Selective Redundancy: Evaluation of Temporal Reliability Enhancement Scheme for Nanoelectronic Circuits

Abstract

Devices in nano-regime have inherent propensity for errors due to their very stochastic nature there by making Reliability modeling and evaluation as one of the major issues. To account for these issues, probabilistic models would be more appropriate than deterministic models as they can represent the transient nature of the nano-devices perfectly. In this work, we have used a probabilistic model to study the erroneous behavior of digital logic circuits. Inference on this probabilistic model is performed using junction tree algorithm. Using the unique feature of the junction tree, namely <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">backtracking</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">or</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Two</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">phase</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">propagation</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">of</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">evidence</i> , we were able to rank or <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">select</i> a subset of input instantiations which are more likely to aggregate error at the output for any given circuit. Using these results we have performed a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">temporal</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">redundancy</i> scheme using triple temporal redundancy (TTR). As safety- centric designs need worst case behavior study, we have focused on both worst case and average behavior. We have also performed a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spatial</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">redundancy</i> scheme using cascaded triple modular redundancy (CTMR) [9], and evaluated the results with those of the temporal redundancy scheme with respect to standard ISCAS'85 benchmark circuits and suggested the best error mitigation scheme for both average and maximum case. Experimental results show that spatial redundancy scheme, irrespective of technique used, is effective in mitigating average output error. Where as Temporal redundancy scheme has out- weighted spatial redundancy scheme in mitigating maximum error.