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This paper considers capacity-achieving coding for the clustered form ofdistributed storage that reflects practical storage networks. To reflect theclustered structure with limited cross-cluster communication bandwidths, nodesin the same cluster are set to communicate $\beta_I$ symbols, while nodes inother clusters can communicate $\beta_c \leq \beta_I$ symbols with one another.We provide two types of exact regenerating codes which achieve the capacity ofclustered distributed storage: the minimum-bandwidth-regenerating (MBR) codesand the minimum-storage-regenerating (MSR) codes. First, we construct MBR codesfor general parameter settings of clustered distributed storage. The suggestedMBR code is a generalization of an existing code proposed by Rashmi et al., forscenarios where storage nodes are dispersed into L > 1 clusters. The proposedMBR code for the $\beta_c = 0$ case requires a much smaller field size comparedto existing local MBR codes. Secondly, we devise MSR codes for clustereddistributed storage. Focus is given on two important cases:$\epsilon=0$ and$\epsilon \in [1/(n-k), 1]$, where $\epsilon=\beta_c/\beta_I$ is the ratio ofthe available cross- to intra-cluster repair bandwidths, n is the total numberof distributed nodes and k is the number of contact nodes in data retrieval.The former represents the scenario where cross-cluster communication is notallowed, while the latter corresponds to the case of minimum node storageoverhead. For $\epsilon=0$, two existing locally repairable codes are proven tobe MSR codes for the clustered model. For $\epsilon \in [1/(n-k), 1]$, existingMSR codes for the non-clustered model are applicable to clustered scenarioswith a simple modification.

Explicit Constructions of MBR and MSR Codes for Clustered Distributed Storage