Negacyclic convolution using polynomial transforms on hypercubes

A polynomial-transform-based algorithm for calculating products modulo Z/sup n/+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.< >