### ROMJIST Volume 20, No. 2, 2017, pp. 161-176, Paper no. 557/2017

**Vladimir CIRIC, Ivan MILENTIJEVIC, Aleksandar CVETKOVIC**

*The Signiﬁcant Bits Propagation Model in Fault-Tolerant System Design*

**ABSTRACT: **With current VLSI technology approaching the scale of individual atoms, and nanotechnology fabrication processes such as self-assembly, the resulting structures become less predictable and less prone to fabrication defects. Fortunately, there are a lot of technical applications that doesn’t require 100% correctness of the output. This fact can be used to increase the fabrication yield and reduce unnecessary hardware overhead. For example, in some DSP applications such as audio or video processing, correctness of the operation can be deﬁned as a threshold up to which a user will not notice the error. The threshold is usually measured as a quantity of correct information in the output, i.e. the number of signiﬁcant digits. In this paper we propose a novel technique for mathematical modeling of signiﬁcant digits propagation under the presence of errors. The model incorporates Euclidean metric, and it can be used to obtain the difference in the number of signiﬁcant digits between any two given intermediate results within the system. The information about loss of signiﬁcant digits, due to the propagation of error through the architecture, will be used to design a partially fault tolerant system. The model is based on Min-Plus algebra, which is chosen to formalize structural dependencies. The evaluation of the proposed model is performed on the example of semi-systolic bit-plane array for FIR ﬁltering, with error deﬁned by Euclidean metric. It is shown that proposed model leads to the signiﬁcant reduction of unavoidable fault-tolerant hardware overhead.**KEYWORDS: **Fault-tolerant systems, Tropical algebra, Error propagation, FIR filter design**Read full text (pdf)**