ALGORITHMS AND ARCHITECTURES FOR REED-SOLOMON CODES

Reed-Solomon encoding and decoding operations are described using a discrete Fourier transform (DFT) defined in a Galois field. A brief derivation of this transform using polynomial algebra and a summary of algorithms for computing it are presented. Reed-Solomon encoding and decoding algorithms are then described. The emphasis here is on decoding as this is a much more complex operation than encoding. This decoding can be carried out in the domain in which the data are received or by transforming the data into another domain through the use of a Galois field DFT. Both classes of algorithm are studied and compared. Methods of reducing the computational and hardware complexities of some of the algorithms are presented and architectures are given for implementing these algorithms using VLSI technology.