The Gamma Network

The Gamma network is an interconnection network connecting N = 2n inputs to N outputs. It is a multistage network with N switches per stage, each of which is a 3 input, 3 output crossbar. The stages are linked via "power of two" and identify connections in such a way that redundant paths exist between the input and output terminals. In this network, a path from a source to a destination may be represented using one of the redundant forms of the difference between the source and destination numbers. The redundancy in paths may thus be studied using the theory of redundant number systems. Results are obtained on the distribution of paths connecting inputs and outputs, and the permuting capabilities of the Gamma network. Frequently used permutations and control mechanisms are discussed briefly. We also perform a detailed terminal reliability analysis of the Gamma network, deriving expressions for the reliability between an input and output terminal.