An analysis of blocking switches using error control codes

The relation between the degree of blocking and the amount of resource speedup necessary for blocking switches to possess the capabilities of nonblocking switches is studied in this paper and considers both multicast and point to point scenarios. We show that the number of configurations that must be supported by a switching interconnection fabric can be significantly reduced even with small speedup values. We construct an analogy between switch configurations and the codewords of certain error control codes for which we use space covering ideas to derive relations between speedup and number of switch configurations. To derive the necessary speedup for non-blocking, we use two sphere packing bounds: the hamming bound and the Gilbert-Varshamov bound to construct nonblocking switches with a given speedup we use maximum distance separable codes.