The Storage Versus Repair-Bandwidth Trade-off for Clustered Storage Systems

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 require that the file be retrievable by downloading the entire content from any subset of k clusters. Nodes represent entities that can fail. We distinguish between intra-cluster and inter-cluster bandwidth (BW) costs during node repair. Node-repair in a cluster is accomplished by downloading β symbols each from any set of d other clusters, dubbed remote helper clusters, and also up to α symbols each from any set of I surviving nodes, dubbed local helper nodes, in the host cluster. We first identify the optimal trade-off between storage-overhead and inter-cluster 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 ℓ > 0. We then obtain sharp lower bounds on the necessary intracluster repair BW to achieve optimal trade-off. Under functional repair, random linear network codes (RLNCs) simultaneously optimize usage of both inter- and intra-cluster repair BW; simulation results based on RLNCs suggest optimality of the bounds on intra-cluster repair-bandwidth. Our bounds reveal the interesting fact that, while it is beneficial to increase the number of local helper nodes I in order to improve the storage-vs-inter-cluster-repair-BW trade-off, increasing I not only increases intracluster BW in the host-cluster, but also increases the intra-cluster BW in the remote helper clusters. We also analyze resilience of the clustered storage system against passive eavesdropping by providing file-size bounds and optimal code constructions.