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 <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> clusters in total, with <inl...

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Vydáno v:IEEE transactions on information theory Ročník 64; číslo 8; s. 5783 - 5805
Hlavní autoři: Prakash, N., Abdrashitov, Vitaly, Medard, Muriel
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.08.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Bandwidth
Bandwidths
Cloud computing
cloud storage
Cluster analysis
clustered storage
coding for storage
Data centers
Data collection
Data models
Distributed storage
Downloading
Eavesdropping
Encoding
Lower bounds
Maintenance engineering
Nodes
Optimization
regenerating codes
Repair
Storage systems
storage vs repair-bandwidth trade-off
Symbols
Tradeoffs
ISSN:0018-9448, 1557-9654
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Shrnutí:We study a generalization of the setting of regenerating codes, motivated by applications to storage systems consisting of clusters of storage nodes. There are <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> clusters in total, with <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> nodes per cluster. A data file is coded and stored across the <inline-formula> <tex-math notation="LaTeX">mn </tex-math></inline-formula> nodes, with each node storing <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula> symbols. For availability of data, we require that the file be retrievable by downloading the entire content from any subset of <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">\beta </tex-math></inline-formula> symbols each from any set of <inline-formula> <tex-math notation="LaTeX">d </tex-math></inline-formula> other clusters, dubbed remote helper clusters, and also up to <inline-formula> <tex-math notation="LaTeX">\alpha </tex-math></inline-formula> symbols each from any set of <inline-formula> <tex-math notation="LaTeX">\ell </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">\ell > 0 </tex-math></inline-formula>. We then obtain sharp lower bounds on the necessary intra-cluster 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 <inline-formula> <tex-math notation="LaTeX">\ell </tex-math></inline-formula> in order to improve the storage-vs-inter-cluster-repair-BW trade-off, increasing <inline-formula> <tex-math notation="LaTeX">\ell </tex-math></inline-formula> 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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2018.2806342