Achievable-Rate-Aware Retention-Error Correction for Multi-Level-Cell NAND Flash Memory

Abstract

Owing to the effect of data retention noise in multi-level-cell NAND flash memory, the initial threshold-voltage distributions and read voltages can no longer be used to accurately calculate log-likelihood ratios (LLRs) as the retention time increases, thus causing retention errors. To solve this problem, we first utilize the so-called “correction factors” to optimize the LLR accuracy by maximizing the achievable rate of a flash-memory system without introducing extra memory-sensing operations. We further prove that the optimization of the correction factors is a convex optimization problem and can be solved analytically. To obtain the optimal correction factors, we propose two retention-error correction schemes, referred to as offline maximum-achievable-rate correction (MARC) algorithm and online MARC algorithm, which enable the flash-memory controller to utilize the corrected LLRs that are stored in a look-up table and correct the inaccurate LLRs in real time, respectively. Motivated by the variation characteristics of the threshold-voltage distributions, we also propose an enhanced expectation–maximization (EM) algorithm to reestimate their corresponding parameters, and then adjust the read voltages. By combining the enhanced EM algorithm with the MARC algorithms, an enhanced EM-based correction strategy is developed to further boost the retention-error endurance of flash memory while avoiding excessive memory-sensing overhead. Theoretical analyses and simulation results illustrate the superiority of the proposed correction mehtods in terms of the robustness against retention errors.