The art of error correcting coding:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 263 S. graph. Darst. |
| ISBN: | 9780470015582 0470015586 |
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| 245 | 1 | 0 | |a The art of error correcting coding |c Robert H. Morelos-Zaragoza |
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| adam_text | THE ART OF ERROR CORRECTING CODING SECOND EDITION ROBERT H.
MORELOS-ZARAGOZA SAN JOSE STATE UNIVERSITY, USA JOHN WILEY & SONS, LTD
CONTENTS PREFACE IX FOREWORD XI THE ECC WEB SITE XIII 1 INTRODUCTION 1
1.1 ERROR CORRECTING CODING: BASIC CONCEPTS 4 1.1.1 BLOCK CODES AND
CONVOLUTIONAL CODES . . . 4 1.1.2 HAMMING DISTANCE, HAMMING SPHERES AND
ERROR CORRECTING CAPABILITY 5 1.2 LINEAR BLOCK CODES 7 1.2.1 GENERATOR
AND PARITY-CHECK MATRICES 7 1.2.2 THE WEIGHT IS THE DISTANCE 8 1.3
ENCODING AND DECODING OF LINEAR BLOCK CODES 8 1.3.1 ENCODING WITH G AND
H 8 1.3.2 STANDARD ARRAY DECODING 10 1.3.3 HAMMING SPHERES, DECODING
REGIONS AND THE STANDARD ARRAY 12 1.4 WEIGHT DISTRIBUTION AND ERROR
PERFORMANCE 13 1.4.1 WEIGHT DISTRIBUTION AND UNDETECTED ERROR
PROBABILITY OVER A BSC . . 14 1.4.2 PERFORMANCE BOUNDS OVER BSC, AWGN
AND FADING CHANNELS .... 15 1.5 GENERAL STRUCTURE OF A HARD-DECISION
DECODER OF LINEAR CODES 23 PROBLEMS 23 2 HAMMING, GOLAY AND REED-MULLER
CODES 27 2.1 HAMMING CODES 27 2.1.1 ENCODING AND DECODING PROCEDURES 28
2.2 THE BINARY GOLAY CODE 29 2.2.1 ENCODING 29 2.2.2 DECODING 30 2.2.3
ARITHMETIC DECODING OF THE EXTENDED (24, 12, 8) GOLAY CODE .... 30 2.3
BINARY REED*MULLER CODES 31 2.3.1 BOOLEAN POLYNOMIALS AND RM CODES 31
2.3.2 FINITE GEOMETRIES AND MAJORITY-LOGIC DECODING 33 PROBLEMS 37 VI
CONTENTS 3 BINARY CYCLIC CODES AND BCH CODES 39 3.1 BINARY CYCLIC CODES
39 3.1.1 GENERATOR AND PARITY-CHECK POLYNOMIALS 39 3.1.2 THE GENERATOR
POLYNOMIAL 40 3.1.3 ENCODING AND DECODING OF BINARY CYCLIC CODES 41
3.1.4 THE PARITY-CHECK POLYNOMIAL 42 3.1.5 SHORTENED CYCLIC CODES AND
CRC CODES 44 3.1.6 FIRE CODES 45 3.2 GENERAL DECODING OF CYCLIC CODES 46
3.2.1 GF(2 M ) ARITHMETIC 48 3.3 BINARY BCH CODES : 52 3.3.1 BCH BOUND
53 3.4 POLYNOMIAL CODES 53 3.5 DECODING OF BINARY BCH CODES 54 3.5.1
GENERAL DECODING ALGORITHM FOR BCH CODES 56 3.5.2 THE BERLEKAMP-MASSEY
ALGORITHM (BMA) 57 3.5.3 PGZ DECODER 60 3.5.4 EUCLIDEAN ALGORITHM 61
3.5.5. CHIEN SEARCH AND ERROR CORRECTION 63 3.5.6 ERRORS-AND-ERASURES
DECODING 63 3.6 WEIGHT DISTRIBUTION AND PERFORMANCE BOUNDS 65 3.6.1
ERROR PERFORMANCE EVALUATION 66 PROBLEMS 69 4 NONBINARY BCH CODES:
REED-SOLOMON CODES 73 4.1 RS CODES AS POLYNOMIAL CODES 73 4.2 FROM
BINARY BCH TO RS CODES 73 4.3 DECODING RS CODES 74 4.3.1 REMARKS ON
