. 143
6.3.1 Berlekamp-Massey Algorithm	p. 143
6.3.2 Euclid's Algorithm	p. 150
6.4 Correction of Errors and Erasures	p. 151
6.4.1 Berlekamp-Massey Algorithm Decoding	p. 151
6.4.2 Euclid's Algorithm Decoding	p. 157
6.5 Computer Simulation Results	p. 161
References	p. 163
7 Multilevel Block-Coded Modulation	p. 165
7.1 Introduction	p. 165
7.2 Encoding and Mapping of Multilevel Block-Coded Modulation	p. 170
7.3 Decoding Methods	p. 183
7.3.1 Maximum-Likelihood Decoding	p. 183
7.3.2 Multistage Decoding	p. 184
7.3.3 Multistage Trellis Decoding	p. 186
7.4 Performance of Multilevel Block-Coded Modulation With Multistage Decoding	p. 191
7.5 Advantages and Disadvantages of Using Multilevel Block-Coded Modulation	p. 192
7.6 Computer Simulation Results	p. 192
References	p. 195
8 Applications of Block Codes	p. 199
8.1 Introduction	p. 199
8.2 Applications to Space Communications	p. 199
8.2.1 Voyager Missions	p. 200
8.2.2 Galileo Mission	p. 201
8.3 Applications to Mobile Communications	p. 202
8.3.1 GSM Digital Radio System	p. 203
8.4 Applications to Compact Discs	p. 207
8.4.1 Encoding	p. 211
8.4.2 Decoding	p. 216
References	p. 219
Appendix A Binary Primitive Polynomials	p. 221
Appendix B Galois Field Tables	p. 223
Appendix C Minimal Polynomials of Elements in GF(2[superscript m])	p. 229
Appendix D Generator Polynomials of Binary, Narrow-Sense, Primitive BCH Codes	p. 231
About the Author	p. 233
Index	p. 235

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Table of Contents