VLSI Circuit Design of Matrix Transposition Using Tensor Product Formulation

Matrix transposition is a simple, but an important computational problem. It explores many key issues on data locality. In this paper, we will design matrix transposition algorithms on various interconnection networks for VLSI circuit design, including omega, baseline and hypercube networks. Since different interconnection networks have their own architectural characteristics and properties, an algorithm needs to be tuned in order to be efficiently implemented on various networks. We use a tensor product based algebraic theory to design matrix transposition algorithms on various interconnection networks. After designing matrix transposition on various interconnection networks, we use a hardware description language, Verilog, to realize algorithms on FPGA. A major goal of this paper is to provide an effective way for designing VLSI circuits of DSP algorithms.