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Negacyclic convolution using polynomial transforms on hypercubes

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1 Author(s)
Fagin, B.S. ; Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH, USA

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

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Signal Processing, IEEE Transactions on  (Volume:40 ,  Issue: 8 )