1st Edition

Fundamentals of Information Theory and Coding Design

ISBN 9781584883104
Published January 13, 2003 by Chapman and Hall/CRC
398 Pages 72 B/W Illustrations

USD $150.00

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Book Description

Books on information theory and coding have proliferated over the last few years, but few succeed in covering the fundamentals without losing students in mathematical abstraction. Even fewer build the essential theoretical framework when presenting algorithms and implementation details of modern coding systems.

Without abandoning the theoretical foundations, Fundamentals of Information Theory and Coding Design presents working algorithms and implementations that can be used to design and create real systems. The emphasis is on the underlying concepts governing information theory and the mathematical basis for modern coding systems, but the authors also provide the practical details of important codes like Reed-Solomon, BCH, and Turbo codes. Also setting this text apart are discussions on the cascading of information channels and the additivity of information, the details of arithmetic coding, and the connection between coding of extensions and Markov modelling.

Complete, balanced coverage, an outstanding format, and a wealth of examples and exercises make this an outstanding text for upper-level students in computer science, mathematics, and engineering and a valuable reference for telecommunications engineers and coding theory researchers.

Table of Contents

Structure in Randomness
First Concepts of Probability Theory
Surprise and Entropy
Units of Entropy
The Minimum and Maximum Values of Entropy
A Useful Inequality
Joint Probability Distribution Functions
Conditional Probability and Bayes' Theorem
Conditional Probability Distributions and Conditional Entropy
Information Sources
Memoryless Information Sources
Markov Sources and n-Gram Models
Stationary Distributions
The Entropy of Markov Sources
Sequences of Symbols
The Adjoint Source of a Markov Source
Extensions of Sources
Infinite Sample Spaces
What Are Information Channels?
BSC and BEC Channels
Mutual Information
Noiseless and Deterministic Channels
Cascaded Channels
Additivity of Mutual Information
Channel Capacity: Maximum Mutual Information
Continuous Channels and Gaussian Channels
Information Capacity Theorem
Rate Distortion Theory
Instantaneous Codes
The Kraft Inequality and McMillan's Theorem
Average Length and Compact Codes
Shannon's Noiseless Coding Theorem
Fano Coding
Huffman Coding
Arithmetic Coding
Higher-Order Modelling
Basic Concepts of Data Compression
Run-Length Coding
The CCITT Standard for Facsimile Transmission
Block-sorting Compression
Dictionary Coding
Statistical Compression
Prediction by Partial Matching
Image Coding
Code Rate
Decoding Rules
Hamming Distance
Bounds on M, Maximal Codes and Perfect Codes
Error Probabilities
Shannon's Fundamental Coding Theorem
Rings and Fields
Linear Spaces
Linear Spaces over the Binary Field
Linear Codes
Encoding and Decoding
Codes Derived from Hadamard Matrices
Rings of Polynomials
Cyclic Codes
Encoding and Decoding of Cyclic Codes
Encoding and Decoding Circuits for Cyclic Codes
The Golay Code
Hamming Codes
Cyclic Redundancy Check Codes
Reed-Muller Codes
Finite Fields
Irreducible Polynomials
Construction of Finite Fields
Bursts of Errors
Fire Codes
Minimum Polynomials
Bose-Chaudhuri-Hocquenghem Codes
Other Fields
Reed-Solomon Codes
ASimple Example
Binary Convolutional Codes
Decoding Convolutional Codes
The Viterbi Algorithm
Sequential Decoding
Trellis Modulation
Turbo Codes

Each chapter also contains a section of exercises and a section of references.

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"This book is one of the few (if not the only) texts that comprehensively deal with both the fundamentals of information theory and coding theory. The extensive use of worked examples throughout the text, especially in the more theoretical chapters 6 and 7, will greatly aid students understanding of the principles and methods discussed. The highlighting of definitions, theorems and results allows students to quickly identify and remember the important concepts. The exercise sets at the end of each chapter are quite complete with the routine questions balanced by more challenging and interesting questions. The introduction to the main concepts of abstract algebra used for the design of advanced error detecting and error correcting codes is rigorous, complete and the use of many worked examples makes it one of the best I have seen. The material is also quite extensive with discussions on additivity of mutual information, implementation details of arithmetic coding, rate distortion theory and the important Hamming and Gilbert bounds for channel codes. Overall, this is an excellent and timely textbook for senior undergraduate courses in information and coding theory for students in computer science, mathematics, and engineering."

-Li Deng, Ph.D., Senior Researcher, Microsoft Research, Redmond, WA, USA