Bounds and Code Constructions for Partially Defect Memory Cells,arXiv - CS - Data Structures and Algorithms

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Bounds and Code Constructions for Partially Defect Memory Cells
arXiv - CS - Data Structures and Algorithms Pub Date : 2020-09-14 , DOI: arxiv-2009.06512
Haider Al Kim, Sven Puchinger, Antonia Wachter-Zeh

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

中文翻译：

部分缺陷存储单元的边界和代码构造

本文考虑对所谓的部分卡住的存储单元进行编码。这种存储单元只能存储部分信息，因为它们的某些级别由于例如磨损而无法使用。首先，我们提出了一种新的代码结构，用于屏蔽这种部分卡住的单元，同时额外纠正错误。这种构造（对于 $q >2$ 级别的单元格）是通过将 [1]（基于二进制代码）中现有的仅掩码构造泛化来纠正错误来实现的。与 [2] 中以前的构造相比，我们的新构造在许多参数集上实现了更高的速率。其次，我们推导出球形堆积（任意数量的 $u$ 部分卡住的单元格）和 Gilbert-Varshamov 界限（$u$

更新日期：2020-10-07

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