部分缺陷存储单元的边界和代码构造
Bounds and Code Constructions for Partially Defect Memory Cells
摘要：
本文考虑了所谓的部分卡住存储单元的编码。这样的存储单元只能存储部分信息，因为它们的一些电平由于例如，磨损。首先，我们提出了一种新的代码结构，用于掩蔽这种部分卡住的细胞，同时还纠正错误。这种构造（对于具有$q >2$电平的单元）是通过推广[1]中现有的仅掩蔽构造（基于二进制码）来实现的，以校正错误。与[2]中的先前构造相比，我们的新构造对于许多参数集实现了更大的速率。其次，我们推导出一个球包装（任何数量的$u$部分卡住的细胞）和Gilbert-Varshamov界（$u<q$部分卡住的细胞）的代码，可以掩盖一定数量的部分卡住的细胞和纠正错误。新的边界和我们以前的PSMCs的情况下$u<q$在[2]中的构造之间的数值比较表明，我们的构造位于Gilbert-Varshamov的几个代码参数的界以上。
英文摘要：
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.
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