Systolic architectures for decoding Reed-Solomon codes

A systolic implementation of a Reed-Solomon decoder is presented which with minor modification is suitable for BCH and Goppa codes. The various operations involved in decoding such codes were analyzed and the results are described. Systolic array architectures are derived for the various steps including the syndrome calculation, key equation solution and error evaluation. Since the throughput of the decoder is effectively determined by the speed of the multipliers, various multiplier architectures are discussed briefly. The architectures presented improve upon previous designs. The result is highly regular and modular, and thus it is more suitable for VLSI implementation.<>