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

• We propose polynomial correlation coefficients as a simple measure of non-linear dependence among random variables.
• We show that importance of modeling non-linear dependence strongly depends on what is to be done with the random variables, i.e., the end function of random variables that is to be estimated.
• We develop closed form expressions to calculate error in estimation of arbitrary moments (e.g., mean, variance, skewness) of the to-be estimated function as a result of assuming true independence of components generated by PCA or ICA techniques.
• We develop a target function driven component analysis algorithm (we refer to as FCA) which minimizes the error caused by ignoring non-linear dependence without increasing the computational complexity of statistical analysis.

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.