DECODING ALGORITHMS 79 4.3.2 ERRORS-AND-ERASURES DECODING 79 4.4 WEIGHT
DISTRIBUTION 84 PROBLEMS 84 5 BINARY CONVOLUTIONAL CODES 87 5.1 BASIC
STRUCTURE 87 5.1.1 RECURSIVE SYSTEMATIC CONVOLUTIONAL CODES 92 5.1.2
FREE DISTANCE 94 5.2 CONNECTIONS WITH BLOCK CODES 94 5.2.1 ZERO-TAIL
CONSTRUCTION 94 5.2.2 DIRECT-TRUNCATION CONSTRUCTION 95 5.2.3
TAIL-BITING CONSTRUCTION 95 5.2.4 WEIGHT DISTRIBUTIONS 95 5.3 WEIGHT
ENUMERATION 97 5.4 PERFORMANCE BOUNDS 99 5.5 DECODING: VITERBI ALGORITHM
WITH HAMMING METRICS 101 5.5.1 MAXIMUM-LIKELIHOOD DECODING AND METRICS
101 CONTENTS VII 5.5.2 THE VITERBI ALGORITHM . . 102 5.5.3
IMPLEMENTATION ISSUES 104 5.6 PUNCTURED CONVOLUTIONAL CODES ., 112 5.6.1
IMPLEMENTATION ISSUES RELATED TO PUNCTURED CONVOLUTIONAL CODES . . . 115
5.6.2 RCPC CODES . 116 PROBLEMS 116 6 MODIFYING AND COMBINING CODES 119
6.1 MODIFYING CODES .. .:-.-, 119 6.1.1 SHORTENING 119 6.1.2 EXTENDING
121 6.1.3 PUNCTURING 122 6.1.4 AUGMENTING, EXPURGATING AND LENGTHENING
122 6.2 COMBINING CODES 124 6.2.1 TIME SHARING OF CODES . - 124 6.2.2
DIRECT SUMS OF CODES 125 6.2.3 THE U U + V -CONSTRUCTION AND RELATED
TECHNIQUES 126 6.2.4 PRODUCTS OF CODES 128 6.2.5 CONCATENATED CODES 134
6.2.6 GENERALIZED CONCATENATED CODES 136 PROBLEMS 140 7 SOFT-DECISION
DECODING 143 7.1 BINARY TRANSMISSION OVER AWGN CHANNELS 144 7.2 VITERBI
ALGORITHM WITH EUCLIDEAN METRIC 145 7.3 DECODING BINARY LINEAR BLOCK
CODES WITH A TRELLIS 146 7.4 THE CHASE ALGORITHM 150 7.5 ORDERED
STATISTICS DECODING 153 7.6 GENERALIZED MINIMUM DISTANCE DECODING 156
7.6.1 SUFFICIENT CONDITIONS FOR OPTIMALITY 157 7.7 LIST DECODING 158 7.8
SOFT-OUTPUT ALGORITHMS 158 7.8.1 SOFT-OUTPUT VITERBI ALGORITHM 158 7.8.2
MAXIMUM-A POSTERIORI (MAP) ALGORITHM 161 7.8.3 LOG-MAP ALGORITHM 163
7.8.4 MAX-LOG-MAP ALGORITHM 164 7.8.5 SOFT-OUTPUT OSD ALGORITHM 164
PROBLEMS 165 8 ITERATIVELY DECODABLE CODES 169 8.1 ITERATIVE DECODING
172 8.2 PRODUCT CODES 174 8.2.1 PARALLEL CONCATENATION: TURBO CODES 174
8.2.2 SERIAL CONCATENATION 183 8.2.3 BLOCK PRODUCT CODES 185 8.3
LOW-DENSITY PARITY-CHECK CODES . ; 190 8.3.1 TANNER GRAPHS 190 VIII
CONTENTS 8.3.2 ITERATIVE HARD-DECISION DECODING: THE BIT-FLIP ALGORITHM
192 8.3.3 ITERATIVE PROBABILISTIC DECODING: BELIEF PROPAGATION 196
PROBLEMS 201 9 COMBINING CODES AND DIGITAL MODULATION 203 9.1 MOTIVATION
203 9.1.1 EXAMPLES OF SIGNAL SETS 204 9.1.2 CODED MODULATION 206 9.1.3
DISTANCE CONSIDERATIONS 207 9.2 TRELLIS-CODED MODULATION (TCM) 208 9.2.1
SET PARTITIONING AND TRELLIS MAPPING 209 9.2.2 MAXIMUM-LIKELIHOOD
DECODING 211 9.2.3 DISTANCE CONSIDERATIONS AND ERROR PERFORMANCE 212
