Abstract
The need for d-dimensional (d >/= 3) interconnection patterns occurs if d-dimensional data cubes have to be interconnected. The formal definition of such patterns, presented here, 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.
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