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

DOI10.1109/TIT.2018.2806342zbMATH Open1401.94092arXiv1701.04909MaRDI QIDQ4682878

Author name not available (Why is that?)

Publication date: 19 September 2018

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: 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 $alpha$ 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 $$ symbols each from any set of $d$ other clusters, dubbed remote helper clusters, and also up to $alpha$ symbols each from any set of $ell$ 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 $ell>0$. We then obtain sharp lower bounds on the necessary intra-cluster repair BW to achieve optimal trade-off. Our bounds reveal the interesting fact that, while it is beneficial to increase the number of local helper nodes $ell$ in order to improve the storage-vs-inter-cluster-repair-BW trade-off, increasing $ell$ not only increases intra-cluster 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.

Full work available at URL: https://arxiv.org/abs/1701.04909

Mathematics Subject Classification ID

Searching and sorting (68P10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Coding theorems (Shannon theory) (94A24)

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