Codes for Partially Stuck-At Memory Cells
Codes for Partially Stuck-At Memory Cells
复制标题
部分卡住的存储单元的代码
DOI：
10.1109/tit.2015.2512581
复制
发表时间：
2015
影响因子：
2.5
通讯作者：
Eitan Yaakobi
中科院分区：
文献类型：
--
作者：
A. Wachter;Eitan Yaakobi
在本文中，我们研究了一种新的缺陷存储单元模型，称为部分固定存储单元，这是由非易失性存储器，如闪存和相变存储器中的多电平单元的行为的动机。如果一个单元可以存储q个电平0，1，.，q - 1，我们说它部分地卡在s层，其中1 ≤ s ≤ q-1，如果它只能存储至少为s的值。我们遵循常见的设置，其中编码器知道部分stuckat单元的位置和电平，而解码器不知道。本文的主要贡献是研究了部分固定细胞的掩蔽码。我们首先推导出这种代码的冗余度的上下界。上界是基于两个平凡的建设。然后，我们提出了三个代码的结构在一个字母表的大小为q，首先考虑的情况下，细胞是部分卡在水平s = 1。第一种构造适用于u <; q，并且如果ii + 1整除q，则是渐近最优的。第二种构造使用矩阵的简化的行阶梯形式来生成针对u ≥ q的情况的代码，并且第三种构造通过使用代码来解决任意ii的情况，该代码屏蔽二进制固定单元。然后，我们将展示如何将所有结构推广到任意卡住的水平。此外，我们研究了双缺陷模型，其中细胞不能达到更高的水平，并表明，代码部分固定在细胞可以用来掩盖这种类型的缺陷。最后，我们分析了部分固定记忆通道的容量，并研究了我们的构式离容量有多远。
In this paper, we study a new model of defect memory cells, called partially stuck-at memory cells, which is motivated by the behavior of multi-level cells in non-volatile memories, such as flash memories and phase change memories. If a cell can store the q levels 0, 1,... ,q - 1, we say that it is partially stuck-at level s, where 1 ≤ s ≤ q -1, if it can only store values, which are at least s. We follow the common setup where the encoder knows the positions and levels of the partially stuckat cells whereas the decoder does not. Our main contribution in this paper is the study of codes for masking ii partially stuck-at cells. We first derive lower and upper bounds on the redundancy of such codes. The upper bounds are based on two trivial constructions. We then present three code constructions over an alphabet of size q, by first considering the case where the cells are partially stuck-at level s = 1. The first construction works for u <; q and is asymptotically optimal if ii + 1 divides q. The second construction uses the reduced row echelon form of matrices to generate codes for the case u ≥ q, and the third construction solves the case of arbitrary ii by using codes, which mask binary stuck-at cells. We then show how to generalize all constructions to arbitrary stuck levels. Furthermore, we study the dual defect model, in which cells cannot reach higher levels, and show that codes for partially stuck-at cells can be used to mask this type of defects as well. Last, we analyze the capacity of the partially stuck-at memory channel and study how far our constructions are from the capacity.