Abstract

If the 2^N nodes of a binary N cube are lexicographically ordered in a 2^N/2 × 2^N/2 array, the total number of different spatial displacements encountered in moving from every node to all its neighbors is 2N. The interconnection graph is thus somewhat space-invariant, because the number of different displacements grows only logarithmically with the number of nodes. If one transmitter and receiver per node are time multiplexed according to the canonical communication scheme for hyper- cubes,¹ it follows that no collisions occur and that the signals from the neighbors of a given node may simply be superposed at the node’s receiver. The admissibility of superposition, together with the low interconnect complexity of the graph resulting from lexicographical placement, makes a hologram-based free-space optical interconnection scheme very practical.

© 1988 Optical Society of America