Fundamentals of Information Theory and Coding Design

Fundamentals of Information Theory and Coding Design

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Books on information theory and coding have proliferated over the last few years, but few succeed in covering the fundamentals without losing students in mathematical abstraction. Even fewer build the essential theoretical framework when presenting algorithms and implementation details of modern coding systems. Without abandoning the theoretical foundations, Fundamentals of Information Theory and Coding Design presents working algorithms and implementations that can be used to design and create real systems. The emphasis is on the underlying concepts governing information theory and the mathematical basis for modern coding systems, but the authors also provide the practical details of important codes like Reed-Solomon, BCH, and Turbo codes. Also setting this text apart are discussions on the cascading of information channels and the additivity of information, the details of arithmetic coding, and the connection between coding of extensions and Markov modelling. Complete, balanced coverage, an outstanding format, and a wealth of examples and exercises make this an outstanding text for upper-level students in computer science, mathematics, and engineering and a valuable reference for telecommunications engineers and coding theory researchers.show more

Product details

  • Hardback | 385 pages
  • 154 x 228 x 28mm | 780.19g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 72 black & white illustrations, 6 black & white tables
  • 1584883103
  • 9781584883104

Review quote

"This book is one of the few (if not the only) texts that comprehensively deal with both the fundamentals of information theory and coding theory. The extensive use of worked examples throughout the text, especially in the more theoretical chapters 6 and 7, will greatly aid students understanding of the principles and methods discussed. The highlighting of definitions, theorems and results allows students to quickly identify and remember the important concepts. The exercise sets at the end of each chapter are quite complete with the routine questions balanced by more challenging and interesting questions. The introduction to the main concepts of abstract algebra used for the design of advanced error detecting and error correcting codes is rigorous, complete and the use of many worked examples makes it one of the best I have seen. The material is also quite extensive with discussions on additivity of mutual information, implementation details of arithmetic coding, rate distortion theory and the important Hamming and Gilbert bounds for channel codes. Overall, this is an excellent and timely textbook for senior undergraduate courses in information and coding theory for students in computer science, mathematics, and engineering." -Li Deng, Ph.D., Senior Researcher, Microsoft Research, Redmond, WA, USAshow more

Table of contents

ENTROPY AND INFORMATION Structure 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 INFORMATION CHANNELS 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 SOURCE CODING Introduction 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 DATA COMPRESSION Introduction 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 FUNDAMENTALS OF CHANNEL CODING Introduction Code Rate Decoding Rules Hamming Distance Bounds on M, Maximal Codes and Perfect Codes Error Probabilities Shannon's Fundamental Coding Theorem ERROR-CORRECTING CODES Introduction Groups Rings and Fields Linear Spaces Linear Spaces over the Binary Field Linear Codes Encoding and Decoding Codes Derived from Hadamard Matrices CYCLIC CODES Introduction 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 BURST-CORRECTING CODES Introduction Finite Fields Irreducible Polynomials Construction of Finite Fields Bursts of Errors Fire Codes Minimum Polynomials Bose-Chaudhuri-Hocquenghem Codes Other Fields Reed-Solomon Codes CONVOLUTIONAL CODES Introduction ASimple Example Binary Convolutional Codes Decoding Convolutional Codes The Viterbi Algorithm Sequential Decoding Trellis Modulation Turbo Codes INDEX Each chapter also contains a section of exercises and a section of references.show more

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