Digital signal processing applications often require the computation of linear systems. These computations can be considerably expensive and require optimizations for lower power consumption, higher throughput, and faster response time. Unfortunately, system designers do not have the necessary tools to take advantage of the wide flexibility in ways to evaluate these expressions. Therefore, we address the problem of efficiently computing a set of linear systems through a tool, Xquasher, that is developed by us to enable elimination of large common subexpression from expressions with an arbitrary number of terms. Xquasher provides a methodology for efficient computation of both single and multiple linear expressions. We also introduce the concept of power set encoding which helps us to provide an effective optimization method and achieves significant improvement over previously published work. Our tool provides optimized designs with 15% less area with the cost of 3% increase in delay by reducing number of additions on average by 45%.

Matrix inversion is an essential computation for various algorithms which are employed in multi-antenna wireless communication systems. FPGAs are ideal platforms for wireless communication; however, the need for vast amounts of customization throughout the design process of a matrix inversion core can overwhelm the designer. Decomposition methods provide the analytic simplicity and computational convenience necessary for computationally intensive matrix inversion. This paper presents automatic generation of different decomposition based matrix inversion architectures using a matrix inversion core generator tool, GUSTO with different parameterization options. We present automatic generation of a variety of general purpose matrix inversion architectures which have comparable results to published matrix inversion architecture implementations, but offer the advantage of providing the designer the ability to study the tradeoffs between architectures with different design parameters.