A low complexity realisation of Winograd number theoretic transform and its application

Abstract

This paper investigates a novel structure for the Winograd number theoretic transform algorithm (WNTA) to reduce the computation load. The proposed computing structure exploits the multiple constant multiplication to replace the standard multiplication, then, the multiplication of the WNTA can be realised in a shift-add way, which definitely decreases the complexity of WNTA and maintains the computing accuracy. Typical applications, such as the convolution and the filtering operation, are tested by computer simulations, while the result demonstrates that the proposed scheme is superior to conventional schemes in terms of the trade-off between the complexity.

A fast realization of new Mersenne number transformation and its applications

“…Similar tests had been adopted in Hua et al 15 to demonstrate the stability and accuracy of NTT. Similar tests had been adopted in Hua et al 15 to demonstrate the stability and accuracy of NTT.…”

“…This section provides a computer experiment to verify the proposed fast algorithm, where we employ the WHNMNT to compute the circular convolution of two sequences. Similar tests had been adopted in Hua et al 15 to demonstrate the stability and accuracy of NTT. The WHNMNT parameter is chosen as (N, M p , 1 , 2 ) = (16, 127, 106, 103).…”