We study a generalization of the setting of regenerating codes, motivated by applications to storage systems consisting of clusters of storage nodes. There are n clusters in total, with m nodes per cluster. A data file is coded and stored across the mn nodes, with each node storing α symbols. For availability of data, we demand that the file is retrievable by downloading the entire content from any subset of k clusters. Nodes represent entities that can fail, and here we distinguish between intra-cluster and inter-cluster bandwidth-costs during node repair. Noderepair is accomplished by downloading β symbols each from any set of d other clusters. The replacement-node also downloads content from any set of surviving nodes in the same cluster during the repair process. We first identity the optimal trade-off between storage-overhead and inter-cluster (IC) repair-bandwidth under functional repair, and also present optimal exact-repair code constructions for a class of parameters. The new trade-off is strictly better than what is achievable via space-sharing existing coding solutions, whenever > 0. We then obtain lower bounds on the necessary intra-cluster repair-bandwidth to achieve optimal trade-off. Our bounds reveal the interesting fact that while it is beneficial to increase the number of local helper nodes in order to improve the storage-vs-IC-repair-bandwidth trade-off, a high value of also demands a higher amount of intra-cluster repairbandwidth. Under functional repair, random linear network codes (RLNCs) simultaneously optimize usage of both inter and intra-cluster repair bandwidth; simulation results based on RLNCs suggest optimality of the bounds on intracluster repair-bandwidth. We also analyze resiliency of the clustered storage system against passive eavesdropping by providing file-size bounds and optimal code constructions.
Prakash REF divided the storage system into k storage clusters, and the nodes in the clusters were fully connected.
The Storage vs Repair-Bandwidth Trade-off for Clustered Storage Systems
IEEE Transactions on Information Theory ( Volume: 64, Issue: 8, Aug. 2018 )
Computer Science Mathematics