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

Author

Truong, T.K. ; Reed, Irving S. ; Hsu, In-shek ; Shyu, Hsuen-chyun ; Shao, H.M.

Author_Institution

Jet Propulsion Lab., Pasadena, CA, USA

Volume

37

Issue

3

fYear

1988

fDate

3/1/1988 12:00:00 AM

Firstpage

266

Lastpage

273

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(qⁿ). A pipeline structure is used to implement this prime-factor DFT over GF(qⁿ). 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(qⁿ) 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 ⁿ) is presented

Keywords

Fourier transforms; codes; pipeline processing; Reed-Solomon codes; Winograd type; complex numbers; cyclic convolutions; fast prime factor DFT; finite field; pipeline design; pipeline structure; Algorithm design and analysis; Convolutional codes; Decoding; Discrete Fourier transforms; Fast Fourier transforms; Fourier transforms; Galois fields; Pipelines; Reed-Solomon codes; Systolic arrays;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.2163

Filename

2163