Asymptotically Optimal Regenerating Codes Over Any Field

TL;DR

This paper introduces two explicit regenerating code constructions over any field, approaching optimal bounds asymptotically, thus enhancing practical implementation in distributed storage systems.

Contribution

It presents novel explicit constructions of regenerating codes using extension fields that work over any field size and approach the cut-set bound asymptotically.

Findings

Codes approach the cut-set bound as reconstruction degree increases

Codes can be realized over any field with sufficiently large file size

First construction attains the MBR bound asymptotically for all parameters

Abstract

The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we obtain two explicit constructions of regenerating codes. These codes approach the cut-set bound as the reconstruction degree increases, and may be realized over any given field if the file size is large enough. Since distributed storage systems are the main purpose of regenerating codes, this file size restriction is trivially satisfied in most conceivable scenarios. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters.