Binary to RNS encoder for the moduli set {2n-1, 2n, 2n+1} with embedded diminished-1 channel for DSP application

Abstract

A binary-to-residues encoder (forward encoder) is an essential building block for the residue number system digital signal processing (RNS DSP) and as such it should be built with a minimal amount of hardware and be efficient in terms of speed and power. The main parts of the forward encoder are residue generators which are usually classified into two categories: the one based on arbitrary moduli-set which make use of look-up tables, and the other based on the special moduli sets. A new memory less architecture of binary-to-RNS encoder based on the special moduli set {2n?1,2n,2n+1} with embedded modulo 2n+1 channel in the diminished-1 representation is presented. Any of two channels (standard modulo 2n +1, or modulo 2n+1 in the diminished-1 representation) operation can be performed by using a single switch. The proposed encoder has been implemented on a Xilinx FPGA chip for the various dynamic range requirements.