Error Correction for Partially Stuck Memory Cells

TL;DR

This paper introduces new coding schemes that efficiently mask partially stuck memory cells with multiple levels and correct errors, improving redundancy and code rates over previous methods.

Contribution

It presents two novel constructions for masking partially stuck cells with error correction, including a general method and one based on cyclic codes, extending to cases with more stuck cells.

Findings

New constructions require less redundancy than previous work.

Efficient error correction bounds using BCH codes.

Extended results to cases with more than q stuck cells.

Abstract

We present code constructions for masking $u$ partially stuck memory cells with $q$ levels and correcting additional random errors. The results are achieved by combining the methods for masking and error correction for stuck cells in [1] with the masking-only results for partially stuck cells in [2]. We present two constructions for masking $u<q$ cells and error correction: one is general and based on a generator matrix of a specific form. The second construction uses cyclic codes and allows to efficiently bound the error-correction capability using the BCH bound. Furthermore, we extend the results to masking $u\geq q$ cells. For $u>1$ and $q>2$, all new constructions require less redundancy for masking partially stuck cells than previous work on stuck cells, which in turn can result in higher code rates at the same masking and error correction capability.