Linear Programming Bounds for Distributed Storage Codes

TL;DR

This paper develops linear programming bounds for robust locally repairable codes in distributed storage, ensuring multiple repair options and addressing update efficiency to improve robustness and minimize data update costs.

Contribution

It introduces linear programming bounds for robust locally repairable codes and characterizes update-efficient storage code properties, providing optimal code examples.

Findings

Established upper bounds on code size for robust locally repairable codes.

Provided examples of optimal robust locally repairable codes.

Characterized conditions for update-efficient storage codes.

Abstract

A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to have multiple repair groups. In this paper we consider robust locally repairable coding schemes which guarantee that there exist multiple distinct (not necessarily disjoint) alternative local repair groups for any single failure such that the failed node can still be repaired locally even if some of the repair groups are not available. We use linear programming techniques to establish upper bounds on the code size of these codes. We also provide two examples of robust locally repairable codes that are optimal regarding our linear programming bound. Furthermore, we address the update efficiency problem of the distributed data storage networks. Any modification on the stored data will result in updating the content of the storage nodes. Therefore, it is essential to minimise the number of nodes which need to be updated by any change in the stored data. We characterise the update-efficient storage code properties and establish the necessary conditions of existence update-efficient locally repairable storage codes.