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.
Ron M. Roth is Professor of Computer Science at the Technion, Israel Institute of Technology.
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.