High Dimensional Error-Correcting Codes

TL;DR

This paper introduces multidimensional error-correcting codes capable of correcting complex error patterns like clusters and bursts, emphasizing high-dimensional redundancy for improved error resilience.

Contribution

It presents novel constructions of high-dimensional codes that efficiently correct clustered and burst errors, focusing on redundancy optimization.

Findings

Codes can correct high-dimensional error clusters

Redundancy is minimized for high-dimensional codes

Effective correction of small error bursts

Abstract

In this paper we construct multidimensional codes with high dimension. The codes can correct high dimensional errors which have the form of either small clusters, or confined to an area with a small radius. We also consider small number of errors in a small area. The clusters which are discussed are mainly spheres such as semi-crosses and crosses. Also considered are clusters with small number of errors such as 2-bursts, two errors in various clusters, and three errors on a line. Our main focus is on the redundancy of the codes when the most dominant parameter is the dimension of the code.