Fundamentals of Classical and Modern Error-Correcting Codes

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.

Shu Lin is an Adjunct Professor in the Department of Electrical and Computer Engineering at the University of California, Davis, and an IEEE Life Fellow. He has authored and co-authored several books, including LDPC Codes Designs, Constructions, and Unification and Channel Codes: Classical and Modern (Cambridge 2016, 2009).
Juane Li is Staff Systems Architect at Micron Technology Inc., San Jose, having previously completed her PhD at the University of California, Davis. She is also a co-author of LDPC Codes Designs, Constructions, and Unification (Cambridge University Press, 2009).