9.2.4 PRAGMATIC TCM AND TWO-STAGE DECODING 213 9.3 MULTILEVEL CODED
MODULATION 217 9.3.1 CONSTRUCTIONS AND MULTISTAGE DECODING 217 9.3.2
UNEQUAL ERROR PROTECTION WITH MCM 221 9.4 BIT-INTERLEAVED CODED
MODULATION 225 9.4.1 GRAY MAPPING 226 9.4.2 METRIC GENERATION:
DE-MAPPING 227 9.4.3 INTERLEAVING 227 9.5 TURBO TRELLIS-CODED MODULATION
. . 227 9.5.1 PRAGMATIC TURBO TCM 228 9.5.2 TURBO TCM WITH SYMBOL
INTERLEAVING 228 9.5.3 TURBO TCM WITH BIT INTERLEAVING 229 PROBLEMS 230
APPENDIX A WEIGHT DISTRIBUTIONS OF EXTENDED BCH CODES 233 A.I LENGTH 8
233 A.2 LENGTH 16 233 A.3 LENGTH 32 234 A.4 LENGTH 64 235 A.5 LENGTH 128
238 BIBLIOGRAPHY 247 INDEX 257
|
| adam_txt |
THE ART OF ERROR CORRECTING CODING SECOND EDITION ROBERT H.
MORELOS-ZARAGOZA SAN JOSE STATE UNIVERSITY, USA JOHN WILEY & SONS, LTD
CONTENTS PREFACE IX FOREWORD XI THE ECC WEB SITE XIII 1 INTRODUCTION 1
1.1 ERROR CORRECTING CODING: BASIC CONCEPTS 4 1.1.1 BLOCK CODES AND
CONVOLUTIONAL CODES . . . 4 1.1.2 HAMMING DISTANCE, HAMMING SPHERES AND
ERROR CORRECTING CAPABILITY 5 1.2 LINEAR BLOCK CODES 7 1.2.1 GENERATOR
AND PARITY-CHECK MATRICES 7 1.2.2 THE WEIGHT IS THE DISTANCE 8 1.3
ENCODING AND DECODING OF LINEAR BLOCK CODES 8 1.3.1 ENCODING WITH G AND
H 8 1.3.2 STANDARD ARRAY DECODING 10 1.3.3 HAMMING SPHERES, DECODING
REGIONS AND THE STANDARD ARRAY 12 1.4 WEIGHT DISTRIBUTION AND ERROR
PERFORMANCE 13 1.4.1 WEIGHT DISTRIBUTION AND UNDETECTED ERROR
PROBABILITY OVER A BSC . . 14 1.4.2 PERFORMANCE BOUNDS OVER BSC, AWGN
AND FADING CHANNELS . 15 1.5 GENERAL STRUCTURE OF A HARD-DECISION
DECODER OF LINEAR CODES 23 PROBLEMS 23 2 HAMMING, GOLAY AND REED-MULLER
CODES 27 2.1 HAMMING CODES 27 2.1.1 ENCODING AND DECODING PROCEDURES 28
2.2 THE BINARY GOLAY CODE 29 2.2.1 ENCODING 29 2.2.2 DECODING 30 2.2.3
ARITHMETIC DECODING OF THE EXTENDED (24, 12, 8) GOLAY CODE . 30 2.3
BINARY REED*MULLER CODES 31 2.3.1 BOOLEAN POLYNOMIALS AND RM CODES 31
2.3.2 FINITE GEOMETRIES AND MAJORITY-LOGIC DECODING 33 PROBLEMS 37 VI
CONTENTS 3 BINARY CYCLIC CODES AND BCH CODES 39 3.1 BINARY CYCLIC CODES
39 3.1.1 GENERATOR AND PARITY-CHECK POLYNOMIALS 39 3.1.2 THE GENERATOR
POLYNOMIAL 40 3.1.3 ENCODING AND DECODING OF BINARY CYCLIC CODES 41
3.1.4 THE PARITY-CHECK POLYNOMIAL 42 3.1.5 SHORTENED CYCLIC CODES AND
CRC CODES 44 3.1.6 FIRE CODES 45 3.2 GENERAL DECODING OF CYCLIC CODES 46
3.2.1 GF(2 M ) ARITHMETIC 48 3.3 BINARY BCH CODES : 52 3.3.1 BCH BOUND
53 3.4 POLYNOMIAL CODES 53 3.5 DECODING OF BINARY BCH CODES 54 3.5.1
GENERAL DECODING ALGORITHM FOR BCH CODES 56 3.5.2 THE BERLEKAMP-MASSEY
ALGORITHM (BMA) 57 3.5.3 PGZ DECODER 60 3.5.4 EUCLIDEAN ALGORITHM 61
3.5.5. CHIEN SEARCH AND ERROR CORRECTION 63 3.5.6 ERRORS-AND-ERASURES
