Efficient SRAM Failure Rate Prediction via Gibbs Sampling
Efficient SRAM Failure Rate Prediction via Gibbs Sampling
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DOI：
10.1145/2024724.2024769
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发表时间：
2011-06
影响因子：
2.9
通讯作者：
Shupeng Sun;Yamei Feng;Changdao Dong;Xin Li
中科院分区：
文献类型：
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作者：
Shupeng Sun;Yamei Feng;Changdao Dong;Xin Li
由于SRAM单元的故障率极低，SRAM的统计分析已成为一个具有挑战性的问题。在本文中，我们开发了一种有效的重要抽样算法来捕捉SRAM单元的罕见故障事件。特别是，我们采用了统计学中的Gibbs抽样技术，以较低的计算成本(即少量的晶体管级模拟)找到了重要抽样的最优概率分布。所提出的Gibbs抽样方法应用集成优化引擎，通过对一维概率分布序列进行抽样，在笛卡尔或球面坐标系中自适应地探索失效区域。为了使Gibbs抽样法在SRAM故障率预测中高效、准确，对一维随机抽样和起点选择等实现问题进行了深入研究。我们对90 nm SRAM单元的实验结果表明，当需要较高的预测精度时(例如，99%可信区间定义的相对误差达到5%)，所提出的Gibbs采样方法的运行时间加速比达到其他技术水平的1.4-4.9倍。此外，我们还给出了一个重要的例子，在传统方法不起作用的情况下，所提出的Gibbs抽样算法能够准确地估计出正确的失效概率。
Statistical analysis of SRAM has emerged as a challenging issue because the failure rate of SRAM cells is extremely small. In this paper, we develop an efficient importance sampling algorithm to capture the rare failure event of SRAM cells. In particular, we adapt the Gibbs sampling technique from the statistics community to find the optimal probability distribution for importance sampling with a low computational cost (i.e., a small number of transistor-level simulations). The proposed Gibbs sampling method applies an integrated optimization engine to adaptively explore the failure region in a Cartesian or spherical coordinate system by sampling a sequence of 1-D probability distributions. Several implementation issues such as 1-D random sampling and starting point selection are carefully studied to make the Gibbs sampling method efficient and accurate for SRAM failure rate prediction. Our experimental results of a 90 nm SRAM cell demonstrate that the proposed Gibbs sampling method achieves 1.4-4.9× runtime speedup over other state-of-the-art techniques when a high prediction accuracy is required (e.g., the relative error defined by the 99% confidence interval reaches 5%). In addition, we further demonstrate an important example for which the proposed Gibbs sampling algorithm accurately estimates the correct failure probability, while the traditional techniques fail to work.