Entropy and Information Theory:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New york [u.a.]
Springer
2011
|
| Ausgabe: | 2. ed. |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3540827&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020874959&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXVII, 409 S. 235 mm x 155 mm |
| ISBN: | 1441979697 9781441979698 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819253407362318336 |
|---|---|
| adam_text | Contents Preface................................................................................................... vii Introduction............................................................................................ xvii 1 Information Sources..................................................................... 1.1 Probability Spaces and Random Variables........................... 1.2 Random Processes and Dynamical Systems.......................... 1.3 Distributions.......................................................................... 1.4 Standard Alphabets................................................................ 1.5 Expectation............................................................................. 1.6 Asymptotic Mean Stationarity............................................... 1.7 Ergodic Properties.................................................................. 1 1 5 7 12 13 16 17 2 Pair Processes: Channels, Codes, and Couplings...................... 2.1 Pair Processes........................................................................ 2.2 Channels................................................................................. 2.3 Stationarity Properties of Channels ..................................... 2.4 Extremes: Noiseless and Completely Random Channels.... 2.5 Deterministic Channels and Sequence Coders.................... 2.6 Stationary and Sliding-Block Codes....................................... 2.7 Block Codes ............................................................................ 2.8 Random Punctuation Sequences
.......................................... 2.9 Memoryless Channels............................................................. 2.10 Finite-Memory Channels........................................................ 2.11 Output Mixing Channels........................................................ 2.12 Block Independent Channels................................................. 2.13 Conditionally Block Independent Channels......................... 2.14 Stationarizing Block Independent Channels........................ 2.15 Primitive Channels.................................................................. 2.16 Additive Noise Channels........................................................ 2.17 Markov Channels................................................................... 21 21 22 25 29 30 31 37 38 42 42 43 45 46 46 48 49 49 xiii
xiv Contents 2.18 Finite-State Channels and Codes.......................................... 2.19 Cascade Channels.................................................................. 2.20 Conununication Systems....................................................... 2.21 Couplings............................................................................... 2.22 Block to Sliding-Block: The Rohlin-Kakutani Theorem......... 3 Entropy.................................................................................................... 61 Entropy and Entropy Rate...................................................... Divergence Inequality and Relative Entropy...................... Basic Properties of Entropy................................................... Entropy Rate ......................................................................... Relative Entropy Rate........................................................... Conditional Entropy and Mutual Information...................... Entropy Rate Revisited................................................ ,........ Markov Approximations.............................................. Relative Entropy Densities.................................................... 61 65 69 78 81 82 90 91 93 The Entropy Ergodic Theorem......................................................... 97 97 100 106 110 114 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 5 50 51 52 52 53 History................................................................................... Stationary Ergodic Sources....................................................
Stationary Nonergodic Sources............................................. AMS Sources........................................................................... The Asymptotic Equipartition Property................................ Distortion and Approximation.......................................................... 117 5.1 Distortion Measures.............................................................. 117 5.2 Fidelity Criteria...................................................................... 120 5.3 Average Limiting Distortion.................................................. 121 5.4 Communications Systems Performance.............................. 123 5.5 Optimal Performance............................................................ 124 5.6 Code Approximation.............................................................. 124 5.7 Approximating Random Vectors and Processes ................ 129 5.8 The Monge/Kantorovich/Vasershtein Distance.................. 132 5.9 Variation and Distribution Distance.................................... 132 5.10 Coupling Discrete Spaces with the Hamming Distance....... 134 5.11 Process Distance and Approximation.................................... 135 5.12 Source Approximation and Codes......................................... 141 5.13 d-bar Continuous Channels.................................................. 142 6 Distortion and Entropy....................................................................... 147 6.1 6.2 6.3 6.4 6.5 6.6 The Fano Inequality................................................................ Code
Approximation and Entropy Rate............................... Pinsker’s and Marton’s Inequalities...................................... Entropy and Isomorphism................................................... Almost Lossless Source Coding........................................... Asymptotically Optimal Almost Lossless Codes................ 147 150 152 156 160 168
