A Systematic Design of Cellular Permutation Arrays

This paper presents a parametrized design technique for cellular permutation arrays based on coset decompositions of symmetric groups. A new type of permutation cell, referred to as a coset generator, is introduced to customize the propagation delay, fan-in, fan-out, and number of edges in the target network. To aid in the design process, a cost function is derived expressing the number of edges in terms of the number of inputs and the sizes of cells. The results provide a spectrum of networks which vary with the size of the coset generator used, and range from a simple bipartite graph to several cellular permutation arrays reported in the literature.