Bit-parallel Multiple Constant Multiplication using Look-Up Tables on FPGA

The research on optimization of Multiple Constant Multiplication (MCM) during the last two decades has been focusing mainly on common subexpression elimination and reduced adder graph algorithms when bit-parallel computation is required. The advancement of FPGA technology enables the implementation of complex MCM instances on FPGA, but the shift-and-add network implementation does not make full use of the fundamental resources of FPGA, like the Look-Up Tables (LUT). Since bit-serial implementation optimized for FPGA is slow, an attempt for bit-parallel LUT-based implementation for single constant multiplication has been made. This paper extends this LUT-based method to multiple constant multiplications. It presents an interesting insight and unexpected outcome that the maximal number of LUTs required can be limited far below the theoretical number by mere enumeration without considering the legitimacy of all possible output combinations. Simulation results show that the required logic slices are comparable to the traditional adder-based MCM optimization methods while the delay is reduced by approximately 33%. The advantages are more prominent with increasing number of constants and the bit width used for their representation.