DECODING 63 3.6 WEIGHT DISTRIBUTION AND PERFORMANCE BOUNDS 65 3.6.1
ERROR PERFORMANCE EVALUATION 66 PROBLEMS 69 4 NONBINARY BCH CODES:
REED-SOLOMON CODES 73 4.1 RS CODES AS POLYNOMIAL CODES 73 4.2 FROM
BINARY BCH TO RS CODES 73 4.3 DECODING RS CODES 74 4.3.1 REMARKS ON
DECODING ALGORITHMS 79 4.3.2 ERRORS-AND-ERASURES DECODING 79 4.4 WEIGHT
DISTRIBUTION 84 PROBLEMS 84 5 BINARY CONVOLUTIONAL CODES 87 5.1 BASIC
STRUCTURE 87 5.1.1 RECURSIVE SYSTEMATIC CONVOLUTIONAL CODES 92 5.1.2
FREE DISTANCE 94 5.2 CONNECTIONS WITH BLOCK CODES 94 5.2.1 ZERO-TAIL
CONSTRUCTION 94 5.2.2 DIRECT-TRUNCATION CONSTRUCTION 95 5.2.3
TAIL-BITING CONSTRUCTION 95 5.2.4 WEIGHT DISTRIBUTIONS 95 5.3 WEIGHT
ENUMERATION 97 5.4 PERFORMANCE BOUNDS 99 5.5 DECODING: VITERBI ALGORITHM
WITH HAMMING METRICS 101 5.5.1 MAXIMUM-LIKELIHOOD DECODING AND METRICS
101 CONTENTS " VII 5.5.2 THE VITERBI ALGORITHM . . 102 5.5.3
IMPLEMENTATION ISSUES 104 5.6 PUNCTURED CONVOLUTIONAL CODES ., 112 5.6.1
IMPLEMENTATION ISSUES RELATED TO PUNCTURED CONVOLUTIONAL CODES . . . 115
5.6.2 RCPC CODES . 116 PROBLEMS 116 6 MODIFYING AND COMBINING CODES 119
6.1 MODIFYING CODES .'.:-.-, 119 6.1.1 SHORTENING 119 6.1.2 EXTENDING
121 6.1.3 PUNCTURING 122 6.1.4 AUGMENTING, EXPURGATING AND LENGTHENING
122 6.2 COMBINING CODES 124 6.2.1 TIME SHARING OF CODES . - 124 6.2.2
DIRECT SUMS OF CODES 125 6.2.3 THE \U\U + V\ -CONSTRUCTION AND RELATED
TECHNIQUES 126 6.2.4 PRODUCTS OF CODES 128 6.2.5 CONCATENATED CODES 134
6.2.6 GENERALIZED CONCATENATED CODES 136 PROBLEMS 140 7 SOFT-DECISION
DECODING 143 7.1 BINARY TRANSMISSION OVER AWGN CHANNELS 144 7.2 VITERBI
ALGORITHM WITH EUCLIDEAN METRIC 145 7.3 DECODING BINARY LINEAR BLOCK
CODES WITH A TRELLIS 146 7.4 THE CHASE ALGORITHM 150 7.5 ORDERED
STATISTICS DECODING 153 7.6 GENERALIZED MINIMUM DISTANCE DECODING 156
7.6.1 SUFFICIENT CONDITIONS FOR OPTIMALITY 157 7.7 LIST DECODING 158 7.8
SOFT-OUTPUT ALGORITHMS 158 7.8.1 SOFT-OUTPUT VITERBI ALGORITHM 158 7.8.2
MAXIMUM-A POSTERIORI (MAP) ALGORITHM 161 7.8.3 LOG-MAP ALGORITHM 163
7.8.4 MAX-LOG-MAP ALGORITHM 164 7.8.5 SOFT-OUTPUT OSD ALGORITHM 164
PROBLEMS 165 8 ITERATIVELY DECODABLE CODES 169 8.1 ITERATIVE DECODING
172 8.2 PRODUCT CODES 174 8.2.1 PARALLEL CONCATENATION: TURBO CODES 174
8.2.2 SERIAL CONCATENATION 183 8.2.3 BLOCK PRODUCT CODES 185 8.3
LOW-DENSITY PARITY-CHECK CODES . ; 190 8.3.1 TANNER GRAPHS 190 VIII
CONTENTS 8.3.2 ITERATIVE HARD-DECISION DECODING: THE BIT-FLIP ALGORITHM
192 8.3.3 ITERATIVE PROBABILISTIC DECODING: BELIEF PROPAGATION 196
PROBLEMS 201 9 COMBINING CODES AND DIGITAL MODULATION 203 9.1 MOTIVATION
