Coding and information theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, N.J.
Prentice-Hall
1986
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 259 S. graph. Darst. |
| ISBN: | 0131390724 0131391399 |
Staff View
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| 245 | 1 | 0 | |a Coding and information theory |
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Record in the Search Index
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|---|---|
| adam_text | Second Edition
Coding
and
Information Theory
RICHARDWHAMMING
Naval Postgraduate School
PRENTICE-HALL / Englewood Cliffs NJ 07632
Contents
Preface
1 Introduction 1
11A Very Abstract Summary 1
1 2 History 2
1 3 Model of the Signaling System 4
1 4 Information Source 5
1 5 Encoding a Source Alphabet 7
1 6 Some Particular Codes 9
1 7 The ASCII Code 10
1 8 Some Other Codes 12
1 9 Radix r Codes 15
1 10 Escape Characters 15
1 11 Outline of the Course 17
2 Error-Detecting Codes 20
2 1 Why Error-Detecting Codes? 20
2 2 Simple Parity Checks 21
2 3 Error-Detecting Codes 22
2 4 Independent Errors: White Noise 23
2 5 Retransmission of Message 25
v
vi Contents
2 6 Simple Burst Error-Detecting Codes 26
2 7 Alphabet Plus Number Codes: Weighted Codes 27
2 8 Review of Modular Arithmetic 30
2 9 ISBN Book Numbers 32
3 Error-Correcting Codes 34
3 1 Need for Error Correction 34
3 2 Rectangular Codes 35
3 3 Triangular, Cubic, and n-Dimensional Codes 37
3 4 Hamming Error-Correcting Codes 39
3 5 Equivalent Codes 42
3 6 Geometric Approach 44
3 7 Single-Error-Correction Plus
Double-Error-Detection Codes 47
3 8 Hamming Codes Using Words 49
3 9 Applications of the Ideas 49
3 10 Summary 50
4 Variable-Length Codes: Huffman Codes 51
4 1 Introduction 51
4 2 Unique Decoding 52
4 3 Instantaneous Codes 53
4 4 Construction of Instantaneous Codes 55
4 5 The Kraft Inequality 57
4 6 Shortened Block Codes 60
4 7 The McMillan Inequality 62
4 8 Huffman Codes 63
4 9 Special Cases of Huffman Coding 68
4 10 Extensions of a Code 72
4 11 Huffman Codes Radix r 73
4 12 Noise in Huffman Coding Probabilities 74
4 13 Use of Huffman Codes 77
4 14 Hamming-Huffman Coding 78
5 Miscellaneous Codes 79
5 1 Introduction 79
5 2 What Is a Markov Process? 80
5 3 Ergodic Markov Processes 84
5 4 Efficient Coding of an Ergodic Markov Process
5 5 Extensions of a Markov Process 87
5 6 Predictive Run Encoding 88
5 7 The Predictive Encoder 89
5 8 The Decoder 90
5 9 Run Lengths 91
5 10 Summary of Predictive Encoding 94
5 11 What Is Hashing? 94
5 12 Handling Collisions 95
5 13 Removals from the Table 96
5 14 Summary of Hashing 96
5 15 Purpose of the Gray Code 97
5 16 Details of a Gray Code 98
5 17 Decoding the Gray Code 99
5 18 Anti-Gray Code 99
5 19 Delta Modulation 100
5 20 Other Codes 101
6 Entropy and Shannon s First Theorem 103
6 1 Introduction 103
6 2 Information 104
6 3 Entropy 107
6 4 Mathematical Properties of
the Entropy Function 114
6 5 Entropy and Coding 119
6 6 Shannon-Fano Coding 121
6 7 How Bad Is Shannon-Fano Coding? 122
6 8 Extensions of a Code 124
6 9 Examples of Extensions 126
6 10 Entropy of a Markov Process 129
6 11 Example of a Markov Process 131
6 12 The Adjoint System 133
6 13 The Robustness of Entropy 136
6 14 Summary 137
7 The Channel and Mutual Information 138
7 1 Introduction 138
7 2 The Information Channel 139
viii Contents
7 3 Channel Relationships 140
7 4 Example of the Binary
Symmetric Channel 142
7 5 System Entropies 145
7 6 Mutual Information 148
8 Channel Capacity 153
8 1 Definition of Channel Capacity 153
8 2 The Uniform Channel 154
8 3 Uniform Input 156
8 4 Error-Correcting Codes 158
8 5 Capacity of a Binary
