The theory of information and coding:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
2002
|
| Edition: | 2. ed. |
| Series: | Encyclopedia of mathematics and its applications
86 |
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 397 S. graph. Darst. |
| ISBN: | 0521000955 9780521000956 |
Staff View
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Record in the Search Index
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Titel: The theory of information and coding
Autor: McEliece, Robert J
Jahr: 2002
Contents Editor s statement page viii Section editor’s foreword ix Preface to the first edition x Preface to the second edition xii Introduction 1 Problems 12 Notes 13 Part one: Information theory 1 Entropy and mutual information 17 1.1 Discrete random variables 17 1.2 Discrete random vectors 33 1.3 Nondiscrete random variables and vectors 37 Problems 44 Notes 49 2 Discrete memoryless channels and their capacity-cost functions 50 2.1 The capacity-cost function 50 2.2 The channel coding theorem 58 Problems 68 Notes 73 3 Discrete memoryless sources and their rate-distortion functions 75 3.1 The rate-distortion function 75 3.2 The source coding theorem 84 Problems 91 Notes 93 v
Contents vi 4 The Gaussian channel and source 95 4.1 The Gaussian channel 95 4.2 The Gaussian source 99 Problems 105 Notes 110 5 The source-channel coding theorem 112 Problems 120 Notes 122 6 Survey of advanced topics for part one 123 6.1 Introduction 123 6.2 The channel coding theorem 123 6.3 The source coding theorem 131 Part two: Coding theory 7 Linear codes 139 7.1 Introduction: The generator and parity-check matrices 139 7.2 Syndrome decoding on g-ary symmetric channels 143 7.3 Hamming geometry and code performance 146 7.4 Hamming codes 148 7.5 Syndrome decoding on general g-ary channels 149 7.6 Weight enumerators and the MacWilliams identities 153 Problems 158 Notes 165 8 Cyclic codes 167 8.1 Introduction 167 8.2 Shift-register encoders for cyclic codes 181 8.3 Cyclic Hamming codes 195 8.4 Burst-error correction 199 8.5 Decoding burst-error correcting cyclic codes 215 Problems 220 Notes 228 9 BCH, Reed-Solomon, and related codes 230 9.1 Introduction 230 9.2 BCH codes as cyclic codes 234 9.3 Decoding BCH codes, Part one: the key equation 236 9.4 Euclid’s algorithm for polynomials 244 9.5 Decoding BCH codes, Part two: the algorithms 249 9.6 Reed-Solomon codes 253 9.7 Decoding when erasures are present 266
Preface vii 9.8 The (23,12) Golay code 277 Problems 282 Notes 292 10 Convolutional codes 293 10.1 Introduction 293 10.2 State diagrams, trellises, and Viterbi decoding 300 10.3 Path enumerators and error bounds 307 10.4 Sequential decoding 313 Problems 322 Notes 329 11 Variable-length source coding 330 11.1 Introduction 330 11.2 Uniquely decodable variable-length codes 331 11.3 Matching codes to sources 334 11.4 The construction of optimal UD codes (Huffman’s algorithm) 337 Problems 342 Notes 345 12 Survey of advanced topics for Part two 347 12.1 Introduction 347 12.2 Block codes 347 12.3 Convolutional codes 357 12.4 A comparison of block and convolutional codes 359 12.5 Source codes 363 Appendices A Probability theory 366 B Convex functions and Jensen’s inequality 370 C Finite fields 375 D Path enumeration in directed graphs 380 References 1 General reference textbooks 384 2 An annotated bibliography of the theory of information and coding 384 3 Original papers cited in the text 386 Index of Theorems 388 Index 390 |
| any_adam_object | 1 |
| author | McEliece, Robert J. 1942-2019 |
| author_GND | (DE-588)1047958058 |
| author_facet | McEliece, Robert J. 1942-2019 |
| author_role | aut |
| author_sort | McEliece, Robert J. 1942-2019 |
| author_variant | r j m rj rjm |
| building | Verbundindex |
| bvnumber | BV014649952 |
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| ctrlnum | (OCoLC)248331386 (DE-599)BVBBV014649952 |
| dewey-full | 003.54 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.54 |
| dewey-search | 003.54 |
| dewey-sort | 13.54 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | McEliece, Robert J. 1942-2019 Verfasser (DE-588)1047958058 aut The theory of information and coding R. J. McEliece 2. ed. Cambridge [u.a.] Cambridge University Press 2002 XII, 397 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 86 Hier auch später erschienene, unveränderte Nachdrucke Codierungstheorie Informationstheorie Teoria dell'informazione sbt Codierung (DE-588)4070059-8 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Information (DE-588)4026899-8 gnd rswk-swf Informationstheorie (DE-588)4026927-9 s Codierungstheorie (DE-588)4139405-7 s 1\p DE-604 Codierung (DE-588)4070059-8 s 2\p DE-604 Information (DE-588)4026899-8 s 3\p DE-604 Encyclopedia of mathematics and its applications 86 (DE-604)BV000903719 86 http://www.loc.gov/catdir/toc/cam027/2001035051.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009945050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McEliece, Robert J. 1942-2019 The theory of information and coding Encyclopedia of mathematics and its applications Codierungstheorie Informationstheorie Teoria dell'informazione sbt Codierung (DE-588)4070059-8 gnd Informationstheorie (DE-588)4026927-9 gnd Codierungstheorie (DE-588)4139405-7 gnd Information (DE-588)4026899-8 gnd |
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| title | The theory of information and coding |
| title_auth | The theory of information and coding |
| title_exact_search | The theory of information and coding |
| title_full | The theory of information and coding R. J. McEliece |
| title_fullStr | The theory of information and coding R. J. McEliece |
| title_full_unstemmed | The theory of information and coding R. J. McEliece |
| title_short | The theory of information and coding |
| title_sort | the theory of information and coding |
| topic | Codierungstheorie Informationstheorie Teoria dell'informazione sbt Codierung (DE-588)4070059-8 gnd Informationstheorie (DE-588)4026927-9 gnd Codierungstheorie (DE-588)4139405-7 gnd Information (DE-588)4026899-8 gnd |
| topic_facet | Codierungstheorie Informationstheorie Teoria dell'informazione Codierung Information |
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