203 9.1.1 EXAMPLES OF SIGNAL SETS 204 9.1.2 CODED MODULATION 206 9.1.3
DISTANCE CONSIDERATIONS 207 9.2 TRELLIS-CODED MODULATION (TCM) 208 9.2.1
SET PARTITIONING AND TRELLIS MAPPING 209 9.2.2 MAXIMUM-LIKELIHOOD
DECODING 211 9.2.3 DISTANCE CONSIDERATIONS AND ERROR PERFORMANCE 212
9.2.4 PRAGMATIC TCM AND TWO-STAGE DECODING 213 9.3 MULTILEVEL CODED
MODULATION 217 9.3.1 CONSTRUCTIONS AND MULTISTAGE DECODING 217 9.3.2
UNEQUAL ERROR PROTECTION WITH MCM 221 9.4 BIT-INTERLEAVED CODED
MODULATION 225 9.4.1 GRAY MAPPING 226 9.4.2 METRIC GENERATION:
DE-MAPPING 227 9.4.3 INTERLEAVING 227 9.5 TURBO TRELLIS-CODED MODULATION
. . 227 9.5.1 PRAGMATIC TURBO TCM 228 9.5.2 TURBO TCM WITH SYMBOL
INTERLEAVING 228 9.5.3 TURBO TCM WITH BIT INTERLEAVING 229 PROBLEMS 230
APPENDIX A WEIGHT DISTRIBUTIONS OF EXTENDED BCH CODES 233 A.I LENGTH 8
233 A.2 LENGTH 16 233 A.3 LENGTH 32 234 A.4 LENGTH 64 235 A.5 LENGTH 128
238 BIBLIOGRAPHY 247 INDEX 257 |
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| index_date | 2024-07-02T16:28:54Z |
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| spelling | Morelos-Zaragoza, Robert H. Verfasser aut The art of error correcting coding Robert H. Morelos-Zaragoza 2. ed. Chichester [u.a.] Wiley 2006 X, 263 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computer algorithms Error-correcting codes (Information theory) Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015431395&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morelos-Zaragoza, Robert H. The art of error correcting coding Computer algorithms Error-correcting codes (Information theory) Fehlerkorrekturcode (DE-588)4124917-3 gnd |
| subject_GND | (DE-588)4124917-3 |
| title | The art of error correcting coding |
| title_auth | The art of error correcting coding |
| title_exact_search | The art of error correcting coding |
| title_exact_search_txtP | The art of error correcting coding |
| title_full | The art of error correcting coding Robert H. Morelos-Zaragoza |
| title_fullStr | The art of error correcting coding Robert H. Morelos-Zaragoza |
| title_full_unstemmed | The art of error correcting coding Robert H. Morelos-Zaragoza |
| title_short | The art of error correcting coding |
| title_sort | the art of error correcting coding |
| topic | Computer algorithms Error-correcting codes (Information theory) Fehlerkorrekturcode (DE-588)4124917-3 gnd |
| topic_facet | Computer algorithms Error-correcting codes (Information theory) Fehlerkorrekturcode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015431395&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT moreloszaragozaroberth theartoferrorcorrectingcoding |