A pipeline design of a fast prime factor DFT on a finite field

Abstract

A conventional prime factor discrete Fourier transform (DFT) algorithm of the Winograd type is used to realize a discrete Fourier-like transform on the finite field GF(q/sup /n). A pipeline structure is used to implement this prime-factor DFT over GF(q/sup /n). This algorithm is developed to compute cyclic convolutions of complex numbers and to aid in decoding the Reed-Solomon codes. Such a pipeline fast prime-factor DFT algorithm over GF(q/sup /n) is regular, simple, expandable, and naturally suitable for most implementation technologies. An example illustrating the pipeline aspect of a 30-point transform over GF(q/sup /n) is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>