Parallel Algorithms for Residue Scaling and Error Correction in Residue Arithmetic

Hao-Yung Lo,Ting-Wei Lin

doi:10.4236/wet.2013.44029

Abstract

In this paper, we present two new algorithms in residue number systems for scaling and error correction. The first algorithm is the Cyclic Property of Residue-Digit Difference (CPRDD). It is used to speed up the residue multiple error correction due to its parallel processes. The second is called the Target Race Distance (TRD). It is used to speed up residue scaling. Both of these two algorithms are used without the need for Mixed Radix Conversion (MRC) or Chinese Residue Theorem (CRT) techniques, which are time consuming and require hardware complexity. Furthermore, the residue scaling can be performed in parallel for any combination of moduli set members without using lookup tables.

Highlights

Because the residue number system (RNS) operations on each residue digit are independent and carry free property of addition between digits, they can be used in highspeed computations such as addition, subtraction and multiplication
Both of these two algorithms are used without the need for Mixed Radix Conversion (MRC) or Chinese Residue Theorem (CRT) techniques, which are time consuming and require hardware complexity
In [12,13,14,15,16] an algorithm for scaling and a residue digital error correction based on mixed radix conversion (MRC) was proposed

Summary

Introduction

Because the residue number system (RNS) operations on each residue digit are independent and carry free property of addition between digits, they can be used in highspeed computations such as addition, subtraction and multiplication. To increase the reliability of these operations, a number of redundant moduli were added to the original RNS moduli [RRNS] This will allow the RNS system the capability of error detection and correction. In [12,13,14,15,16] an algorithm for scaling and a residue digital error correction based on mixed radix conversion (MRC) was proposed. The first algorithm is used for these purposes, through the residue digit difference cyclic property (CPRDD) within the range of 0 x M t 1 , where. This paper is organized as follows: Section II will describe the scheme the cyclic property of residue digit difference (CPRDD).

Error Detection and Correction Using

Scaling with Error Correction k3 6

Conclusions