Resource-optimized Time-multiplexed Constant Multiplication via Adjacency Matrix Modeling

This article presents TmCM-AM, a new time-multiplexed constant multiplication framework based on adjacency matrix modeling. The TmCM-AM framework provides a universal and efficient approach for digital signal processing applications using much fewer resources and with greater adaptability based on conventional methods. By transforming adder graphs into adjacency matrices and using an optimization algorithm, the proposed framework minimizes the number of required adders and multiplexers to a large degree. In particular, three mathematical properties of adjacency matrices based on properties of adder graphs are presented. Meanwhile, the adjacency matrix is employed to model time-multiplexed adder graphs in detail, making hardware architecture analysis possible through matrix computation. Finally, heuristic algorithms are used to generate the best possible solution from matrices calculated. Experimental verification through FPGA and ASIC implementations further confirms the feasibility of TmCM-AM, presenting enormous reductions in area and power dissipation, as well as delay metrics across random data and various real-life coefficient sets.