Distributed storage over unidirectional ring networks

Data storage over networks with topological structures is one of issues discussed in storage theory. In this paper, we study data storage problems over unidirectional ring networks, one type of simple and representative networks. A lower bound on the reconstructing bandwidth (total communicated bandwidth in the network) for each user to download entire original data is proposed, and it is achievable for arbitrary parameters that are number of nodes, n, storage capacity per node, α, original data size, M. If a distributed storage scheme can achieve this lower bound with equality for every user, we call 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 for each failed storage node is obtained. Particularly, 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, by using the concept of Euclidean division, we present an efficient approach to construct ORDSSes over the smallest finite field F₂ for arbitrary parameters (n, α, M). Finally, an example is proposed to characterize the above approach.