Distributed Storage over Unidirectional Ring Networks

TL;DR

This paper investigates optimal distributed storage schemes over unidirectional ring networks, establishing bounds on reconstructing and repair bandwidths, and proposing two efficient constructions for such schemes.

Contribution

It introduces the concept of optimal reconstructing distributed storage schemes (ORDSS) over unidirectional rings, providing bounds, proofs of achievability, and two novel constructions including an efficient ED method.

Findings

Lower bound on reconstructing bandwidth is achievable.

Every node can be repaired with optimal bandwidth.

Two constructions for ORDSS, MDS and ED, are proposed.

Abstract

In this paper, we study distributed storage problems over unidirectional ring networks, whose storage nodes form a directed ring and data is transmitted along the same direction. The original data is distributed to store on these nodes. Each user can connect one and only one storage node to download the total data. A lower bound on the reconstructing bandwidth to recover the original data for each user is proposed, and it is achievable for arbitrary parameters. If a distributed storage scheme can achieve this lower bound with equality for every user, we say it an optimal reconstructing distributed storage scheme (ORDSS). Furthermore, the repair problem for a failed storage node in ORDSSes is under consideration and a tight lower bound on the repair bandwidth is obtained. In particular, we indicate the fact that for any ORDSS, every storage node can be repaired with repair bandwidth achieving the lower bound with equality. In addition, we present two constructions for ORDSSes of arbitrary parameters, called MDS construction and ED construction, respectively. Particularly, ED construction, by using the concept of Euclidean division, is more efficient by our analysis in detail.