Statistical timing and power analysis of VLSI considering non-linear dependence

Lerong Cheng, Wenyao Xu, Fengbo Ren, Fang Gong, Puneet Gupta, Lei He

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Majority of practical multivariate statistical analysis and optimizations model interdependence among random variables in terms of the linear correlation. Though linear correlation is simple to use and evaluate, in several cases non-linear dependence between random variables may be too strong to ignore. In this paper, we propose polynomial correlation coefficients as simple measure of multi-variable non-linear dependence and show that the need for modeling non-linear dependence strongly depends on the end function that is to be evaluated from the random variables. Then, we calculate the errors in estimation resulting from assuming independence of components generated by linear de-correlation techniques, such as PCA and ICA. The experimental results show that the error predicted by our method is within 1% error compared to the real simulation of statistical timing and leakage analysis. In order to deal with non-linear dependence, we further develop a target-function-driven component analysis algorithm (FCA) to minimize the error caused by ignoring high order dependence. We apply FCA to statistical leakage power analysis and SRAM cell noise margin variation analysis. Experimental results show that the proposed FCA method is more accurate compared to the traditional PCA or ICA.

Original languageEnglish (US)
Pages (from-to)487-498
Number of pages12
JournalIntegration, the VLSI Journal
Issue number4
StatePublished - Sep 2014
Externally publishedYes


  • Statistical modeling
  • VLSI
  • Yield analysis

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Electrical and Electronic Engineering


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