# Error Correction Coding: Mathematical Methods and Algorithms

John Wiley & Sons, Jun 6, 2005 - Computers - 800 pages
An unparalleled learning tool and guide to error correction coding

Error correction coding techniques allow the detection and correction of errors occurring during the transmission of data in digital communication systems. These techniques are nearly universally employed in modern communication systems, and are thus an important component of the modern information economy.

Error Correction Coding: Mathematical Methods and Algorithms provides a comprehensive introduction to both the theoretical and practical aspects of error correction coding, with a presentation suitable for a wide variety of audiences, including graduate students in electrical engineering, mathematics, or computer science. The pedagogy is arranged so that the mathematical concepts are presented incrementally, followed immediately by applications to coding. A large number of exercises expand and deepen students' understanding. A unique feature of the book is a set of programming laboratories, supplemented with over 250 programs and functions on an associated Web site, which provides hands-on experience and a better understanding of the material. These laboratories lead students through the implementation and evaluation of Hamming codes, CRC codes, BCH and R-S codes, convolutional codes, turbo codes, and LDPC codes.

This text offers both "classical" coding theory-such as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codes-as well as modern codes and decoding methods, including turbo codes, LDPC codes, repeat-accumulate codes, space time codes, factor graphs, soft-decision decoding, Guruswami-Sudan decoding, EXIT charts, and iterative decoding. Theoretical complements on performance and bounds are presented. Coding is also put into its communications and information theoretic context and connections are drawn to public key cryptosystems.

Ideal as a classroom resource and a professional reference, this thorough guide will benefit electrical and computer engineers, mathematicians, students, researchers, and scientists.

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### Contents

 A Context for Error Correction Coding 2 Groups and Vector Spaces 62 Linear Block Codes 83 Cyclic Codes Rings and Polynomials 113 A Linear Feedback Shift Registers 154 Polynomial Division and Linear Feedback Shift Registers 161 Rudiments of Number Theory and Algebra 171 A How Many Irreducible Polynomials Are There? 218
 Bounds on Codes 406 10Bursty Channels Interleavers and Concatenation 425 SoftDecision Decoding Algorithms 439 Convolutional Codes 452 Trellis Coded Modulation 535 Turbo Codes 583 LowDensity ParityCheck Codes 634 Decoding Algorithms on Graphs 680

 Programming Galois Field Arithmetic 224 Designer Cyclic Codes 235 Alternate Decoding Algorithms for ReedSolomon Codes 293 Other Important Block Codes 369
 Fading Channels and SpaceTime Codes 710 A Log Likelihood Algebra 735 Index 750 Copyright