Organization of k × k switches (k => 4) interconnected by d-dimensional (d => 2) regular optical patterns

The concept for the generation of arbitrary permutations of d-dimensional data cubes in a multistage manner is presented. In particular, d-dimensional switching cubes are proposed, and the geometry of the ports of the switches and their locations within the switching cubes (d = 3,4) are discussed. A new addressing scheme for the ports of these switches is presented, which is called the horizontal coding of addresses because the ports of the switches are distributed to the subsequently arranged arrays of the cube(s) in a horizontal manner. This addressing scheme permits any desired organization of the switches and the ports by reordering the absolute d-tuple addresses. This reordering is described by permutation matrices and explained by means of several examples. Within this addressing scheme relative addresses of the ports of the switches (which are a subset of the common absolute addresses) are introduced. Relative addresses offer an additional saving of hardware if applied within the concept of rearrangeability.

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