Fundamentals of Information Theory and Coding Design

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Introduces the principles and mathematics of information theory Emphasizes how a code is designed and strategies for selecting codes for specific applications Includes proofs and worked examples explaining all concepts, formulations, and design methodologies Offers basic and advanced exercises in each chapter Explores advanced topics such as PPM compression and turbo codes In a clear, concise, and modular format, this book introduces the fundamental concepts and mathematics of information and coding theory. The authors emphasize how a code is designed and discuss the main properties and characteristics of different coding algorithms along with strategies for selecting the appropriate codes to meet specific requirements. They provide comprehensive coverage of source and channel coding, address arithmetic, BCH, and Reed-Solomon codes and explore some more advanced topics such as PPM compression and turbo codes. Worked examples and sets of basic and advanced exercises in each chapter reinforce the text's clear explanations of all concepts and methodologies.

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Product Details

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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