Symmetric Channel 159
8 6 Conditional Mutual Information 161
9 Some Mathematical Preliminaries 164
9 1 Introduction 164
9 2 The Stirling Approximation to n 165
93A Binomial Bound 170
9 4 The Gamma Function T(/i) 173
9 5 n-Dimensional Euclidean Space 176
96A Paradox 179
9 7 Chebyshev s Inequality and the Variance 181
9 8 The Law of Large Numbers 183
9 9 Other Metrics 189
10 Shannon s Main Theorem 191
10 1 Introduction 191
10 2 Decision Rules 192
10 3 The Binary Symmetric Channel 195
10 4 Random Encoding 196
10 5 Average Random Code 201
10 6 The General Case 204
10 7 The Fano Bound 205
10 8 The Converse of Shannon s Theorem 207
11 Algebraic Coding Theory 209
11 1 Introduction 209
11 2 Error-Detecting Parity Codes Revisited 210
Contents ix
11 3 Hamming Codes Revisited 211
11 4 Double-Error-Detecting Codes Revisited 213
11 5 Polynomials versus Vectors 214
11 6 Prime Polynomials 215
11 7 Primitive Roots 219
11 8 A Special Case 220
11 9 Shift Registers for Encoding 224
11 10 Decoding Single-Error-Correcting Codes 227
11 11 A Double-Error-Correcting Code 228
11 12 Decoding Multiple-Error Codes 234
11 13 Summary 234
Appendix A: Bandwidth and the Sample Theorem 237
A l Introduction 237
A 2 The Fourier Integral 238
A 3 The Sampling Theorem 240
A 4 Bandwidth versus Rapid Change 242
A 5 AM Signaling 242
A 6 FM Signaling 244
A 7 Pulse Signaling 245
A 8 Bandwidth Generally 246
A 9 Continuous Signals 247
Appendix B: Some Tables for Entropy Calculations 250
References 253
Index 255
|
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| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Hamming, Richard W. 1915-1998 Verfasser (DE-588)131671863 aut Coding and information theory 2. ed. Englewood Cliffs, N.J. Prentice-Hall 1986 XII, 259 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Codage Information, Théorie de l' Information, Théorie de l' ram Signal, Théorie du (télécommunications) - Mathématiques ram Coding theory Information theory Codierung (DE-588)4070059-8 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Codierungstheorie (DE-588)4139405-7 s Informationstheorie (DE-588)4026927-9 s DE-604 Codierung (DE-588)4070059-8 s 1\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001501479&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 |
| spellingShingle | Hamming, Richard W. 1915-1998 Coding and information theory Codage Information, Théorie de l' Information, Théorie de l' ram Signal, Théorie du (télécommunications) - Mathématiques ram Coding theory Information theory Codierung (DE-588)4070059-8 gnd Codierungstheorie (DE-588)4139405-7 gnd Informationstheorie (DE-588)4026927-9 gnd |
| subject_GND | (DE-588)4070059-8 (DE-588)4139405-7 (DE-588)4026927-9 |
| title | Coding and information theory |
| title_auth | Coding and information theory |
| title_exact_search | Coding and information theory |
| title_full | Coding and information theory |
| title_fullStr | Coding and information theory |
| title_full_unstemmed | Coding and information theory |
| title_short | Coding and information theory |
| title_sort | coding and information theory |
| topic | Codage Information, Théorie de l' Information, Théorie de l' ram Signal, Théorie du (télécommunications) - Mathématiques ram Coding theory Information theory Codierung (DE-588)4070059-8 gnd Codierungstheorie (DE-588)4139405-7 gnd Informationstheorie (DE-588)4026927-9 gnd |
| topic_facet | Codage Information, Théorie de l' Signal, Théorie du (télécommunications) - Mathématiques Coding theory Information theory Codierung Codierungstheorie Informationstheorie |
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