Explicit Constructions of MBR and MSR Codes for Clustered Distributed Storage

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 βI symbols, while nodes in other clusters can communicate βc ≤ βI 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 βc = 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: = 0 and ∈ [ 1 n−k , 1], where = βc/βI 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 = 0, two existing locally repairable codes are proven to be MSR codes for the clustered model. For ∈ [ 1 n−k , 1], existing MSR codes for the non-clustered model are applicable to clustered scenarios with a simple modification. Finally, under the settings of = 1 n−k and n = kL, an MSR code is suggested which is based on simple MDS codes and requires a smaller field size for symbols than the existing code for L ≥ 3.

Capacity of Clustered Distributed Storage

“…Thus, according to [11], there exists a linear network coding scheme which achieves capacity C. Although the existence of a coding scheme is verified, explicit network coding schemes which achieve capacity need to be specified for implementing practical systems. Recently, under the setting of clustered DSS modeled in the present paper, MBR codes for all n, k, L, are constructed in [36] and MSR codes for limited parameters are designed in [37]. Explicit code construction for general parameters and/or construction of codes that requires small field size are interesting remaining issues.…”

Explicit Construction of Minimum Storage Rack-Aware Regenerating Codes for All Parameters

“…Then we note d ≥ k is not an intrinsic condition for the rack-aware storage model, although the work of [2], [4], [6], [8], [9] all restricted to the case d ≥ k. On the other hand, reducing the number of helper racks can greatly improve the repair efficiency, which is exactly the motivation for studying locally repairable codes [12]. Therefore, we further investigate the MBRR code in the case 0 < d < k. A cut-set bound is derived and parameters of MBRR codes are accordingly determined.…”

“…The authors of [8] assumed a fixed ratio of the cross-cluster to intra-cluster bandwidth and defined the repair bandwidth as the sum of cross-cluster and intra-cluster repair bandwidth. They constructed explicit codes [9] for minimizing the repair bandwidth when all the remaining nodes participate in the repair of one node failure.…”

Rack-Aware Regenerating Codes with Multiple Erasure Tolerance

“…The authors of [8] assumed a fixed ratio of the cross-cluster to intra-cluster bandwidth and defined the repair bandwidth as the sum of cross-cluster and intra-cluster repair bandwidth. They constructed explicit codes [9] for minimizing the repair bandwidth when all the remaining nodes participate in the repair of one node failure. However, this model does not allow data processing within these helper racks, thus are not directly comparable with our findings.…”