Distributed Storage Schemes over Unidirectional Ring Networks
  In this paper, we study distributed storage problems over unidirectional ring networks. A lower bound on the reconstructing bandwidth to recover total 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 each 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 for each 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, we present an efficient approach to construct ORDSSes for arbitrary parameters by using the concept of Euclidean division. Finally, we take an example to characterize the above approach. 
Jiyong Lu, Xuan Guang, and Fang-Wei Fu
cs.IT math.IT