The organization of permutation architectures with bused interconnections

The problem of efficiently permuting data stored in VLSI chips in accordance with a predetermined set of permutations is explored. By connecting chips with shared bus interconnections, as opposed to point-to-point interconnections, it is shown that the number of pins per chip can often be reduced. As an example, for infinitely many n, the authors exhibit permutation architectures that can realize any of the n cyclic shifts on n chips in one clock tick, where the upper limit on the number of pins per chip is the greatest integer ⩽√n. When the set of permutations forms a group with p elements, any permutation in the group can be realized in one clock tick by an architecture with O(√ plg p) pins per chip. When the permutation group is abelian, O(√p) pins suffice. These results are all derived from a mathematical characterization of uniform permutation architectures based on the combinatorial notion of a difference cover. The authors also consider uniform permutation architectures that realize permutations in several clock ticks instead of one, and show that further savings in the number of pins per chip can be obtained