Reduced-Complexity Reed--Solomon Decoders Based on Cyclotomic FFTs

Abstract: In this paper, we reduce the computational complexities of partial and dual partial cyclotomic FFTs (CFFTs), which are discrete Fourier transforms where spectral and temporal components are constrained, based on their properties as well as a common subexpression elimination algorithm. Our partial CFFTs achieve smaller computational complexities than previously proposed partial CFFTs. Utilizing our CFFTs in both transform- and time-domain Reed--Solomon decoders, we achieve significant complexity reductions.