Mathematical Models of Critical Soft Error in Synchronous and Self-Timed Pipeline

Igor Sokolov, Yuri Stepchenkov (), Yuri Diachenko and Dmitry Khilko
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Igor Sokolov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russia
Yuri Stepchenkov: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russia
Yuri Diachenko: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russia
Dmitry Khilko: Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russia

Mathematics, 2025, vol. 13, issue 5, 1-15

Abstract: This paper analyzes the impact of a single soft error on the performance of a synchronous and self-timed pipeline. A nuclear particle running through the integrated circuit body is considered the most probable soft error source. The existing estimates show that self-timed circuits offer an advantage in terms of single soft error tolerance. The paper proves these estimates on the basis of a comparative probability analysis of a critical fault in two types of pipelines. The mathematical models derived in the paper describe the probability of a critical fault depending on the circuit’s characteristics, its operating discipline, and the soft error parameters. The self-timed pipeline operates in accordance with a two-phase discipline, based on the request–acknowledge interaction within the pipeline’s stages, which provides it with increased immunity to soft errors. Quantitative calculations performed on the basis of the derived mathematical models show that the self-timed pipeline has about 6.1 times better tolerance to a single soft error in comparison to its synchronous counterpart. The obtained results are in good agreement with empirical estimates of the soft error tolerance level of synchronous and self-timed circuits.

Keywords: synchronous pipeline; self-timed pipeline; soft error tolerance; single soft error; probability; Gauss law distribution; stochastic mathematical model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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