Wang Cheng, Mei Zhen, Li Jun, Shu Feng, He Xuan, Kong Lingjun
School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China.
Entropy (Basel). 2023 Jun 21;25(7):965. doi: 10.3390/e25070965.
As the technology scales down, two-dimensional (2D) NAND flash memory has reached its bottleneck. Three-dimensional (3D) NAND flash memory was proposed to further increase the storage capacity by vertically stacking multiple layers. However, the new architecture of 3D flash memory leads to new sources of errors, which severely affects the reliability of the system. In this paper, for the first time, we derive the channel probability density function of 3D NAND flash memory by taking major sources of errors. Based on the derived channel probability density function, the mutual information (MI) for 3D flash memory with multiple layers is derived and used as a metric to design the quantization. Specifically, we propose a dynamic programming algorithm to jointly optimize read-voltage thresholds for all layers by maximizing the MI (MMI). To further reduce the complexity, we develop an MI derivative (MID)-based method to obtain read-voltage thresholds for hard-decision decoding (HDD) of error correction codes (ECCs). Simulation results show that the performance with jointly optimized read-voltage thresholds can closely approach that with read-voltage thresholds optimized for each layer, with much less read latency. Moreover, the MID-based MMI quantizer almost achieves the optimal performance for HDD of ECCs.
随着技术的不断缩小，二维（2D）NAND闪存已达到其瓶颈。三维（3D）NAND闪存被提出以通过垂直堆叠多层来进一步增加存储容量。然而，3D闪存的新架构导致了新的错误源，这严重影响了系统的可靠性。在本文中，我们首次通过考虑主要错误源推导了3D NAND闪存的通道概率密度函数。基于推导的通道概率密度函数，推导了多层3D闪存的互信息（MI）并将其用作设计量化的指标。具体而言，我们提出了一种动态规划算法，通过最大化MI（MMI）来联合优化所有层的读取电压阈值。为了进一步降低复杂度，我们开发了一种基于MI导数（MID）的方法来获得用于纠错码（ECC）硬判决解码（HDD）的读取电压阈值。仿真结果表明，联合优化读取电压阈值的性能可以非常接近为每层优化读取电压阈值的性能，同时读取延迟要少得多。此外，基于MID的MMI量化器几乎实现了ECC的HDD的最佳性能。
