Abstract

One-dimensional perfect-shuffle networks are extended to two-dimensional perfect-shuffle networks, and this extension is analyzed by means of the finite-state model. The routing algorithm presented is based on quaternary numbers for 4 × 4 switches, and its extension to k × k switches is briefly discussed. In order to take full advantage of the three-dimensional interconnection capability and two-dimensional space–bandwidth product of free-space optics, we map one-dimensional perfect-shuffle networks into two-dimensional perfect-shuffle networks, with both having 4 × 4 switching elements. Finally we compare the permutation capability of two-dimensional perfect-shuffle networks with one-dimensional perfect-shuffle networks.

© 1993 Optical Society of America

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