Introduction to Information Theory and Data Compression

Introduction to Information Theory and Data Compression

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An effective blend of carefully explained theory and practical applications, this text imparts the fundamentals of both information theory and data compression. Although the two topics are related, this unique text allows either topic to be presented independently, and it was specifically designed so that the data compression section requires no prior knowledge of information theory. The treatment of information theory, while theoretical and abstract, is quite elementary, making this text less daunting than many others. After presenting the fundamental definitions and results of the theory, the authors then apply the theory to memoryless, discrete channels with zeroth-order, one-state sources. The chapters on data compression acquaint students with a myriad of lossless compression methods and then introduce two lossy compression methods. Students emerge from this study competent in a wide range of techniques. The authors' presentation is highly practical but includes some important proofs, either in the text or in the exercises, so instructors can, if they choose, place more emphasis on the mathematics. Introduction to Information Theory and Data Compression, Second Edition is ideally suited for an upper-level or graduate course for students in mathematics, engineering, and computer science. Features: * Expanded discussion of the historical and theoretical basis of information theory that builds a firm, intuitive grasp of the subject * Reorganization of theoretical results along with new exercises, ranging from the routine to the more difficult, that reinforce students' ability to apply the definitions and results in specific situations. * Simplified treatment of the algorithm(s) of Gallager and Knuth * Discussion of the information rate of a code and the trade-off between error correction and information rate * Treatment of probabilistic finite state source automata, including basic results, examples, references, and exercises * Octave and MATLAB image compression codes included in an appendix for use with the exercises and projects involving transform methods * Supplementary materials, including software, available for download from the authors' Web site at www.dms.auburn.edu/compressionshow more

Product details

  • Hardback | 384 pages
  • 162.56 x 236.22 x 22.86mm | 680.39g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • United States
  • English
  • Revised
  • 2nd Revised edition
  • 31 black & white illustrations, 7 black & white tables
  • 1584883138
  • 9781584883135

Review quote

"Statisticians, applied mathematicians, engineers, and computer scientists will find this well-written book useful." -Journal of Statistical Computation and Simulationshow more

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 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 INDEXshow more

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