Ensemble dependent matrix methodology for probabilistic-based fault-tolerant nanoscale circuit design

Two probabilistic-based models, namely the Ensemble-Dependent Matrix model [1][3] and the Markov Random Field model [2], have been proposed to deal with faults in nanoscale system. The MRF design can provide excellent noise tolerance in nanoscale circuit design. However, it is complicated to be applied to model circuit behavior at system level. Ensemble dependent matrix methodology is more effective and suitable for CAD tools development and to optimize nanoscale circuit and system design. In this paper, we show that the ensemble-dependent matrices describe the actual circuit performances when signal errors are present. We then propose a new criterion to compare circuit error-tolerance capability. We also prove that the Matrix model and the Markov model converge when signals are digital