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The theory of information and coding

Author: Robert J McEliece
Publisher: Cambridge ; New York : Cambridge University Press, 2002.
Series: Encyclopedia of mathematics and its applications, v. 86.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

This is a self-contained introduction to the basics of the theory of information and coding.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Robert J McEliece
ISBN: 0521000955 9780521000956
OCLC Number: 46785392
Description: xii, 397 pages : illustrations ; 24 cm.
Contents: Part 1 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 --
2 Discrete memoryless channels and their capacity-cost functions 50 --
2.1 The capacity-cost function 50 --
2.2 The channel coding theorem 58 --
3 Discrete memoryless sources and their rate-distortion functions 75 --
3.1 The rate-distortion function 75 --
3.2 The source coding theorem 84 --
4 The Gaussian channel and source 95 --
4.1 The Gaussian channel 95 --
4.2 The Gaussian source 99 --
5 The source-channel coding theorem 112 --
6 Survey of advanced topics for part one 123 --
6.2 The channel coding theorem 123 --
6.3 The source coding theorem 131 --
Part 2 Coding theory --
7 Linear codes 139 --
7.1 Introduction: The generator and parity-check matrices 139 --
7.2 Syndrome decoding on q-ary symmetric channels 143 --
7.3 Hamming geometry and code performance 146 --
7.4 Hamming codes 148 --
7.5 Syndrome decoding on general q-ary channels 149 --
7.6 Weight enumerators and the MacWilliams identities 153 --
8 Cyclic codes 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 --
9 BCH, Reed-Solomon, and related codes 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 --
9.8 The (23,12) Golay code 277 --
10 Convolutional codes 293 --
10.2 State diagrams, trellises, and Viterbi decoding 300 --
10.3 Path enumerators and error bounds 307 --
10.4 Sequential decoding 313 --
11 Variable-length source coding 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 --
12 Survey of advanced topics for Part two 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 --
A Probability theory 366 --
B Convex functions and Jensen's inequality 370 --
C Finite fields 375 --
D Path enumeration in directed graphs 380 --
1 General reference textbooks 384 --
2 An annotated bibliography of the theory of information and coding 384.
Series Title: Encyclopedia of mathematics and its applications, v. 86.
Responsibility: R.J. McEliece.
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'... [An] outstanding book ...'. Albert A. Mullin, Zentralblatt MATH

 
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