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

TL;DR

This paper introduces reduced-complexity Reed--Solomon decoders by optimizing cyclotomic FFTs, leading to significant computational efficiency improvements in decoding processes.

Contribution

The paper presents novel partial and dual partial cyclotomic FFTs with lower complexity, enhancing Reed--Solomon decoder efficiency.

Findings

Smaller computational complexities for partial CFFTs.

Significant complexity reductions in Reed--Solomon decoders.

Effective use of optimized CFFTs in both transform- and time-domain decoding.

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.