Multidimensional Costas Arrays and Their Enumeration Using GPUs and FPGAs

Abstract EN

The enumeration of two-dimensional Costas arrays is a problem with factorial time complexity and has been solved for sizes up to 29 using computer clusters.

Costas arrays of higher dimensionality have recently been proposed and their properties are beginning to be understood.

This paper presents, to the best of our knowledge, the first proposed implementations for enumerating these multidimensional arrays in GPUs and FPGAs, as well as the first discussion of techniques to prune the search space and reduce enumeration run time.

Both GPU and FPGA implementations rely on Costas array symmetries to reduce the search space and perform concurrent explorations over the remaining candidate solutions.

The fine grained parallelism utilized to evaluate and progress the exploration, coupled with the additional concurrency provided by the multiple instanced cores, allowed the FPGA (XC5VLX330-2) implementation to achieve speedups of up to 30× over the GPU (GeForce GTX 580).