The extra stage gamma network

The augmented data manipulator (ADM), inverse augmented data manipulator (IADM), and the gamma network are based on the Plus-Minus-2i connection patterns. In such a network there exist multiple paths to connect a source S to a destination D except when S=D. The number of paths for (S,D) is a function of the tag value (D-S) modulo N, and the size of the network N. par>It is shown in this paper that by adding an extra stage to the original PM21 interconnection network, multiple paths are provided for all the tag value including 0. The extra stage can be any stage out of n=log2N stages of the original network. The analyses on the distribution of the number of paths for various tag values are performed for n possible choices of the extra stage. It is shown that the extra stage of 0, +1, -1 connection patterns gives the most uniform distribution, and also results in a 1-fault tolerant interconnection network.