A course in error correcting codes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
2004
|
| Series: | EMS textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 194 S. |
| ISBN: | 3037190019 |
Staff View
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Record in the Search Index
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| adam_text | J0RN JUSTESEN TOM H0HOLDT A COURSE IN ERROR CORRECTING CODES EUROPEAN
^MATHEMATICAL VJBCIETY CONTENTS PREFACE IX 1 BLOCK CODES FOR
ERROR-CORRECTION 1.1 LINEAR CODES AND VECTOR SPACES 1 1.2 MINIMUM
DISTANCE AND MINIMUM WEIGHT 4 1.3 SYNDROME DECODING AND THE HAMMING
BOUND 8 1.4 WEIGHT DISTRIBUTIONS 11 1.5 PROBLEMS 13 2 FINITE FIELDS 2.1
FUNDAMENTAL PROPERTIES OF FINITE FIELDS 19 2.2 THE FINITE FIELD 2 - 22
2.3 MINIMAL POLYNOMIALS AND FACTORIZATION OF X * 1 25 2.4 PROBLEMS 29 3
BOUNDS ON ERROR PROBABILITY FOR ERROR-CORRECTING CODES 3.1 SOME
PROBABILITY DISTRIBUTIONS 33 3.2 THE PROBABILITY OF FAILURE AND ERROR
FOR BOUNDED DISTANCE DECODING . . 34 3.3 BOUNDS FOR MAXIMUM LIKELIHOOD
DECODING OF BINARY BLOCK CODES ... 37 3.4 PROBLEMS 39 4 COMMUNICATION
CHANNELS AND INFORMATION THEORY 4.1 DISCRETE MESSAGES AND ENTROPY 41 4.2
MUTUAL INFORMATION AND CAPACITY OF DISCRETE CHANNELS 42 4.2.1 DISCRETE
MEMORYLESS CHANNELS 42 4.2.2 CODES AND CHANNEL CAPACITY 45 4.3 PROBLEMS
47 5 REED-SOLOMON CODES AND THEIR DECODING 5.1 BASIC DEFINITIONS 49 5.2
DECODING REED-SOLOMON CODES 51 5.3 VANDERMONDE MATRICES 53 5.4 ANOTHER
DECODING ALGORITHM 57 5.5 PROBLEMS 61 VI CONTENTS 6 CYCLIC CODES 6.1
INTRODUCTION TO CYCLIC CODES 63 6.2 GENERATOR-AND PARITY CHECK MATRICES
OF CYCLIC CODES 65 6.3 A THEOREM ON THE MINIMUM DISTANCE OF CYCLIC CODES
66 6.4 CYCLIC REED-SOLOMON CODES AND BCH-CODES 67 6.4.1 CYCLIC
REED-SOLOMON CODES 68 6.4.2 BCH-CODES 68 6.5 PROBLEMS 70 7 FRAMES 7.1
DEFINITIONS OF FRAMES AND THEIR EFFICIENCY 73 7.2 FRAME QUALITY 76 7.2.1
MEASURES OF QUALITY 76 7.2.2 PARITY CHECKS ON FRAMES 76 7.3 ERROR
DETECTION AND ERROR CORRECTION 77 7.3.1 SHORT BLOCK CODES 77 7.3.2
CONVOLUTIONAL CODES 79 7.3.3 REED-SOLOMON CODES 79 7.3.4 LOW DENSITY
CODES AND TURBO CODES 80 7.4 PROBLEMS 80 8 CONVOLUTIONAL CODES 8.1
PARAMETERS OF CONVOLUTIONAL CODES 83 8.2 TAIL-BITING CODES 86 8.3 PARITY
CHECKS AND DUAL CODES 87 8.4 DISTANCES OF CONVOLUTIONAL CODES 89 8.5
PUNCTURED CODES 90 8.6 LINEAR SYSTEMS AS ENCODERS 91 8.7 UNIT MEMORY
CODES 93 8.8 PROBLEMS 95 9 MAXIMUM LIKELIHOOD DECODING OF CONVOLUTIONAL
CODES 9.1 FINITE STATE DESCRIPTIONS OF CONVOLUTIONAL CODES 97 9.2
MAXIMUM LIKELIHOOD DECODING 102 9.3 PROBLEMS 106 10 COMBINATIONS OF
SEVERAL CODES 10.1 PRODUCT CODES 109 10.2 CONCATENATED CODES (SERIAL
ENCODING) 112 10.2.1 PARAMETERS OF CONCATENATED CODES 112 10.2.2
PERFORMANCE OF CONCATENATED CODES 113 10.2.3 INTERLEAVING AND INNER
CONVOLUTIONAL CODES 114 10.3 PROBLEMS 116 11 DECODING REED-SOLOMON AND
BCH-CODES WITH THE EUCLIDIAN ALGORITHM 11.1 THE EUCLIDIAN ALGORITHM 119
CONTENTS VII 11.2 DECODING REED-SOLOMON AND BCH CODES 121 11.3 PROBLEMS
125 12 LIST DECODING OF REED-SOLOMON CODES 12.1 A LIST DECODING
ALGORITHM 127 12.2 AN EXTENDED LIST DECODING ALGORITHM 130 12.3
FACTORIZATION OF Q(X,Y) 132 12.4 PROBLEMS 135 13 ITERATIVE DECODING 13.1
LOW DENSITY PARITY CHECK CODES 137 13.2 ITERATIVE DECODING OF LDPC CODES
