Introduction to Coding Theory

This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

Ron Roth (Author)

9780521845045, Cambridge University Press

Hardback, published 23 February 2006

580 pages, 66 b/w illus. 12 tables 348 exercises
24.6 x 17.5 x 3.8 cm, 1.13 kg

'The reader will find many well-chosen examples throughout the book and will be challenged by over 300 exercises, many of which have hints. Some of the exercises develop concepts that are not contained within the main body of the text. For example, the very first problem of the book, filling up more than an entire page of the text, introduces the AWGN channel and requires the reader to check the crossover probability of a memoryless binary symmetric channel. Zentralblatt MATH

Error-correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems. This 2006 book introduces the reader to the theoretical foundations of error-correcting codes, with an emphasis on Reed-Solomon codes and their derivative codes. After reviewing linear codes and finite fields, the author describes Reed-Solomon codes and various decoding algorithms. Cyclic codes are presented, as are MDS codes, graph codes, and codes in the Lee metric. Concatenated, trellis, and convolutional codes are also discussed in detail. Homework exercises introduce additional concepts such as Reed-Muller codes, and burst error correction. The end-of-chapter notes often deal with algorithmic issues, such as the time complexity of computational problems. While mathematical rigor is maintained, the text is designed to be accessible to a broad readership, including students of computer science, electrical engineering, and mathematics, from senior-undergraduate to graduate level.

Preface
1. Introduction
2. Linear codes
3. Introduction to finite fields
4. Bounds on the parameters of codes
5. Reed-Solomon codes and related codes
6. Decoding of Reed-Solomon codes
7. Structure of finite fields
8. Cyclic codes
9. List decoding of Reed-Solomon codes
10. Codes in the Lee metric
11. MDS codes
12. Concatenated codes
13. Graph codes
14. Trellis codes and convolutional codes
Appendix A. Basics in modern algebra
Bibliography
List of symbols
Index.

Subject Areas: Signal processing [UYS], Computer networking & communications [UT], Electrical engineering [THR], Applied mathematics [PBW]