Locality in Crisscross Error Correction

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 Singletonlike 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.

Multilayer crisscross error and erasure correction

“…The work [11] focuses on codes with locality for the rank metric, allowing to locally correct full columns, whereas a more general case is considered in [13].…”

“…Since then, codes in the cover metric with other correcting features (e.g., probabilistic, list-decoding, etc.) were subsequently studied [1,11,13,23,24,25].…”