Bit-Level Optimization of Adder-Trees for Multiple Constant Multiplications for Efficient FIR Filter Implementation

Multiple constant multiplication (MCM) scheme is widely used for implementing transposed direct-form FIR filters. While the research focus of MCM has been on more effective common subexpression elimination, the optimization of adder-trees, which sum up the computed sub-expressions for each coefficient, is largely omitted. In this paper, we have identified the resource minimization problem in the scheduling of adder-tree operations for the MCM block, and presented a mixed integer programming (MIP) based algorithm for more efficient MCM-based implementation of FIR filters. Experimental result shows that up to 15% reduction of area and 11.6% reduction of power (with an average of 8.46% and 5.96% respectively) can be achieved on the top of already optimized adder/subtractor network of the MCM block.