Rrecursive reduction in finite ring computations

Abstract

where the symbol C, implies summation modulo m. This &mg This paper discusses computation over finite rings using recursive reduction networks modelled after the general neural network approach. In this case the neurons are arithmetic elements that have modulo operator characteristics, rather than the usual non-linear, saturating characteristics of learning and associative memory neural network applications. Following an analysis of finite ring arithmetic, a computing model is built based on an iterative, bit-level, modulo reduction scheme, from which is extracted a basic operator. A corresponding sub-net is designed to implement this operator, and its effectiveness is illustrated with an example of a Chinese Remainder Theorem (CRV convener for RNS arithmetic. A structure is developed that is suitable for implementing at the full-custom, or gate array level, and example VLSI layouts illustrate that the technique is efficient Recently, a novel neural-like network computing mechanism for finite ring computational system has been developed, and its effectiveness has been illustrated by simulations[ll. In order to put the technique into practice, an imponant task is to develop an architecture that efficiently maps the basic principles of the FRNN to the VLSI medium. In this paper, we develop such a VLSI architecture,and show that the entire circuitry can be constructed with a sinele cell tvoe.The efficiencv of the