Four Reduced Precision Redundancy by Approximation (4RPA): Design and Analysis of 4-Module Systems

Abstract

Reduced precision redundancy (RPR) has been widely used as an alternative to triple modular redundancy to enhance reliable computing with tolerance to errors and faults; however, it still has stringent requirements for power and area as well as complex decision hardware. Recent works have focused on reduced precision redundancy by approximation (RPA) to attain lower delay, smaller power dissipation, and smaller area because RPA operates using only logic operations (so no arithmetic unit is involved as decision hardware). The proposed RPA-based designs can tolerate up to two erroneous modules, so adding a further data word to the decision process compared to previous three-module based RPA designs found in the technical literature. The proposed designs consist of four modules, two exact data words and two approximate data words (denoted as 2E2A), where E (A) stands for exact (approximate) data words. The probability of generating an output exact data word by RPA under one and both data parts of erroneous modules is analytically found; simulation results are also provided. The difference between simulated and analytical probabilities is at most 7.3%. Figures of merits (such as delay, power dissipation, and area) of the proposed designs are assessed by simulation and compared with RPR and the three-module RPA. The proposed designs incur a similar delay as a three-module RPA; power dissipation and area (due to the additional module) can be adjusted by increasing the number of approximate bits while still retaining a two-module error tolerance. This article also presents its application to image processing, and arithmetic (i.e., the addition operation); the results show that the proposed schemes are very efficient.