A Comparison between RADIX-2r Recoding and Hosangadi’s Heuristic

Abstract

Multiple Constant Multiplication (MCM) is an operation that multiplies a set of fixed-point constants with the same fixed-point variable. MCM is a fundamental operation in the design of linear time invariant (LTI) systems, such as in DSP transforms and digital controllers. It has been proved in published works that $RADIX-2^{r}$ recoding and Hosangadi’s heuristic achieve an important compression factor of the number of additions in the case of multiplierless implementation of the MCM problem. This has a positive impact on design parameters, like area occupation, timing performance, and power consumption. In this paper, $RADIX-2^{r}$ recoding is confronted to Hosangadi’s heuristic through a number of benchmark FIR filters of growing complexity. Results show a clear superiority in adder-cost of $RADIX-2^{r}$ over Hosangadi’s heuristic. Furthermore, $RADIX-2^{r}$ is much easier to be implemented and requires much less running time than Hosangadi’s heuristic.