Error Correction Coding

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.

Preface vii

List of Program Files xxxi

List of Laboratory Exercises xxxii

List of Algorithms xxxiv

List of Figures xl

List of Tables xlii

List of Boxes xliii

Part I: Introduction and Foundations 1

1 A Context for Error Correction Coding 2

Part II: Block Codes 61

2 Groups and Vector Spaces 62

3 Linear Block Codes 83

4 Cyclic Codes, Rings, and Polynomials 113

5 Rudiments of Number Theory and Algebra 171

6 BCH and Reed-Solomon Codes: Designer Cyclic Codes 235

7 Alternate Decoding Algorithms for Reed-Solomon Codes 293

8 Other Important Block Codes 369

9 Bounds on Codes 406

10 Bursty Channels, Interleavers, and Concatenation 425

11 Soft-Decision Decoding Algorithms 439

Part III: Codes on Graphs 451

12 Convolutional Codes 452

13 Trellis Coded Modulation 535

Part IV: Iteratively Decoded Codes 581

14 Turbo Codes 582

15 Low-Density Parity-Check Codes 634

16 Decoding Algorithms on Graphs 680

Part V: Space-Time Coding 709

17 Fading Channels and Space-Time Codes 710

A Log Likelihood Algebra 735

References 739

Index 750