Abstract—This paper proposes a look up table (LUT) based fitting method to approximate the mixtures of various sloped-Gamma tail distributions by an adaptive segmentation Gaussian mixtures model (GMM). The concepts central to the proposed method are 1) LUT based fitting of all parameters of GMM and segmentation width and 2) adaptive segmentation of the long tailed distributions such that the log-likelihood of GMM in each partition is maximized. This allows the LUT based GMM model to apply any arbitrary shaped tail distribution even with multiple convex and concave folding curves, while eliminating the need of any EM iterations. It is verified that the LUT based GMM model can reduce the error of the fail-bit predictions by 2-orders of magnitude at the interest point of the fail probability of 10-12 which corresponds to the design point to realize a 99.9% yield of 1Gbit chips.
Index Terms—Mixtures of Gaussian, random telegraph noise, EM algorithm, look up table, long-tail distribution, fail-bit analysis, static random access memory, guard band design.
The authors are with the Information Intelligent System Fukuoka Institute of Technology, 3-30-1, Wajiro-Higashi, Higashi-ku, Fukuoka, Japan (e-mail: bd12002@ bene.fit.ac.jp, firstname.lastname@example.org).
Cite:Worawit Somha and Hiroyuki Yamauchi, "A Look up Table Based Adaptive Segmentation Gaussian Mixtures Model for Fitting Complex Long-Tail RTN Distributions," International Journal of Materials, Mechanics and Manufacturing vol. 1, no. 3, pp. 245-250, 2013.