Contents XV 6.7 Modeling and Simulation ...................................................... 169 7 Relative Entropy........................................................................... 173 7.1 Divergence.............................................................................. 173 7.2 Conditional Relative Entropy................................................. 189 7.3 Limiting Entropy Densities...................................................... 202 7.4 Information for General Alphabets....................................... 204 7.5 Convergence Results.............................................................. 216 8 Information Rates........................................................................... 219 8.1 Information Rates for Finite Alphabets.................................. 219 8.2 Information Rates for General Alphabets............................... 221 8.3 A Mean Ergodic Theorem for Densities.................................. 225 8.4 Information Rates of Stationary Processes............................. 227 8.5 The Data Processing Theorem................................................. 234 8.6 Memoryless Channels and Sources......................................... 235 9 Distortion and Information.......................................................... 237 9.1 The Shannon Distortion-Rate Function.................................. 237 9.2 Basic Properties ....................................................................... 239 9.3 Process Definitions of the Distortion-Rate Function............ 242 9.4 The Distortion-Rate Function as a
Lower Bound................... 250 9.5 Evaluating the Rate-Distortion Function................................ 252 10 Relative Entropy Rates.................................................................. 265 10.1 Relative Entropy Densities and Rates..................................... 265 10.2 Markov Dominating Measures................................................. 268 10.3 Stationary Processes................................................................ 272 10.4 Mean Ergodic Theorems.......................................................... 275 11 Ergodic Theorems for Densities ................................................. 281 11.1 Stationary Ergodic Sources...................................................... 281 11.2 Stationary Nonergodic Sources................................................286 11.3 AMS Sources.............................................................................. 290 11.4 Ergodic Theorems for Information Densities.......................... 293 12 Source Coding Theorems............................................................. 295 12.1 Source Coding and Channel Coding....................................... 295 12.2 Block Source Codes for AMS Sources..................................... 296 12.3 Block Source Code Mismatch................................................... 307 12.4 Block Coding Stationary Sources............................................ 310 12.5 Block Coding AMS Ergodic Sources......................................... 312 12.6 Subadditive Fidelity Criteria................................................... 319
12.7 Asynchronous Block Codes.....................................................321 12.8 Sliding-Block Source Codes .....................................................323 12.9 A Geometric Interpretation.................................................... 333
xvi Contents 13 Properties of Good SourceCodes................................................ 335 13.1 Optimal and Asymptotically Optimal Codes.......................... 335 13.2 Block Codes............................................................................ 337 13.3 Sliding-Block Codes................................................................ 343 14 Coding for Noisy Channels ......................................................... 14.1 Noisy Channels...................................................................... 14.2 Feinstein s Lemma................................................................. 14.3 Feinstein’s Theorem.............................................................. 14.4 Channel Capacity................................................................... 14.5 Robust Block Codes................................................................ 14.6 Block Coding Theorems for Noisy Channels........................ 14.7 Joint Source and Channel Block Codes................................ 14.8 Synchronizing Block Channel Codes ................................... 14.9 Sliding-block Source and Channel Coding........................... 359 359 361 364 367 372 375 377 380 384 References............................................................................................ 395 Index........................................................................................................ 405
|
| any_adam_object | 1 |
| author | Gray, Robert M. 1943- |
| author_GND | (DE-588)134262336 |
| author_facet | Gray, Robert M. 1943- |
| author_role | aut |
| author_sort | Gray, Robert M. 1943- |
| author_variant | r m g rm rmg |
| building | Verbundindex |
| bvnumber | BV036960060 |
| classification_rvk | SK 880 |
| ctrlnum | (OCoLC)706971421 (DE-599)DNB1007151617 |
| discipline | Maschinenbau / Maschinenwesen Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV036960060 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T14:45:26Z |
| institution | BVB |
| isbn | 1441979697 9781441979698 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020874959 |
| oclc_num | 706971421 |
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| owner | DE-473 DE-BY-UBG DE-739 |
| owner_facet | DE-473 DE-BY-UBG DE-739 |
| physical | XXVII, 409 S. 235 mm x 155 mm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| spellingShingle | Gray, Robert M. 1943- Entropy and Information Theory Informationstheorie (DE-588)4026927-9 gnd Entropie (DE-588)4014894-4 gnd Codierungstheorie (DE-588)4139405-7 gnd Information (DE-588)4026899-8 gnd Entropie Informationstheorie (DE-588)4743861-7 gnd |
| subject_GND | (DE-588)4026927-9 (DE-588)4014894-4 (DE-588)4139405-7 (DE-588)4026899-8 (DE-588)4743861-7 |
| title | Entropy and Information Theory |
| title_auth | Entropy and Information Theory |
| title_exact_search | Entropy and Information Theory |
| title_full | Entropy and Information Theory Robert M. Gray |
| title_fullStr | Entropy and Information Theory Robert M. Gray |
| title_full_unstemmed | Entropy and Information Theory Robert M. Gray |
| title_short | Entropy and Information Theory |
| title_sort | entropy and information theory |
| topic | Informationstheorie (DE-588)4026927-9 gnd Entropie (DE-588)4014894-4 gnd Codierungstheorie (DE-588)4139405-7 gnd Information (DE-588)4026899-8 gnd Entropie Informationstheorie (DE-588)4743861-7 gnd |
| topic_facet | Informationstheorie Entropie Codierungstheorie Information Entropie Informationstheorie |
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