Polynomial Theory of Error Correcting Codes

Giovanni Cancellieri is full professor of Telecommunications at Polytechnic University of Marche, Italy. His main research activities relate to optical communications, multimedia services, networks, mobile communications, and channel coding. He is a member of various worldwide and European technical associations and standardization bodies.

• Generator matrix approach to linear block codes.- Wide-sense time-invariant block codes in their generator matrix.- Generator matrix approach to s.s. time-invariant convolutional codes.- Wide-sense time-invariant convolutional codes in their generator matrix.- Parity check matrix approach to linear block codes.- Wide-sense time-invariant block codes in their parity check matrix.- Strict-sense time-invariant convolutional codes in their parity check matrix.- Wide-sense time-invariant convolutional codes in their parity check matrix.- Turbo codes.- Low density parity check codes.- Binomial product generator LDPC block codes.- LDPC convolutional codes.- Appendix A. Matrix algebra in a binary finite field.- Appendix B. Polynomial representation of binary sequences.- Appendix C. Electronic circuits for multiplication or division in polynomial representation of binary sequences.- Appendix D. Survey on the main performance of error correcting codes.

"The unified approach of polynomials makes this book quite interesting. It will be quite useful for researchers and engineers working in the field. It can also be used as supplementary material for an advanced undergraduate course or a graduate-level course in coding theory. ... the book is good reading. I enjoyed it and I strongly recommend it to any coding theorists." (Manish Gupta, Computing Reviews, August, 2015)