In this paper, we propose a novel methodology for statistical SRAM design and analysis. It relies on an efficient form of importance sampling, mixture importance sampling. The method is comprehensive, computationally efficient and the results are in excellent agreement with those obtained via standard Monte Carlo techniques. All this comes at significant gains in speed and accuracy, with speedup of more than 100/spl times/ compared to regular Monte Carlo. To the best of our knowledge, this is the first time such a methodology is applied to the analysis of SRAM designs.

/pdf/mixture-importance-sampling-and-its-application-to-the-i8j6h1an62.pdf

Mixture importance sampling and its application to the analysis of SRAM designs in the presence of rare failure events

At the nanoscale, no circuit parameters are truly deterministic; most quantities of practical interest present themselves as probability distributions. Thus, Monte Carlo techniques comprise the strategy of choice for statistical circuit analysis. There are many challenges in applying these techniques efficiently: circuit size, nonlinearity, simulation time, and required accuracy often conspire to make Monte Carlo analysis expensive and slow. Are we-the integrated circuit community-alone in facing such problems? As it turns out, the answer is “no.” Problems in computational finance share many of these characteristics: high dimensionality, profound nonlinearity, stringent accuracy requirements, and expensive sample evaluation. We perform a detailed experimental study of how one celebrated technique from that domain-quasi-Monte Carlo (QMC) simulation-can be adapted effectively for fast statistical circuit analysis. In contrast to traditional pseudorandom Monte Carlo sampling, QMC uses a (shorter) sequence of deterministically chosen sample points. We perform rigorous comparisons with both Monte Carlo and Latin hypercube sampling across a set of digital and analog circuits, in 90 and 45 nm technologies, varying in size from 30 to 400 devices. We consistently see superior performance from QMC, giving 2× to 8× speedup over conventional Monte Carlo for roughly 1% accuracy levels. We present rigorous theoretical arguments that support and explain this superior performance of QMC. The arguments also reveal insights regarding the (low) latent dimensionality of these circuit problems; for example, we observe that over half of the variance in our test circuits is from unidimensional behavior. This analysis provides quantitative support for recent enthusiasm in dimensionality reduction of circuit problems.

Why Quasi-Monte Carlo is Better Than Monte Carlo or Latin Hypercube Sampling for Statistical Circuit Analysis

Circuit reliability under random parametric variation is an area of growing concern. For highly replicated circuits, e.g., static random access memories (SRAMs), a rare statistical event for one circuit may induce a not-so-rare system failure. Existing techniques perform poorly when tasked to generate both efficient sampling and sound statistics for these rare events. Statistical blockade is a novel Monte Carlo technique that allows us to efficiently filter-to block-unwanted samples that are insufficiently rare in the tail distributions we seek. The method synthesizes ideas from data mining and extreme value theory and, for the challenging application of SRAM yield analysis, shows speedups of 10 - 100 times over standard Monte Carlo.

/pdf/statistical-blockade-very-fast-statistical-simulation-and-1rmg7rpubz.pdf

Statistical Blockade: Very Fast Statistical Simulation and Modeling of Rare Circuit Events and Its Application to Memory Design

Circuit reliability under statistical process variation is an area of growing concern. For highly replicated circuits such as SRAMs and flip flops, a rare statistical event for one circuit may induce a not-so-rare system failure. Existing techniques perform poorly when tasked to generate both efficient sampling and sound statistics for these rare events. Statistical blockade is a novel Monte Carlo technique that allows us to efficiently filter - to block - unwanted samples insufficiently rare in the tail distributions we seek. The method synthesizes ideas from data mining and extreme value theory, and shows speed-ups of 10times - 100times over standard Monte Carlo

/pdf/statistical-blockade-a-novel-method-for-very-fast-monte-3oy1e4ex4j.pdf

Statistical blockade: a novel method for very fast Monte Carlo simulation of rare circuit events, and its application

Statistical Blockade: A Novel Method for Very Fast Monte Carlo Simulation of Rare Circuit Events, and its Application

The efficiency of several variance reduction techniques (in particular, importance sampling, stratified sampling, and control variates) are studied with respect to their application in estimating circuit yields. This study suggests that one essentially has to have a good approximation of the region of acceptability in order to achieve significant variance reduction. Further, all the methods considered are based, either explicitly or implicity, on the use of a model. The control variate method appears to be more practical for implementation in a general purpose statistical circuit analysis program. Stratified sampling is the most simple to implement, but yields only very modest reductions in the variance of the yield estimator. Lastly, importance sampling is very useful when there are few parameters and the yield is very high or very low; however, a good practical technique for its implementation, in general, has not been found.

A Study of Variance Reduction Techniques for Estimating Circuit Yields

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A Study of Variance Reduction Techniques for Estimating Circuit Yields