Error Correction Coding: Mathematical Methods and Algorithms

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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
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About the author (2005)

TODD K. MOON is a Professor in the Electrical and Computer Engineering Department at Utah State University and a senior member of the IEEE. His research interests include application of mathematical principles to problems involving the transmission, extraction, modeling, compression or analysis of signals. He is the coauthor of a widely-adopted graduate-level textbook in signal processing and author of numerous articles and conference presentations, as well as a children's book on programming. He also consults widely for industry.

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