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The art of error correcting coding
Personal Author:
2nd ed.
Publication Information:
West Sussex, Englang : John Wiley & Sons, 2006


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30000010106538 QA268 M674 2006 Open Access Book Book

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Building on the success of the first edition, which offered apractical introductory approach to the techniques of errorconcealment, this book, now fully revised and updated, provides acomprehensive treatment of the subject and includes a wealth ofadditional features. The Art of Error Correcting Coding,Second Edition explores intermediate and advanced levelconcepts as well as those which will appeal to the novice.

All key topics are discussed, including Reed-Solomon codes,Viterbi decoding, soft-output decoding algorithms, MAP, log-MAP andMAX-log-MAP. Reliability-based algorithms GMD and Chase areexamined, as are turbo codes, both serially and parallelconcatenated, as well as low-density parity-check (LDPC) codes andtheir iterative decoders.

Features additional problems at the end of each chapter and aninstructor?s solutions manual Updated companion website offers new C/C ++programs and MATLABscripts, to help with the understanding and implementation of basicECC techniques Easy to follow examples illustrate the fundamental concepts oferror correcting codes Basic analysis tools are provided throughout to help in theassessment of the error performance block and convolutional codesof a particular error correcting coding (ECC) scheme for aselection of the basic channel models

This edition provides an essential resource to engineers,computer scientists and graduate students alike for understandingand applying ECC techniques in the transmission and storage ofdigital information.

Author Notes

Robert H. Morelos-Zaragoza received BSEE and MSEE degrees from the National Autonomous University of Mexico (UNAM) in 1985 and 1987 respectively, and a PhD in Electrical Engineering from the University of Hawaii at Manoa in 1992. He has held numerous research posts in Mexico and Japan. In 2002, Robert joined the Department of Electrical Engineering at San José State University, as an Associate Professor. His current research interests include error correcting coding (ECC/FEC), advanced digital communication receiver design, software-defined radio (SDR), space-time signal processing techniques and ultra-wideband (UWB) communication systems. Prof. Morelos-Zaragoza is a senior member of IEEE, and member of IEICE (Japan) and of Eta Kappa Nu.

Table of Contents

The ECC web site
1 Introduction
1.1 Error correcting coding: Basic concepts
1.1.1 Block codes and convolutional codes
1.1.2 Hamming distance, Hamming spheres and error correcting capability
1.2 Linear block codes
1.2.1 Generator and parity-check matrices
1.2.2 The weight is the distance
1.3 Encoding and decoding of linear block codes
1.3.1 Encoding withG andH
1.3.2 Standard array decoding
1.3.3 Hamming spheres, decoding regions and the standard array
1.4 Weight distribution and error performance
1.4.1 Weight distribution and undetected error probability over a BSC
1.4.2 Performance bounds over BSC, AWGN and fading channels
1.5 General structure of a hard-decision decoder of linear codes.
2 Hamming, Golay and Reed-Muller codes
2.1 Hamming codes
2.1.1 Encoding and decoding procedures
2.2 The binary Golay code
2.2.1 Encoding
2.2.2 Decoding
2.2.3 Arithmetic decoding of the extended (24, 12, 8) Golay code
2.3 Binary Reed-Muller codes
2.3.1 Boolean polynomials and RM codes
2.3.2 Finite geometries and majority-logic decoding
3 Binary cyclic codes and BCH codes
3.1 Binary cyclic codes
3.1.1 Generator and parity-check polynomials
3.1.2 The generator polynomial
3.1.3 Encoding and decoding of binary cyclic codes
3.1.4 The parity-check polynomial
3.1.5 Shortened cyclic codes and CRC codes
3.1.6 Fire codes
3.2 General decoding of cyclic codes
3.2.1 GF(2m) arithmetic
3.3 Binary BCH codes
3.3.1 BCH bound
3.4 Polynomial codes
3.5 Decoding of binary BCH codes
3.5.1 General decoding algorithm for BCH codes
3.5.2 The Berlekamp-Massey algorithm (BMA)
3.5.3 PGZ decoder
3.5.4 Euclidean algorithm
3.5.5 Chien search and error correction
3.5.6 Errors-and-erasures decoding
3.6 Weight distribution and performance bounds
3.6.1 Error performance evaluation
4 Nonbinary BCH codes: Reed-Solomon codes
4.1 RS codes as polynomial codes
4.2 From binary BCH to RS codes
4.3 Decoding RS codes
4.3.1 Remarks on decoding algorithms
4.3.2 Errors-and-erasures decoding
4.4 Weight distribution
5 Binary convolutional codes
5.1 Basic structure
5.1.1 Recursive systematic convolutional codes
5.1.2 Free distance
5.2 Connections with block codes
5.2.1 Zero-tail construction
5.2.2 Direct-truncation construction
5.2.3 Tail-biting construction
5.2.4 Weight distributions
5.3 Weight enumeration
5.4 Performance bounds
5.5 Decoding: Viterbi algorithm with Hamming metrics
5.5.1 Maximum-likelihood decoding and metrics
5.5.2 The Viterbi algorithm
5.5.3 Implementation issues
5.6 Punctured convolutional codes
5.6.1 Implementation issues related to punctured convolutional codes
5.6.2 RCPC codes
6 Modifying and combining codes
6.1 Modifying codes
6.1.1 Shortening
6.1.2 Extending
6.1.3 Puncturing
6.1.4 Augmenting, expurgating and lengthening
6.2 Combining codes
6.2.1 Time sharing of codes
6.2.2 Direct sums of codes
6.2.3 The
6.2.4 Products of codes
6.2.5 Concatenated codes
6.2.6 Generalized concatenated codes
7 Soft-decision decoding
7.1 Binary transmission over AWGN channels
7.2 Viterbi algorithm with Euclidean metric
7.3 Decoding binary linear block codes with a trellis
7.4 The Chase algorithm
7.5 Ordered statistics decoding
7.6 Generalized minimum distance decoding
7.6.1 Sufficient conditions for optimality
7.7 List decoding
7.8 Soft-outpu
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