Decision Directed Estimation of Threshold Voltage Distribution in NAND Flash Memory
High-density NAND flash memory suffers from the data retention problem because even small charge leakage incurs a large threshold voltage shift as the transistor size shrinks. In this paper, we develop a decision directed estimation (DDE) algorithm to know the effects of charge leakage in NAND flash memory using the error pattern of the accessed data. While the conventional sensing directed estimation (SDE) method demands extra memory sensing to know the signal distribution, the proposed DDE algorithm induces no sensing overheads. The proposed algorithm approximates the threshold voltage distribution as a Gaussian mixture and also assumes that the increase of standard deviation is linearly proportional to the amount of mean shift. Since the threshold voltage distribution in real devices is not a perfect Gaussian mixture, we conduct error analysis of the proposed algorithm to examine the sources of estimation errors and quantify their impact on the estimation accuracy. We also present a combined estimation scheme that employs the DDE and the SDE algorithms to minimize the number of memory sensing operations while maintaining high estimation accuracy. The developed algorithm is applied to both simulated and real NAND flash memory, and the estimation errors are measured.