Introduction to Coding Theory

ISBN-13: 9780521845045 / Angielski / Twarda / 2006 / 580 str.

Ron M. Roth

Opis

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, Ron Roth 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.

Recenzje

'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

Spis treści

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.