Bounds and Code Constructions for Partially Defect Memory Cells

TL;DR

This paper introduces a new coding scheme for partially stuck memory cells that improves data masking and error correction, along with theoretical bounds that demonstrate its advantages over previous methods.

Contribution

It generalizes existing masking codes to include error correction and derives bounds showing the effectiveness of the new constructions.

Findings

New code construction for masking and error correction in partially stuck cells

The new construction achieves higher rates than previous methods for many parameters

Numerical analysis shows the new codes outperform Gilbert-Varshamov bounds in certain cases

Abstract

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.