Read Reference Calibration and Tracking for Non-Volatile Flash Memories

The performance and reliability of nonvolatile NAND flash memories deteriorate as the number of program/erase cycles grows. The reliability also suffers from cell-to-cell interference, long data retention time, and read disturb. These processes effect the read threshold voltages. The aging of the cells causes voltage shifts which lead to high bit error rates (BER) with fixed predefined read thresholds. This work proposes two methods that aim on minimizing the BER by adjusting the read thresholds. Both methods utilize the number of errors detected in the codeword of an error correction code. It is demonstrated that the observed number of errors is a good measure for the voltage shifts and is utilized for the initial calibration of the read thresholds. The second approach is a gradual channel estimation method that utilizes the asymmetrical error probabilities for the one-to-zero and zero-to-one errors that are caused by threshold calibration errors. Both methods are investigated utilizing the mutual information between the optimal read voltage and the measured error values. Numerical results obtained from flash measurements show that these methods reduce the BER of NAND flash memories significantly.

The Runs Test for Autocorrelated Errors: Unacceptable Properties

The runs test is frequently recommended as a method of testing for nonindependent errors in time-series regression models. A Monte Carlo investigation was carried out to evaluate the empirical properties of this test using (a) several intervention and nonintervention regression models, (b) sample sizes ranging from 12 to 100, (c) three levels of α, (d) directional and nondirectional tests, and (e) 19 levels of autocorrelation among the errors. The results indicate that the runs test yields markedly asymmetrical error rates in the two tails and that neither directional nor nondirectional tests are satisfactory with respect to Type I error, even when the ratio of degrees of freedom to sample size is as high as .98. It is recommended that the test generally not be employed in evaluating the independence of the errors in time-series regression models.