Implementation of dyadic correlation and autocorrelation on graphics processors

Abstract

The convolution and related operators of correlation and autocorrelation are essential and powerful mathematical tools in machine learning, signal processing, systems theory, and related areas. In particular, representation and handling of systems with binary encoded input and output signals requires intensive computation of the correlation and autocorrelation functions which are defined on the finite dyadic groups as the underlying algebraic structure. This paper presents methods for computing the dyadic correlation and autocorrelation functions on graphics processing units (GPUs). The proposed algorithms are based on the convolution and the Wiener–Khinchin theorems and implemented using the Open Computing Language (OpenCL). We address several key issues in developing an efficient mapping of the computations to the GPU architecture. The experimental results confirm that the application of the proposed method leads to significant computational speedups over traditional C/C++ implementations processed on central processing units (CPUs).