An information theoretic framework to compute the MAX/MIN operations in parameterized statistical timing analysis

The MAX/MIN algorithms play a crucial role in development of efficient and accurate parameterized statistical static timing analysis (SSTA) tools. Most of the existing techniques to compute the MAX/MIN in parameterized SSTA model spatial and path-based statistical dependences of variation sources using the second order statistical methods. Unfortunately, such methods have limited capabilities to measure the statistical relations between random variables (RVs). This results in significant decreasing the accuracy of the statistical timing. In contrast, information theory (IT) provides powerful techniques that can take into account complete structure of the statistical relations of RVs and allow a natural PDF-based analysis of the probabilistic dependences. So, in this paper we propose a new framework to perform the MAX/MIN operations based on IT concepts. The key ideas behind our framework are 1) exploiting information entropy to measure unconditional equivalence between actual MAX/MIN outputs and their approximate parameterized representations, and 2) using mutual information to measure equivalence of actual and parameterized MAX/MIN outputs from the viewpoint of their statistical relations to process variations. The experimental results validate the correctness and demonstrate a high accuracy of the new IT-based method to compute the MAX/MIN.