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

: Giglmayr, J.

Applied optics 31 (1992), Nr.11, S.1695-1708
ISSN: 0003-6935
ISSN: 1539-4522
ISSN: 1559-128X
Fraunhofer HHI ()
integrated optoelectronics; optical interconnections; optical switches; d-dimensional shuffle interconnection patterns; d-dimensional data cubes; mixed radix numbering; d-tuple data points; frequency domain; three-dimensional layout; multistage interconnection networks

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.