Explicit Constructions of MBR and MSR Codes for Clustered Distributed Storage

TL;DR

This paper develops explicit capacity-achieving regenerating codes tailored for clustered distributed storage systems, optimizing for limited cross-cluster communication and providing new constructions for MBR and MSR codes.

Contribution

It introduces novel explicit constructions of MBR and MSR codes for clustered storage, generalizing existing codes and reducing field size requirements in certain cases.

Findings

Proposed MBR codes for general clustered parameters.

MSR codes for zero and limited cross-cluster bandwidth scenarios.

Existing non-clustered MSR codes are adaptable to clustered systems.

Abstract

This paper considers capacity-achieving coding for the clustered form of distributed storage that reflects practical storage networks. To reflect the clustered structure with limited cross-cluster communication bandwidths, nodes in the same cluster are set to communicate $\beta_I$ symbols, while nodes in other clusters can communicate $\beta_c \leq \beta_I$ symbols with one another. We provide two types of exact regenerating codes which achieve the capacity of clustered distributed storage: the minimum-bandwidth-regenerating (MBR) codes and the minimum-storage-regenerating (MSR) codes. First, we construct MBR codes for general parameter settings of clustered distributed storage. The suggested MBR code is a generalization of an existing code proposed by Rashmi et al., for scenarios where storage nodes are dispersed into L > 1 clusters. The proposed MBR code for the $\beta_c = 0$ case requires a much smaller field size compared to existing local MBR codes. Secondly, we devise MSR codes for clustered distributed 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 of the available cross- to intra-cluster repair bandwidths, n is the total number of distributed nodes and k is the number of contact nodes in data retrieval. The former represents the scenario where cross-cluster communication is not allowed, while the latter corresponds to the case of minimum node storage overhead. For $\epsilon=0$, two existing locally repairable codes are proven to be MSR codes for the clustered model. For $\epsilon \in [1/(n-k), 1]$, existing MSR codes for the non-clustered model are applicable to clustered scenarios with a simple modification.