Estimation of NAND Flash Memory Threshold Voltage Distribution for Optimum Soft-Decision Error Correction

Abstract

As the feature size of NAND flash memory decreases, the threshold voltage signal becomes less reliable, and its distribution varies significantly with the number of program-erase (PE) cycles and the data retention time. We have developed parameter estimation algorithms to find the means and variances of the threshold voltage distribution that is modeled as a Gaussian mixture. The proposed methods find the best-fit parameters by minimizing the squared Euclidean distance between the measured threshold voltage values and those obtained from the Gaussian mixture model. For the parameter estimation, the gradient descent (GD) and the Levenberg-Marquardt (LM) based methods are employed. The developed algorithms are applied to both simulated and real NAND flash memory. It is also demonstrated that error correction with the estimated mean and variance values yields much better performance when compared to the method that only updates the mean.