Maximal sharing of partial terms in MCM under minimal signed digit representation

Abstract

We propose a new algorithm that maximizes the sharing of partial terms in Multiple Constant Multiplication (MCM) operations. MCM operations are required by many algorithms in digital signal processing and have been the subject of extensive research. Recently, the Minimal Signed Digit (MSD) number representation has been proposed as an extension to the Canonical Signed Digit (CSD) representation. By properly exploiting the redundancy of the MSD representation, the hardware implementation can be significantly optimized. The initial algorithm described in this paper is able to perform a better search for the optimal sharing of the redundant coefficient representations under MSD than previous methods. However, during its search the depth of adder-steps is not considered. We present a modified version of this algorithm that is able to reduce the maximum depth of partial terms at the expense of some extra hardware. The results show that for more complex problems our algorithm performs significantly better than previous approaches, in some cases obtaining solutions that require 25% less hardware.