Introduction to Error-correcting Codes

By: Michael Purser

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Hardcover | 30 November 1994

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148 Pages

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23.5 x 15.88 x 1.91

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Accuracy is an increasingly critical issue in digital communication, but few books have provided the nonspecialist user with the fundamentals of error-correcting codes -- until now. Guiding you from general concepts through the most common error-correcting codes applied to bit transmission in packet-switched networks and personal cellular systems, this book explains error-correction techniques using redundant bits. It enables users to design and implement error-correcting systems with less effort than ever before.

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Non-Fiction Computing & I.T.Computer Science Digital Signal Processing (DSP)Reference, Information & Interdisciplinary Subjects Research & Information Information theory Engineering & Technology Electronics & Communications Engineering Communications Engineering & Telecommunications Energy Technology & Engineering Electrical Engineering

Technology in General

Preface
Introduction	p. 1
Bit Strings and Codes	p. 1
Hamming Distance and Sphere-Packing	p. 7
Shannon's Theorem	p. 8
Linear Codes	p. 11
Matrix Representation	p. 11
The Null Matrix or Parity-Check Matrix	p. 14
Perfect Codes	p. 18
Further Bounds on Linear Codes	p. 19
Nonbinary Linear Codes	p. 25
Cyclic Codes	p. 31
The Generating Polynomial	p. 31
The Roots of g(x) and the Null Matrix	p. 35
Error Detection with Cyclic Codes	p. 38
Error Correction with Cyclic Codes	p. 42
Nonbinary Cyclic Codes	p. 44
BCH Codes	p. 47
Minimum Polynomials	p. 47
The Roots of BCH Codes	p. 48
Some Examples of BCH Codes	p. 51
Error Correction of Binary BCH Codes	p. 53
Error Correction of Nonbinary BCH Codes	p. 56
Reed-Solomon (RS) Codes	p. 59
Convolutional Codes	p. 69
Tree and Trellis Codes	p. 69
Linear Convolutional Codes	p. 72
Analysis of Convolutional Codes	p. 78
Error-Correcting with Convolutional Codes	p. 81
Block Codes and Convolutional Codes	p. 91
App. A: Information Theory	p. 95
App. B: Some Binomial Approximations	p. 113
App. C: Finite Fields	p. 117
App. D: The Berlekamp-Massey Algorithm	p. 125
References	p. 129
Index	p. 131
Table of Contents provided by Blackwell. All Rights Reserved.

Introduction to Error-correcting Codes

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