A common subexpression sharing approach for multiplierless synthesis of multiple constant multiplications

Abstract

In the context of multiple constant multiplication (MCM) filter design, we propose a search space that combines the shifted sum/difference of coefficients as well as minimal signed digit (MSD) representation. The search space further reduces the number of adders/subtractors in the synthesis of MCM from MSD representation. A novel common subexpression elimination (CSE) algorithm is adapted to the proposed search space. Our synthesized multiplierless filters are benchmarked against representative examples and found to achieve hardware reduction in most cases.