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Encyclopedia of Mathematics and its Applications : The Theory of Information and Coding Series Number 86 - Robert J. McEliece

Encyclopedia of Mathematics and its Applications

The Theory of Information and Coding Series Number 86


Published: 6th May 2002
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This is a revised edition of McEliece's classic. It is a self-contained introduction to all basic results in the theory of information and coding (invented by Claude Shannon in 1948). This theory was developed to deal with the fundamental problem of communication, that of reproducing at one point, either exactly or approximately, a message selected at another point. There is a short and elementary overview introducing the reader to the concept of coding. Then, following the main results, the channel and source coding theorems, there is a study of specific coding schemes which can be used for channel and source coding. This volume can be used either for self-study, or for a graduate/undergraduate level course at university. It includes dozens of worked examples and several hundred problems for solution. The exposition will be easily comprehensible to readers with some prior knowledge of probability and linear algebra.

'... [An] outstanding book ...'. Albert A. Mullin, Zentralblatt MATH

Editor's statementp. viii
Section editor's forewordp. ix
Preface to the first editionp. x
Preface to the second editionp. xii
Introductionp. 1
Problemsp. 12
Notesp. 13
Information theory
Entropy and mutual informationp. 17
Discrete random variablesp. 17
Discrete random vectorsp. 33
Nondiscrete random variables and vectorsp. 37
Problemsp. 44
Notesp. 49
Discrete memoryless channels and their capacity-cost functionsp. 50
The capacity-cost functionp. 50
The channel coding theoremp. 58
Problemsp. 68
Notesp. 73
Discrete memoryless sources and their rate-distortion functionsp. 75
The rate-distortion functionp. 75
The source coding theoremp. 84
Problemsp. 91
Notesp. 93
The Gaussian channel and sourcep. 95
The Gaussian channelp. 95
The Gaussian sourcep. 99
Problemsp. 105
Notesp. 110
The source-channel coding theoremp. 112
Problemsp. 120
Notesp. 122
Survey of advanced topics for part onep. 123
Introductionp. 123
The channel coding theoremp. 123
The source coding theoremp. 131
Coding theory
Linear codesp. 139
Introduction: The generator and parity-check matricesp. 139
Syndrome decoding on q-ary symmetric channelsp. 143
Hamming geometry and code performancep. 146
Hamming codesp. 148
Syndrome decoding on general q-ary channelsp. 149
Weight enumerators and the MacWilliams identitiesp. 153
Problemsp. 158
Notesp. 165
Cyclic codesp. 167
Introductionp. 167
Shift-register encoders for cyclic codesp. 181
Cyclic Hamming codesp. 195
Burst-error correctionp. 199
Decoding burst-error correcting cyclic codesp. 215
Problemsp. 220
Notesp. 228
BCH, Reed-Solomon, and related codesp. 230
Introductionp. 230
BCH codes as cyclic codesp. 234
Decoding BCH codes, Part one: the key equationp. 236
Euclid's algorithm for polynomialsp. 244
Decoding BCH codes, Part two: the algorithmsp. 249
Reed-Solomon codesp. 253
Decoding when erasures are presentp. 266
The (23,12) Golay codep. 277
Problemsp. 282
Notesp. 292
Convolutional codesp. 293
Introductionp. 293
State diagrams, trellises, and Viterbi decodingp. 300
Path enumerators and error boundsp. 307
Sequential decodingp. 313
Problemsp. 322
Notesp. 329
Variable-length source codingp. 330
Introductionp. 330
Uniquely decodable variable-length codesp. 331
Matching codes to sourcesp. 334
The construction of optimal UD codes (Huffman's algorithm)p. 337
Problemsp. 342
Notesp. 345
Survey of advanced topics for Part twop. 347
Introductionp. 347
Block codesp. 347
Convolutional codesp. 357
A comparison of block and convolutional codesp. 359
Source codesp. 363
Probability theoryp. 366
Convex functions and Jensen's inequalityp. 370
Finite fieldsp. 375
Path enumeration in directed graphsp. 380
General reference textbooksp. 384
An annotated bibliography of the theory of information and codingp. 384
Original papers cited in the textp. 386
Index of Theoremsp. 388
Indexp. 390
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521000956
ISBN-10: 0521000955
Series: Encyclopedia of Mathematics and Its Applications
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 410
Published: 6th May 2002
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.6 x 15.8  x 2.7
Weight (kg): 0.68
Edition Number: 2
Edition Type: Revised