Information theory: a tutorial introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Erscheinungsort nicht ermittelbar]
Sebtel Press
2015
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | 243 Seiten Illustrationen, Diagramme |
| ISBN: | 9780956372857 9780993367953 |
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Record in the Search Index
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| adam_text | Titel: Information theory
Autor: Stone, James V
Jahr: 2015
Contents
Preface
1. What Is Information? 1
1.1. Introduction..................................................1
1.2. Information, Eyes and Evolution..........................2
1.3. Finding a Route, Bit by Bit................................3
1.4. A Million Answers to Twenty Questions..................8
1.5. Information, Bits and Binary Digits ......................10
1.6. Example 1: Telegraphy......................................11
1.7. Example 2: Binary Images................. 13
1.8. Example 3: Grey-Level Images.............. 15
1.9. Summary.......................... 20
2. Entropy of Discrete Variables 21
2.1. Introduction......................... 21
2.2. Ground Rules and Terminology.............. 21
2.3. Shannon s Desiderata ......................................31
2.4. Information, Surprise and Entropy........................31
2.5. Evaluating Entropy..........................................38
2.6. Properties of Entropy ......................................41
2.7. Independent and Identically Distributed Values..........43
2.8. Bits, Shannons, and Bans..................................43
2.9. Summary....................................................44
3. The Source Coding Theorem 45
3.1. Introduction..................................................45
3.2. Capacity of a Discrete Noiseless Channel..................46
3.3. Shannon s Source Coding Theorem........................49
3.4. Calculating Information Rates..............................50
3.5. Data Compression..........................................54
3.6. Huffman Coding............................................57
3.7. The Entropy of English Letters............................61
3.8. Why the Theorem is True..................................71
3.9. Kolmogorov Complexity....................................76
3.10. Summary....................................................78
4. The Noisy Channel Coding Theorem 79
4.1. Introduction..................................................79
4.2. Joint Distributions..........................................80
4.3. Mutual Information ........................................88
4.4. Conditional Entropy........................................92
4.5. Noise and Cross-Talk........................................95
4.6. Noisy Pictures and Coding Efficiency......................98
4.7. Error Correcting Codes ..................101
4.8. Capacity of a Noisy Channel...............104
4.9. Shannon s Noisy Channel Coding Theorem.......104
4.10. Why the Theorem is True.................109
4.11. Summary..........................110
5. Entropy of Continuous Variables 111
5.1. Introduction.........................Ill
5.2. The Trouble With Entropy ................112
5.3. Differential Entropy ....................115
5.4. Under-Estimating Entropy.................118
5.5. Properties of Differential Entropy.............119
5.6. Maximum Entropy Distributions.............121
5.7. Making Sense of Differential Entropy...........127
5.8. What is Half a Bit of Information : ............128
5.9. Summary..........................132
6. Mutual Information: Continuous 133
6.1. Introduction.........................133
6.2. Joint Distributions.....................135
6.3. Conditional Distributions and Entropy..........139
6.4. Mutual Information and Conditional Entropy......143
6.5. Mutual Information is Invariant..............147
6.6. Kullback-Leibler Divergence and Bayes .........148
6.7. Summary..........................150
7. Channel Capacity: Continuous 151
7.1. Introduction.........................151
7.2. Channel Capacity......................151
7.3. The Gaussian Channel...................152
7.4. Error Rates of Noisy Channels..............158
7.5. Using a Gaussian Channel.................160
7.6. Mutual Information and Correlation...........162
7.7. The Fixed Range Channel.................164
7.8. Summary..........................170
8. Thermodynamic Entropy and Information 171
8.1. Introduction.........................171
8.2. Physics, Entropy and Disorder ..............171
8.3. Information and Thermodynamic Entropy........174
8.4. Ensembles, Macrostates and Microstates.........176
8.5. Pricing Information: The Landauer Limit........177
8.6. The Second Law of Thermodynamics...........179
8.7. Maxwell s Demon......................180
8.8. Quantum Computation ..................183
8.9. Summary..........................184
9. Information As Nature s Currency 185
9.1. Introduction.........................185
9.2. Satellite TVs, MP3 and All That.............185
9.3. Does Sex Accelerate Evolution?..............188
9.4. The Human Genome: How Much Information?.....193
9.5. Enough DNA to Wire Up a Brain?............194
9.6. Are Brains Good at Processing Information? ......195
9.7. A Very Short History of Information Theory.......206
9.8. Summary..........................206
Further Reading 207
A. Glossary 209
B. Mathematical Symbols 217
C. Logarithms 221
D. Probability Density Functions 223
E. Averages From Distributions 227
F. The Rules of Probability 229
G. The Gaussian Distribution 233
H. Key Equations 235
Bibliography 237
Index 241
|
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| indexdate | 2024-07-10T07:22:02Z |
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| language | English |
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| spelling | Stone, James V. (DE-588)1082255777 aut Information theory a tutorial introduction James V Stone First edition [Erscheinungsort nicht ermittelbar] Sebtel Press 2015 243 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Informationstheorie (DE-588)4026927-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Informationstheorie (DE-588)4026927-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028696755&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stone, James V. Information theory a tutorial introduction Informationstheorie (DE-588)4026927-9 gnd |
| subject_GND | (DE-588)4026927-9 (DE-588)4151278-9 |
| title | Information theory a tutorial introduction |
| title_auth | Information theory a tutorial introduction |
| title_exact_search | Information theory a tutorial introduction |
| title_full | Information theory a tutorial introduction James V Stone |
| title_fullStr | Information theory a tutorial introduction James V Stone |
| title_full_unstemmed | Information theory a tutorial introduction James V Stone |
| title_short | Information theory |
| title_sort | information theory a tutorial introduction |
| title_sub | a tutorial introduction |
| topic | Informationstheorie (DE-588)4026927-9 gnd |
| topic_facet | Informationstheorie Einführung |
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