Gaussian Belief Propagation on a Field-Programmable Gate Array for Solving Linear Equation Systems

Abstract

Solving Linear Equation System (LESs) is a common problem in numerous fields of science. Even though the problem is well studied and powerful solvers are available nowadays, solving LES is still a bottleneck in many numerical applications concerning computation time. This issue especially pertains to applications in mobile robotics constrained by real-time requirements, where on-top power consumption and weight play an important role. This paper provides a general framework to approximately solve large LESs by Gaussian Belief Propagation (GaBP), which is extremely suitable for parallelization and implementation in hardware on a Field-Programmable Gate Array (FPGA). We derive the simple update rules of the Message Passing Algorithm for GaBP and show how to implement the approach efficiently on a System on a Programmable Chip (SoPC). In particular, multiple dedicated co-processors take care of recurring computations in GaBP. Exploiting multiple Direct Memory Access (DMA) controllers in scatter-gather mode and available arithmetic logic slices for numerical calculations accelerate the algorithm. Presented evaluations demonstrate that the approach does not only provide an accurate approximative solution of the LES. It also outperforms traditional solvers with respect to computation time for certain LESs.