Introduction to Information Theory and Data Compression

ISBN-10: 1584883138
ISBN-13: 9781584883135
Edition: 2nd 2003 (Revised)
List price: $132.95
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Description: This book provides a basic introduction to both information theory and data compression. Although the two topics are related, this unique treatment allows readers to explore either topic independently of the other. The authors' presentation of  More...

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Book details

List price: $132.95
Edition: 2nd
Copyright year: 2003
Publisher: CRC Press LLC
Publication date: 2/26/2003
Binding: Hardcover
Pages: 384
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.540
Language: English

This book provides a basic introduction to both information theory and data compression. Although the two topics are related, this unique treatment allows readers to explore either topic independently of the other. The authors' presentation of information theory is pitched at an elementary level, making the book less daunting than most other texts. The second edition includes a detailed history of information theory that provides a solid background for the quantification of the topic as developed by Claude Shannon. It also covers the information rate of a code and the trade-off between error correction and rate of information transmission, probabilistic finite state source automata, and wavelet methods.

Preface
Information Theory
Elementary Probability
Introduction
Events
Conditional probability
Independence
Bernoulli trials
An elementary counting principle
On drawing without replacement
Random variables and expected, or average, value
The Law of Large Numbers
Information and Entropy
How is information quantified?
Naming the units
Information connecting two events
The inevitability of Shannon's quantification of information
Systems of events and mutual information
Entropy
Information and entropy
Channels and Channel Capacity
Discrete memoryless channels
Transition probabilities and binary symmetric channels
Input frequencies
Channel capacity
Proof of Theorem 3.4.3, on the capacity equations
Coding Theory
Encoding and decoding
Prefix-condition codes and the Kraft-McMillan inequality
Average code word length and Huffman's algorithm
The validity of Huffman's algorithm
Optimizing the input frequencies
Error correction, maximum likelihood decoding, nearest code word decoding, and reliability
Shannon's Noisy Channel Theorem
Error correction with binary symmetric channels and equal source frequencies
The information rate of a code
Data Compression
Lossless Data Compression by Replacement Schemes
Replacement via encoding scheme
Review of the prefix condition
Choosing an encoding scheme
Shannon's method
Fano's method
Huffman's algorithm
The Noiseless Coding Theorem and Shannon's bound
Arithmetic Coding
Pure zeroth-order arithmetic coding: dfwld
Rescaling while encoding
Decoding
What's good about dfwld coding: the compression ratio
What's bad about dfwld coding and some ways to fix it
Supplying the source word length
Computation
Must decoding wait until encoding is completed?
Implementing arithmetic coding
Notes
Higher-order Modeling
Higher-order Huffman encoding
The Shannon bound for higher-order encoding
Higher-order arithmetic coding
Statistical models, statistics, and the possibly unknowable truth
Probabilistic finite state source automata
Adaptive Methods
Adaptive Huffman encoding
Compression and readjustment
Higher-order adaptive Huffman encoding
Maintaining the tree in adaptive Huffman encoding: the method of Knuth and Gallager
Gallager's method
Knuth's algorithm
Adaptive arithmetic coding
Interval and recency rank encoding
Interval encoding
Recency rank encoding
Dictionary Methods
LZ77 (sliding window) schemes
An LZ77 implementation
Case study: GNU zip
The LZ78 approach
The LZW variant
Case study: Unix compress
Notes
Transform Methods and Image Compression
Transforms
Periodic signals and the Fourier transform
The Fourier transform and compression: an example
The cosine and sine transforms
A general orthogonal transform
Summary
Two-dimensional transforms
The 2D Fourier, cosine, and sine transforms
Matrix expressions for 2D transforms
An application: JPEG image compression
A brief introduction to wavelets
2D Haar wavelets
Notes
Appendices
JPEGtool User's Guide
Using the tools
Reference
Obtaining Octave
Source Listing for LZRW1-A
Resources, Patents, and Illusions
Resources
Data compression and patents
Illusions
Notes on and Solutions to Some Exercises
Bibliography
Index

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