EMS Textbooks in Mathematics 2004; 192 pp; hardcover Volume: 1 ISBN10: 3037190019 ISBN13: 9783037190012 List Price: US$45 Member Price: US$36 Order Code: EMSTEXT/1
 This book is written as a text for a course aimed at advanced undergraduates. Only some familiarity with elementary linear algebra and probability is directly assumed, but some maturity is required. The students may specialize in discrete mathematics, computer science, or communication engineering. The book is also a suitable introduction to coding theory for researchers from related fields or for professionals who want to supplement their theoretical basis. It gives the coding basics for working on projects in any of the above areas, but material specific to one of these fields has not been included. Chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts. In addition, some problems and suggestions for projects indicate direction for further work. The presentation encourages the use of programming tools for studying codes, implementing decoding methods, and simulating performance. Specific examples of programming exercise are provided on the book's home page. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in information and communication and circuits. Table of Contents  Block codes for errorcorrection
 Finite fields
 Bounds on error probability for errorcorrecting codes
 Communication channels and information theory
 ReedSolomon codes and their decoding
 Cyclic Codes
 Frames
 Convolutional codes
 Maximum likelihood decoding of convolutional codes
 Combinations of several codes
 Decoding ReedSolomon and BCHcodes with the Euclidian algorithm
 List decoding of ReedSolomon codes
 Iterative decoding
 Algebraic geometry codes
 Bibliography
 Index
