Stochastic behavioral modeling of analog/mixed-signal circuits by maximizing entropy

Maximum entropy (MAXENT) is a powerful and flexible method for estimating the arbitrary probabilistic distribution of a stochastic variable with moment constraints. However, modeling the stochastic behavior of analog/mixed-signal (AMS) circuits using MAXENT is still unknown. In this paper, we present a MAXENT based approach to efficiently model the arbitrary behavioral distribution of AMS circuits with high accuracy. The exact behavioral distribution can be approximated by a product of exponential functions with different Lagrangian multipliers. The closest approximation can be obtained by maximizing Shannon's information entropy subject to moment constraints, leading to a nonlinear system. Classic Newton's method is used to solve the nonlinear system for the Lagrangian multipliers, which can further recover the arbitrary behavioral distribution of AMS circuits. Extensive experiments on different circuits demonstrate that the proposed MAXENT based approach offers better stability and improves the accuracy up to 110% when compared to previous AWE-based moment matching approaches, and offers up to 592x speedup when compared to Monte Carlo method.

[1]  Jiang Hu,et al.  Standard cell characterization considering lithography induced variations , 2006, 2006 43rd ACM/IEEE Design Automation Conference.

[2]  P. Lugli,et al.  The Monte Carlo Method for Semiconductor Device Simulation , 1990 .

[3]  Lei He,et al.  Stochastic Behavioral Modeling and Analysis for Analog/Mixed-Signal Circuits , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[4]  Sani R. Nassif,et al.  Modeling and analysis of manufacturing variations , 2001, Proceedings of the IEEE 2001 Custom Integrated Circuits Conference (Cat. No.01CH37169).

[5]  H J Gundersen,et al.  The efficiency of systematic sampling in stereology and its prediction * , 1987, Journal of microscopy.

[6]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[7]  E. L. Lehmann,et al.  Theory of point estimation , 1950 .

[8]  Sarma B. K. Vrudhula,et al.  Hermite Polynomial Based Interconnect Analysis in the Presence of Process Variations , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  Ximing Wu,et al.  Calculation of Maximum Entropy Densities with Application to Income Distribtuions , 2002 .

[10]  R. W. Kelsall,et al.  The Monte Carlo method for semiconductor device simulation , 1995 .

[11]  L. Pileggi,et al.  Asymptotic probability extraction for non-normal distributions of circuit performance , 2004, IEEE/ACM International Conference on Computer Aided Design, 2004. ICCAD-2004..

[12]  W. C. Elmore.  The Transient Response of Damped Linear Networks with Particular Regard to Wideband Amplifiers , 1948 .

[13]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[14]  B. Chen,et al.  Computing Maximum Entropy Densities: A Hybrid Approach , 2010 .

[15]  M. Nakhla,et al.  Asymptotic Waveform Evaluation: And Moment Matching for Interconnect Analysis , 1993 .

[16]  L. Pileggi,et al.  Asymptotic probability extraction for non-normal distributions of circuit performance , 2004, ICCAD 2004.

[17]  Kishore Singhal,et al.  Computer Methods for Circuit Analysis and Design , 1983 .

[18]  L. Mead,et al.  Maximum entropy in the problem of moments , 1984 .

[19]  T. Hughes,et al.  Signals and systems , 2006, Genome Biology.

[20]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[21]  Hao Yu,et al.  Stochastic analog circuit behavior modeling by point estimation method , 2011, ISPD '11.

[22]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[23]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[24]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[25]  Douglas J. Miller,et al.  Maximum entropy econometrics: robust estimation with limited data , 1996 .

[26]  Lara Dolecek,et al.  A fast estimation of SRAM failure rate using probability collectives , 2012, ISPD '12.