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.
• 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
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.
'… a most welcome addition. … well tested as a course text. Features include, the extensive collections of interesting and nontrivial problems at the end of chapters, the clear and insightful explanations of some of the deeper aspects of the subject and the extensive, interesting and useful historical notes on the development of the subject. This is an excellent volume that will reward the participants in any course that uses it with a deep understanding and appreciation for the subject.' Ian F, Blake, University of Toronto
'This book introduces the reader to the theoretical foundations of error-correctiong codes ... 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.' L'enseignement mathematique
'The mathematical style of this book is clear, concise and scholarly with a pleasing layout. There are numerous exercises, many with hints and many introducing further new concepts. Altogether this is an excellent book covering a wide range of topics in this area, and including an extensive bibliography.' Publication of the International Statistical Institute
'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