Locality in Crisscross Error Correction

TL;DR

This paper investigates cover-metric codes with locality for correcting crisscross errors in arrays, deriving bounds and proposing constructions that improve local recovery in distributed data storage.

Contribution

It introduces a Singleton-like bound for cover-metric codes with locality and provides a construction that achieves this bound, enhancing error correction capabilities.

Findings

Derived a Singleton-like bound for cover-metric codes with locality

Proposed a bound-achieving code construction

Compared performance with rank-metric based codes

Abstract

The cover metric is suitable for describing the resilience against correlated errors in arrays, in particular crisscross errors, which makes it interesting for applications such as distributed data storage (DDS). In this work, we consider codes designed for the cover metric that have locality, that means lost symbols can be recovered by using only a few other (local) symbols. We derive and prove a Singleton-like bound on the minimum cover distance of cover-metric codes with locality and propose a bound-achieving construction. Further, we explore the performance of our construction in comparison to a known construction based on rank-metric codes.