Universal Switch-Module Design for Symmetric-Array-Based FPGAs

A switch module M with W terminals on each side is said to be universal if every set of nets satisfying the dimensional constraint (the number of nets on each side of M is at most W) is simultaneously routable through M. In this paper, we present a class of universal switch modules. Each of our switch modules has 6W switches and switch-module flexiblity three (Fs = 3). We prove that no switch module with less than 6W switches can be universal. We also compare our switch modules with those used in the Xilinx XC4000 family FPGA´s and the anti-symmetric switch modules (with Fs = 3^1) suggested by [Flexibility of interconnection structures for field-programmable gate arrays]. Although these two kinds of switch modules also have Fs = 3 and 6W switches, we show that they are not universal. Based on combinatorial counting techniques, we show that each of our universal switch modules can accommodate up to 25% more routing instances, compared with the XC4000-type one of the same size. Experimental results demonstrate that our universal switch modules improve routability at the chip level. Finally, our work also provides a theoretical insight into the important observation by Rose and Brown [Flexibility of interconnection structures for field-programmable gate arrays] that Fs = 3 is often sufficient to provide high routability.