Introduction to Information Theory and Data Compression, Second Edition

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
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