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A General Framework to Perform the MAX/MIN Operations in Parameterized Statistical Timing Analysis Using Information Theoretic Concepts

机译:使用信息论概念在参数化统计时序分析中执行MAX / MIN运算的通用框架

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摘要

As integrated circuit technologies are scaled down to the nanometer regime, process variations have increasing impact on circuit timing. To address this issue, parameterized statistical static timing analysis (SSTA) has been recently developed. In parameterized SSTA, process variations are represented as random variables (RVs) and timing quantities (delays and others) are expressed as functions of these variables. Most of the existing algorithms to compute the $MAX/MIN$ operations in parameterized SSTA model spatial and path-based statistical dependencies of variation sources using the second-order statistical methods. Unfortunately, such methods have limited capabilities to determine statistical relations between RVs. This results in decreasing the accuracy of the $MAX/MIN$ algorithms, especially when process parameters follow non-Gaussian probability density functions (PDFs) and/or affect timing quantities nonlinearly. In contrast, information theory (IT) provides powerful techniques that allow a natural PDF-based analysis of probabilistic relations between RVs. 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 an actual $MAX/MIN$ output and its approximate parameterized representation, 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. We construct a general IT-based $MAX/MIN$ algor-n-nithm that allows a number of particular realizations accounting for statistical properties of parameterized RVs. The experimental results validate the correctness and demonstrate a high accuracy of the new IT-based approach to compute the $MAX/MIN$.
机译:随着集成电路技术的规模缩小到纳米级,工艺变化对电路时序的影响越来越大。为了解决这个问题,最近开发了参数化统计静态时序分析(SSTA)。在参数化的SSTA中,过程变化表示为随机变量(RV),定时量(延迟等)表示为这些变量的函数。现有的大多数算法都可以在参数化SSTA模型的基于空间和路径的统计依存关系中计算 $ MAX / MIN $ 操作变量来源使用二阶统计方法。不幸的是,这种方法确定RV之间的统计关系的能力有限。这会导致 $ MAX / MIN $ 算法的准确性下降,尤其是当过程参数遵循非高斯概率密度函数时(PDF)和/或非线性影响时序量。相反,信息理论(IT)提供了强大的技术,可以对RV之间的概率关系进行基于PDF的自然分析。因此,在本文中,我们提出了一个基于IT概念执行 $ MAX / MIN $ 操作的新框架。我们框架背后的关键思想是:1)利用信息熵来衡量实际 $ MAX / MIN $ 输出之间的无条件等效及其近似的参数化表示形式,以及2)使用互信息来衡量实际和参数化的 $ MAX / MIN $ 输出的等价性他们对过程变化的统计关系的观点。我们构造了一个基于IT的常规 $ MAX / MIN $ algor-n-nithm,该算法允许许多特殊的实现参数化RV的统计特性。实验结果验证了这种正确性,并证明了基于IT的新方法计算 $ MAX / MIN $ 的准确性。 。

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