论文标题
部分缺陷存储单元的界限和代码构造
Bounds and Code Constructions for Partially Defect Memory Cells
论文作者
论文摘要
本文考虑编码所谓的部分卡住的存储单元。这样的记忆单元只能存储部分信息，因为由于磨损，无法使用它们的某些水平。首先，我们提出了一个新的代码构建，用于掩盖这种部分卡住的单元，同时纠正错误。这种结构（对于$ q> 2 $级别的单元格）是通过在[1]中（基于二进制代码）中概括现有的仅掩模构造来纠正错误来实现的。与[2]中的先前结构相比，我们的新结构在许多参数方面达到了更高的速率。其次，我们得出了一个球体包装（任何数量的$ u $部分卡住的单元格）和吉尔伯特·瓦尔沙莫夫（Gilbert-Varshamov Bond）（$ u <q $部分卡住的单元），以用于可以掩盖一定数量的部分卡住单元格并纠正错误并纠正错误的代码。新界限与我们先前对案例的PSMC构建[2]中的PSMC之间的数值比较表明，我们的构造位于Gilbert-Varshamov类似于几个代码参数的Gilbert-Varshamov样。
This paper considers coding for so-called partially stuck memory cells. Such memory cells can only store partial information as some of their levels cannot be used due to, e.g., wear out. First, we present a new code construction for masking such partially stuck cells while additionally correcting errors. This construction (for cells with $q >2$ levels) is achieved by generalizing an existing masking-only construction in [1] (based on binary codes) to correct errors as well. Compared to previous constructions in [2], our new construction achieves larger rates for many sets of parameters. Second, we derive a sphere-packing (any number of $u$ partially stuck cells) and a Gilbert-Varshamov bound ($u<q$ partially stuck cells) for codes that can mask a certain number of partially stuck cells and correct errors additionally. A numerical comparison between the new bounds and our previous construction of PSMCs for the case $u<q$ in [2] shows that our construction lies above the Gilbert-Varshamov-like bound for several code parameters.