138 13.3 DECODING PRODUCT CODES 143 13.4 PARALLEL CONCATENATION OF
CONVOLUTIONAL CODES ( TURBO CODES ) 145 13.5 PROBLEMS 149 14 ALGEBRAIC
GEOMETRY CODES 14.1 HERMITIAN CODES 151 14.2 DECODING HERMITIAN CODES
155 14.3 PROBLEMS 157 A COMMUNICATION CHANNELS A.I GAUSSIAN CHANNELS 159
A.2 GAUSSIAN CHANNELS WITH QUANTIZED INPUT AND OUTPUT 160 A.3 ML
DECODING 161 B SOLUTIONS TO SELECTED PROBLEMS B.I SOLUTIONS TO PROBLEMS
IN CHAPTER 1 163 B.2 SOLUTIONS TO PROBLEMS IN CHAPTER 2 166 B.3
SOLUTIONS TO PROBLEMS IN CHAPTER 3 168 B.4 SOLUTIONS TO PROBLEMS IN
CHAPTER 4 169 B.5 SOLUTIONS TO PROBLEMS IN CHAPTER 5 170 B.6 SOLUTIONS
TO PROBLEMS IN CHAPTER 6 171 B.7 SOLUTIONS TO PROBLEMS IN CHAPTER 7 173
B.8 SOLUTIONS TO PROBLEMS IN CHAPTER 8 173 B.9 SOLUTIONS TO PROBLEMS IN
CHAPTER 9 175 B.10 SOLUTIONS TO PROBLEMS IN CHAPTER 10 176 B.LL
SOLUTIONS TO PROBLEMS IN CHAPTER 11 178 B.12 SOLUTIONS TO PROBLEMS IN
CHAPTER 12 180 B.13 SOLUTIONS TO PROBLEMS IN CHAPTER 13 182 B.14
SOLUTIONS TO PROBLEMS IN CHAPTER 14 182 C TABLE OF MINIMAL POLYNOMIALS
185 BIBLIOGRAPHY 187 INDEX 191
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| any_adam_object | 1 |
| author | Justesen, Jørn 1944-2019 Høholdt, Tom |
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| author_sort | Justesen, Jørn 1944-2019 |
| author_variant | j j jj t h th |
| building | Verbundindex |
| bvnumber | BV017873237 |
| classification_rvk | SK 170 SK 880 ST 273 ST 276 |
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| ctrlnum | (OCoLC)249316760 (DE-599)BVBBV017873237 |
| discipline | Informatik Mathematik |
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| physical | VII, 194 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
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| publisher | European Mathematical Society |
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| spelling | Justesen, Jørn 1944-2019 Verfasser (DE-588)128905042 aut A course in error correcting codes Jørn Justesen ; Tom Høholdt A course in error-correcting codes Zürich European Mathematical Society 2004 VII, 194 S. txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Fehlerkorrekturcode Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 s DE-604 Høholdt, Tom Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010723282&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Justesen, Jørn 1944-2019 Høholdt, Tom A course in error correcting codes Fehlerkorrekturcode Fehlerkorrekturcode (DE-588)4124917-3 gnd |
| subject_GND | (DE-588)4124917-3 |
| title | A course in error correcting codes |
| title_alt | A course in error-correcting codes |
| title_auth | A course in error correcting codes |
| title_exact_search | A course in error correcting codes |
| title_full | A course in error correcting codes Jørn Justesen ; Tom Høholdt |
| title_fullStr | A course in error correcting codes Jørn Justesen ; Tom Høholdt |
| title_full_unstemmed | A course in error correcting codes Jørn Justesen ; Tom Høholdt |
| title_short | A course in error correcting codes |
| title_sort | a course in error correcting codes |
| topic | Fehlerkorrekturcode Fehlerkorrekturcode (DE-588)4124917-3 gnd |
| topic_facet | Fehlerkorrekturcode |
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