The Theory of Information and Coding 2nd Edition by Robert Mceliece 9780521000956 0521000955

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ISBN 10: 0521000955
ISBN 13: 9780521000956
Author: Robert Mceliece 

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.

The Theory of Information and Coding 2nd Table of contents:

Part one Information theory
1 Entropy and mutual information

• Discrete random variables
• Discrete random vectors
• Nondiscrete random variables and vectors
• Problems
• Notes

2 Discrete memoryless channels and their capacity-cost functions

• The capacity-cost function
• The channel coding theorem
• Problems
• Notes

3 Discrete memoryless sources and their rate-distortion functions

• The rate-distortion function
• The source coding theorem
• Problems
• Notes

4 The Gaussian channel and source

• The Gaussian channel
• The Gaussian source
• Problems
• Notes

5 The source–channel coding theorem

• Problems
• Notes

6 Survey of advanced topics for Part one

• Introduction
• The channel coding theorem
• The source coding theorem

Part two Coding theory
7 Linear codes

• Introduction: The generator and parity-check matrices
• Syndrome decoding on q-ary symmetric channels
• Hamming geometry and code performance
• Hamming codes
• Syndrome decoding on general q-ary channels
• Weight enumerators and the MacWilliams identities
• Problems
• Notes

8 Cyclic codes

• Introduction
• Shift-register encoders for cyclic codes
• Cyclic Hamming codes
• Burst-error correction
• Decoding burst-error-correcting cyclic codes
• Problems
• Notes

9 BCH, Reed–Solomon, and related codes

• Introduction
• BCH codes as cyclic codes
• Decoding BCH codes, part one: the key equation
• Euclid’s algorithm for polynomials
• Decoding BCH codes, part two: the algorithms
• Reed–Solomon codes
• Decoding when erasures are present
• The (23, 12) Golay code
• Problems
• Notes

10 Convolutional codes

• Introduction
• State diagrams, trellises, and Viterbi decoding
• Path enumerators and error bounds
• Sequential decoding
• Problems
• Notes

11 Variable-length source coding

• Introduction
• Uniquely decodable variable-length codes
• Matching codes to sources
• The construction of optimal UD codes (Huffman’s algorithm)
• Problems
• Notes

12 Survey of advanced topics for Part two

• Introduction
• Block codes
• Convolutional codes
• A comparison of block and convolutional codes
• Source codes

Appendices

• Appendix A: Probability theory
• Appendix B: Convex functions and Jensen’s inequality
• Appendix C: Finite fields
• Appendix D: Path enumeration in directed graphs

References

• General reference textbooks
• An annotated bibliography of the theory of information and coding
• Original papers cited in the text

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