Synopses & Reviews
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 theorysuch as Hamming, BCH, Reed-Solomon, Reed-Muller, and convolutional codesas 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.
Error Control Coding (EEC) is the detection and correction of errors in the message transmission in a digital communications system by codes inserted in a data stream which are everywhere, from the Internet to compact disk and CD-ROMs, to cell phones and wireless connections. An understanding of those codes is therefore paramount for anyone involved in digital communications (modems, cell phones, wireless networking, DSL, DSP, etc...). This new proposal's main goal is to supply a modern approach with an implementation-oriented viewpoint. Hands-on programming exercises of important algorithms are provided throughout. The book presents background information on information and decision theory, the classical coding methods still in use (Reed Solomon codes, trellis-codes, etc...) as well as the new iteratively-decode codes (including Turbo codes).
An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
About the Author
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.
Table of Contents
List of Program Files.
List of Laboratory Exercises.
List of Algorithms.
List of Figures.
List of Tables.
List of Boxes.
PART I: INTRODUCTION AND FOUNDATIONS.
1. A Context for Error Correcting Coding.
PART II: BLOCK CODES.
2. Groups and Vector Spaces.
3. Linear Block Codes.
4. Cyclic Codes, Rings, and Polynomials.
5. Rudiments of Number Theory and Algebra.
6. BCH and Reed-Solomon Codes: Designer Cyclic Codes.
7. Alternate Decoding Algorithms for Reed-Solomon Codes.
8. Other Important Block Codes.
9. Bounds on Codes.
10. Bursty Channels, Interleavers, and Concatenation.
11. Soft-Decision Decoding Algorithms.
PART III: CODES ON GRAPHS.
12. Convolution Codes.
13. Trefils Coded Modulation.
PART IV: INTERATIVELY DECODED CODES.
14. Turbo Codes.
15. Low-Density Parity-Check Codes.
16. Decoding Algorithms on Graphs.
PART V: SPACE-TIME CODING.
17. Fading Channels and Space-Time Coding.