The Modulus Replication RNS (MRRNS): A Comparative Study

Abstract

There have been several recent initiatives to use computations on finite polynomial rings as a tool for evaluating digital signal processing algorithms. A technique was recently introduced, by the authors [9], that allows a direct mapping from the bit pattern of the input numbers to the polynomial coefficients. The mapping strategy is simple, and some of the magnitude information of the resulting computations is preserved in the resulting finite ring operations. This is in contrast to the use of a standard residue number system where magnitude information requires invoking the Chinese Remainder Theorem (or some mixed radix counterpart) across the entire dynamic range of the calculation. Disadvantages of the technique are associated with the relatively large redundancy required in the finite ring computational hardware compared to that required for nonredundant integer calculations (binary, RNS etc.). This paper performs a comparative study of the RNS and MRRNS techniques to show that this redundancy in computational hardware is adequately compensated by the simplicity in mapping, scaling and redundancy considerations for WSI implementation.