Information and Coding Theory

Name: Information and Coding Theory
Availability: InStock
ISBN: 9781852336226

ISBN-10: 1852336226

ISBN-13: 9781852336226

Edition: 2000

Authors: Gareth A. Jones, J. Mary Jones

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Description:

This book provides an elementary introduction to Information Theory and Coding Theory - two related aspects of the problem of how to transmit information efficiently and accurately. The first part of the book focuses on Information Theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon's Fundamental Theorem. In the second part, on Coding Theory, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes.The book emphasises carefully explained proofs and worked examples; exercises (with solutions) are integrated into the text as part of the learning process. Only some…

Book details

List price: $49.99
Copyright year: 2000
Publisher: Springer London, Limited
Publication date: 6/26/2000
Binding: Paperback
Pages: 210
Size: 6.10" wide x 9.25" long x 0.24" tall
Weight: 0.836
Language: English



Preface


Notes to the Reader



Source Coding



Definitions and Examples



Uniquely Decodable Codes



Instantaneous Codes



Constructing Instantaneous Codes



Kraft's Inequality



McMillan's Inequality



Comments on Kraft's and McMillan's Inequalities



Supplementary Exercises



Optimal Codes



Optimality



Binary Huffman Codes



Average Word-length of Huffman Codes



Optimality of Binary Huffman Codes



r-ary Huffman Codes



Extensions of Sources



Supplementary Exercises



Entropy



Information and Entropy



Properties of the Entropy Function



Entropy and Average Word-length



Shannon-Fano Coding



Entropy of Extensions and Products



Shannon's First Theorem



An Example of Shannon's First Theorem



Supplementary Exercises



Information Channels



Notation and Definitions



The Binary Symmetric Channel



System Entropies



System Entropies for the Binary Symmetric Channel



Extension of Shannon's First Theorem to Information Channels



Mutual Information



Mutual Information for the Binary Symmetric Channel



Channel Capacity



Supplementary Exercises



Using an Unreliable Channel



Decision Rules



An Example of Improved Reliability



Hamming Distance



Statement and Outline Proof of Shannon's Theorem



The Converse of Shannon's Theorem



Comments on Shannon's Theorem



Supplementary Exercises



Error-correcting Codes



Introductory Concepts



Examples of Codes



Minimum Distance



Hamming's Sphere-packing Bound



The Gilbert-Varshamov Bound



Hadamard Matrices and Codes



Supplementary Exercises



Linear Codes



Matrix Description of Linear Codes



Equivalence of Linear Codes



Minimum Distance of Linear Codes



The Hamming Codes



The Golay Codes



The Standard Array



Syndrome Decoding



Supplementary Exercises


Suggestions for Further Reading



Proof of the Sardinas-Patterson Theorem



The Law of Large Numbers



Proof of Shannon's Fundamental Theorem


Solutions to Exercises


Bibliography


Index of Symbols and Abbreviations


Index