Constructing transition matrices for routing BPC permutations on shuffle-exchange recirculating networks

This paper introduces an approach that is intended for assigning extra bits in a transition matrix when routing a BPC (bit-permute-complement) permutation on a shuffle-exchange recirculating network with the required number of passes through the network greater than log₂ N. The approach can be applied to electronic shuffle-exchange networks and to their optical implementations as well. It is supposed that before constructing the transition matrix, minimal number of passes through the recirculating network necessary for admissibility of a given permutation, should be determined, using any of the known methods, what allows to reduce the transmission delay in the network on average and simplify constructing the transition matrix.