Fundamentals of Classical and Modern Error-Correcting Codes

An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.

Shu Lin (Author), Juane Li (Author)

9781316512623, Cambridge University Press

Hardback, published 9 December 2021

840 pages
25.3 x 19.5 x 4.4 cm, 1.85 kg

'The book truly explains these highly mathematical subjects to a level that can be accessed and applied with as little background in mathematics as possible. It provides step-by-step explanation of all covered topics, both more theoretical or applied, and includes sufficient illustrative examples to assist understanding.' Nikolay Yankov, zbMATH

Using easy-to-follow mathematics, this textbook provides comprehensive coverage of block codes and techniques for reliable communications and data storage. It covers major code designs and constructions from geometric, algebraic, and graph-theoretic points of view, decoding algorithms, error control additive white Gaussian noise (AWGN) and erasure, and dataless recovery. It simplifies a highly mathematical subject to a level that can be understood and applied with a minimum background in mathematics, provides step-by-step explanation of all covered topics, both fundamental and advanced, and includes plenty of practical illustrative examples to assist understanding. Numerous homework problems are included to strengthen student comprehension of new and abstract concepts, and a solutions manual is available online for instructors. Modern developments, including polar codes, are also covered. An essential textbook for senior undergraduates and graduates taking introductory coding courses, students taking advanced full-year graduate coding courses, and professionals working on coding for communications and data storage.

Preface
Acknowledgments
1. Coding for reliable digital information transmission and storage
2. Some elements of modern algebra and graphs
3. Linear block codes
4.Binary cyclic codes
5. BCH codes
6. Nonbinary BCH codes and Reed-Solomon codes
7. Finite geometries, cyclic finite geometry codes, and majority-logic decoding
8. Reed-Muller codes
9. Some coding techniques
10. Correction of error-bursts and erasures
11. Introduction to low-density parity-check codes
12. Cyclic and quasi-cyclic LDPC codes on finite geometries
13. Partial geometries and their associated QC-LDPC codes
14. Quasi-cyclic LDPC codes based on finite fields
15. Graph-theoretic LDPC codes
16. Collective encoding and soft-decision decoding of cyclic codes of prime lengths in Galois Fourier transform domain
17. Polar codes
Appendices.

Subject Areas: Signal processing [UYS], Communications engineering / telecommunications [TJK], Coding theory & cryptology [GPJ], Information theory [GPF]