Efficient moment estimation with extremely small sample size via bayesian inference for analog/mixed-signal validation
A critical problem in pre-Silicon and post-Silicon validation of analog/mixed-signal circuits is to estimate the distribu- tion of circuit performances, from which the probability of failure and parametric yield can be estimated at all circuit configurations and corners. With extremely small sample size, traditional estimators are only capable of achieving a very low confidence level, leading to either over-validation or under-validation. In this paper, we propose a multi- population moment estimation method that significantly im- proves estimation accuracy under small sample size. In fact, the proposed estimator is theoretically guaranteed to out- perform usual moment estimators. The key idea is to ex- ploit the fact that simulation and measurement data col- lected under different circuit configurations and corners can be correlated, and are conditionally independent. We exploit such correlation among different populations by employing a Bayesian framework, i.e., by learning a prior distribution and applying maximum a posteriori estimation using the prior. We apply the proposed method to several datasets including post-silicon measurements of a commercial high- speed I/O link, and demonstrate an average error reduction of up to 2×, which can be equivalently translated to signifi- cant reduction of validation time and cost. Copyright © 2013 ACM.
