Algorithms for block error control codes

The authors review existing algorithms and present new algorithms for implementing algebraic codes which are increasingly being used for achieving high data integrity in digital communication systems. The emphasis is on Reed-Solomon and BCH codes, although the techniques described may be applicable in other coding areas. They consider encoding and decoding as spectral operations, where the frequency domain is defined using a principle root of unity in a Galois field. They first consider frequency domain techniques and describe algorithms for implementing decoders efficiently using VLSI technology. They then consider time domain decoding and present a new algorithm for achieving significant savings in computations. They study the implementation of time domain decoding techniques and conclude with a comparison of time and frequency decoding algorithms