Efficient Stochastic Pruning for Variability-Driven Dual-Vth Leakage Optimization

VLSI design optimization requires evaluation of different solutions, to determine the superiority of one over the other. Typically, a solution is superior if it has a better associated timing and cost. In the presence of fabrication variability, the timing and cost of a solution become random variables with spatial and functional correlations. Therefore the evaluation of solutions shall be performed probabilistically (probability that a solution has better cost and timing). In this paper we propose three methods for fast and accurate probabilistic superiority evaluation, for the dual-Vth leakage optmization problem under process variations. These include regular Monte Carlo simulation (as a basis of comparison), joint-pdf approximation using moment matching, and bound-based Conditional Monte Carlo simulation. Experimental results show that joint-pdf based approximation is very fast, however it results in suboptimal solutions due to lower accuracy. The Conditional Monte Carlo method is on average 20 times faster than regular Monte Carlo, but slower than approximating jointpdf. It also results in on average about 18% improvement in leakage, when compared to joint-pdf approximation. The Monte Carlo simulation is extremely slow and incapable of being incorporated in an optimization framework.