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A Course in Error-Correcting Codes
Jørn Justesen and Tom Høholdt, Technical University of Denmark, Lyngby, Denmark
A publication of the European Mathematical Society.
EMS Textbooks in Mathematics
2004; 192 pp; hardcover
Volume: 1
ISBN-10: 3-03719-001-9
ISBN-13: 978-3-03719-001-2
List Price: US$45
Member Price: US$36
Order Code: EMSTEXT/1
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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 error-correction
  • Finite fields
  • Bounds on error probability for error-correcting codes
  • Communication channels and information theory
  • Reed-Solomon codes and their decoding
  • Cyclic Codes
  • Frames
  • Convolutional codes
  • Maximum likelihood decoding of convolutional codes
  • Combinations of several codes
  • Decoding Reed-Solomon and BCH-codes with the Euclidian algorithm
  • List decoding of Reed-Solomon codes
  • Iterative decoding
  • Algebraic geometry codes
  • Bibliography
  • Index
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