Essays on Coding Theory

Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, significantly mitigating costs for governments and corporations that maintain server systems containing large amounts of data. This book surveys the basic ideas of these coding techniques, which tend not to be covered in the graduate curricula, including pointers to further reading. Written in an informal style, it avoids detailed coverage of proofs, making it an ideal refresher or brief introduction for students and researchers in academia and industry who may not have the time to commit to understanding them deeply. Topics covered include fountain codes designed for large file downloads; LDPC and polar codes for error correction; network, rank metric, and subspace codes for the transmission of data through networks; post-quantum computing; and quantum error correction. Readers are assumed to have taken basic courses on algebraic coding and information theory.

Preface; 1. Introduction; 2. Coding for erasures and fountain codes; 3. Low density parity check codes; 4. Polar codes; 5. Network codes; 6. Coding for distributed storage; 7. Locally repairable codes; 8. Locally decodable codes; 9. Private information retrieval; 10. Batch codes; 11. Expander codes; 12. Rank metric and subspace codes; 13. List decoding; 14. Sequences sets with low correlation; 15. Post-quantum cryptography; 16. Quantum error correcting codes; 17. Other types of coding; Appendix A: Finite geometries, linearized polynomials and Gaussian coefficients; Appendix B: Hasse derivatives and zeros of multivariate polynomials; References; Index.

Ian F. Blake is Honorary Professor in the Departments of Mathematics and Electrical and Computer Engineering at the University of British Columbia. He is a Fellow of the Royal Society of Canada, the Institute for Combinatorics and its Applications, the Canadian Academy of Engineers, and a Life Fellow of the IEEE. In 2000, he was awarded an IEEE Millennium Medal. He received his undergraduate degree at Queen's University and doctorate degree at Princeton University in 1967. He also worked in industry, spending sabbatical leaves with IBM and M/A-Com Linkabit, and working with the Hewlett-Packard Labs from 1996 to 1999. His research interests include cryptography and algebraic coding theory, and he has written several books in these areas.