Efficient implementation of modular multiplication by constants applied to RNS reverse converters

This paper presents a procedure to optimize modular multiplication by constants. Such operations have been demonstrated to be crucial to design efficient reverse converters, which are the bottleneck of RNS. The focus of this work is the use of Residue Number System (RNS) moduli sets without limitation of the number of channels, which are useful for Digital Signal Processing (DSP) applications. Moreover, an improved hardware architecture for a reverse converter algorithm by using balanced generic moduli sets is presented too. The experimental results show that the optimization of modular multiplication by constant on reverse converters provides a speedup of 1.40 times and average area reduction of 27% for maximum dynamic ranges presented in the state of the art.