What is a good theoretical, yet somewhat practical, book about error correction codes?

Question

I have started to develop some interest in error correcting codes. More Particularly I am interested in CRC's and I would like a book that treats this subject both in the theoretical aspects and in the practical one (e.g will allow me to implement code that can check CRC or create it for given data).

It seems reasonable that some field theory might be involved since CRC's are defined using some polynomial over $GF(2)$, which seems irreducible, so I would prefer a book that assumes some knowledge in Abstract Algebra rather than avoiding it.

Can someone please give such book recommendations ?

Answer 1

Here are some recommendations which could be useful.

Comprehensive Books:

The following books are playing presumably in the same league as W.W. Petersons Error-Correcting Codes from 1972 which was recommended by Antonios-Alexandros-Robotis.

You may check the table of contents of these books and you will see a wealth of information around error control coding with substantial chapters containing cyclic codes, resp. CRCs. I've consulted parts of each of them with benefit, especially with focus on CRCs.

Error Control Coding by S.Lin and D.J. Costello

The Theory of Error-Correcting Codes by F.J. MacWilliams and N.J.A. Sloane (founder of OEIS)

Coding and Information Theory by S. Roman

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Finite Fields:

Some basic knowledge around finite fields is definitely helpful.

Finite Fields for Computer Scientists and Engineers by R.J. McEliece is a very nice, easy to read introductory book. It was so delightful, that I also bought The Theory of Information and Coding from him.

Introduction to finite fields and their applications by R. Lidl and H. Niederreiter is much more comprehensive and provides a thorough introduction to the theme.

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Specific literature:

Sometimes when I have to work with certain CRCs in my job, there are questions regarding the undetected error probability of certain codes. I could find helpful information in

Codes for Error Detection by Torleiv Klove.

Hint: You might also visit my answer to Error correcting codes in real life where I put some references to papers regarding CRCs and undetected error probability.

Answer 2

This is not my expertise, but some of my friends who are currently doing work with error-correcting codes informed me that Peterson's Error Correcting Codes might be the book you are looking for.

I've heard it's mathematically rigorous, although I am uncertain as to what extent it will delve into the algebra you are interested in.