Correcting Grain-Errors in Magnetic Media

TL;DR

This paper introduces new bounds and constructions for grain-error-correcting codes in magnetic media, improving upon existing methods and demonstrating the effectiveness of permutation-based codes.

Contribution

It provides novel bounds and constructions for grain-error correction, including permutation of classical group codes, with improved performance over previous bounds.

Findings

New bounds on maximum code size for grain-error correction

Permutation of classical group codes can correct a single grain-error

Results improve upon existing bounds and constructions in many cases

Abstract

This paper studies new bounds and constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to other channel models.