Introduction to Coding Theory(ISBN=9780521845045)

Contains classical introductory material and classical research material as well as more recent developments ? Accessible to computer scientists, electrical engineers and mathematicians ? Contains over 340 exercises (many with hints) and over 100 worked examples

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 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