Negacyclic convolution using polynomial transforms on hypercubes

Author

Fagin, Barry S.

Author_Institution

Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH, USA

Volume

40

Issue

8

fYear

1992

fDate

8/1/1992 12:00:00 AM

Firstpage

1845

Lastpage

1851

Abstract

A polynomial-transform-based algorithm for calculating products modulo Zⁿ+1 on a hypercube is presented. All interprocessor communication in this algorithm occurs over a Hamming distance of one; that is processors communicate only with their immediate neighbors. This algorithm has been implemented on a Connection Machine, and the performance results are discussed. Current figures show a time of 358 ms for negacyclic convolution of 1 K 16 bit samples, up to about 8 s for a 64 K data set. The authors discuss the use of this algorithm in the calculation of convolution, compare communication costs with the FFT, and discuss directions for future work

Keywords

computerised signal processing; hypercube networks; parallel algorithms; polynomials; transforms; Connection Machine; Hamming distance; digital signal processing; hypercubes; interprocessor communication; negacyclic convolution; polynomial transforms; Arithmetic; Contracts; Convolution; Costs; Hamming distance; Hypercubes; Multidimensional systems; Multiprocessor interconnection networks; Polynomials; Signal processing algorithms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.149987

Filename

149987