d-dimensional (d > or = 3) shuffle interconnections

The need for d-dimensional (d>or=3) interconnection patterns occurs if d-dimensional data cubes have to be interconnected. The formal definition of such patterns, presented in the paper is based on the mixed radix numbering of the d-tuple data points. Because each coordinate of a d-dimensional data cube may be factorized in a different way, a family of interconnection patterns is obtained that increases with respect to the dimension of the data cubes. The properties of d-dimensional patterns are analyzed, and their realization in the frequency domain is described. Methods for the three-dimensional layout of the patterns are presented. The application of d-dimensional patterns within multistage interconnection networks is discussed.