Introduction to Information Theory and Data Compression, Second Edition
by Johnson, Jr.; Peter D.Edition: 2nd
Format: Hardcover
Pub. Date: 2003-02-26
Publisher(s): Chapman & Hall/
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Summary
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.
Table of Contents
| Part I: 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? | |
| 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 | |
| Part II: Data Compression | |
| LOSSLESS DATA COMPRESSION BY REPLACEMENT SCHEMES | |
| Replacement via Encoding Scheme | |
| Review of the Prefix Condition | |
| Choosing an Encoding Scheme | |
| The Noiseless Coding Theorem and Shannon's bound | |
| ARITHMETIC CODING | |
| Pure Zeroth-Order Arithmetic Coding: dfwld | |
| What's Good about dfwld Coding: The Compression Ratio | |
| What's Bad about dfwld Coding and Some Ways to Fix It | |
| 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 | |
| Maintaining the Tree in Adaptive Huffman Encoding: The Method of Knuth and Gallager | |
| Adaptive Arithmetic Coding | |
| Interval and Recency Rank Encoding | |
| DICTIONARY METHODS | |
| LZ77 (Sliding Window) Schemes | |
| The LZ78 Approach | |
| Notes | |
| TRANSFORM METHODS AND IMAGE COMPRESSION | |
| Transforms | |
| Periodic Signals and the Fourier Transform | |
| The Cosine and Sine Transforms | |
| Two-Dimensional Transforms | |
| An Application: JPEG Image Compression | |
| A Brief Introduction to Wavelets | |
| Notes | |
| APPENDICES | |
| JPEGtool User's Guide | |
| Source Listing for LZRW1-A | |
| Resources, Patents, And Illusions | |
| NOTES ON AND SOLUTIONS TO SOME EXERCISES | |
| BIBLIOGRAPHY | |
| INDEX |
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