On BPC Permutations Admissibility to Variable-Stage Hybrid Optical Shuffle-Exchange Networks

Gennady Veselovsky


Interconnection Networks, Algorithms, Optical Networks, BPC Permutations


This paper introduces a simple algorithm for determining the minimum number of stages in a variable–stage hybrid optical multistage shuffle-exchange interconnection network necessary for admissibility of a given bit-permute-complement (BPC) permutation. Here admissibility means that a permutation can be realized without conflicts for one pass through the network. It is suggested that in shuffle-exchange network (SEN) optical signals are switched, but the switches (directional couplers) are controlled electronically. Depending on the kind of a permutation the number of stages m can be varied from 1 to 2n-1. For solving this problem Das, Bhattacharya, and Bezrukov developed an algorithm with time complexity. In this paper we offer an approach which makes possible to do the same in time only. In an optical SEN minimizing the number of stages for realizing a given BPC permutation helps to reduce path-dependent loss on average, moreover, as we have shown, it alleviates also solving the crosstalk problem.

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