*d*-Dimensional (*d* ≥ 3) shuffle interconnections

Applied Optics, Vol. 31, Issue 11, pp. 1695-1708 (1992)

http://dx.doi.org/10.1364/AO.31.001695

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### 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.

© 1992 Optical Society of America

**History**

Original Manuscript: June 26, 1989

Published: April 10, 1992

**Citation**

Josef Giglmayr, "d-Dimensional (d ≥ 3) shuffle interconnections," Appl. Opt. **31**, 1695-1708 (1992)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-31-11-1695

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