A Class of MSR Codes for Clustered Distributed Storage

Clustered distributed storage models real data centers where intra- and cross-cluster repair bandwidths are different. In this paper, exact-repair minimum-storage-regenerating (MSR) codes achieving capacity of clustered distributed storage are designed. Focus is given on two cases: $\epsilon=0$ and $\epsilon=1/(n-k)$, where $\epsilon$ is the ratio of the available cross- and 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 cross-cluster bandwidth that is possible under the minimum storage overhead constraint. For the $\epsilon=0$ case, two types of locally repairable codes are proven to achieve the MSR point. As for $\epsilon=1/(n-k)$, an explicit MSR coding scheme is suggested for the two-cluster situation under the specific condition of $n = 2k$.Comment: 9 pages, a part of this paper is submitted to IEEE ISIT201

Explicit Construction of Minimum Bandwidth Rack-Aware Regenerating Codes

In large data centers, storage nodes are organized in racks, and the cross-rack communication dominates the system bandwidth. We explicitly construct codes for exact repair of single node failures that achieve the optimal tradeoff between the storage redundancy and cross-rack repair bandwidth at the minimum bandwidth point (i.e., the cross-rack bandwidth equals the storage size per node). Moreover, we explore the node repair when only a few number of helper racks are connected. Thus we provide explicit constructions of codes for rack-aware storage with the minimum cross-rack repair bandwidth, lowest possible redundancy, and small repair degree (i.e., the number of helper racks connected for repair).Comment: 4 pages, 1 figure. arXiv admin note: text overlap with arXiv:2101.0873

Global repair bandwidth cost optimization of generalized regenerating codes in clustered distributed storage systems

In clustered distributed storage systems (CDSSs), one of the main design goals is minimizing the transmission cost during the failed storage nodes repairing. Generalized regenerating codes (GRCs) are proposed to balance the intra-cluster repair bandwidth and the inter-cluster repair bandwidth for guaranteeing data availability. The trade-off performance of GRCs illustrates that, it can reduce storage overhead and inter-cluster repair bandwidths simultaneously. However, in practical big data storage scenarios, GRCs cannot give an effective solution to handle the heterogeneity of bandwidth costs among different clusters for node failures recovery. This paper proposes an asymmetric bandwidth allocation strategy (ABAS) of GRCs for the inter-cluster repair in heterogeneous CDSSs. Furthermore, an upper bound of the achievable capacity of ABAS is derived based on the information flow graph (IFG), and the constraints of storage capacity and intra-cluster repair bandwidth are also elaborated. Then, a metric termed global repair bandwidth cost (GRBC), which can be minimized regarding of the inter-cluster repair bandwidths by solving a linear programming problem, is defined. The numerical results demonstrate that, maintaining the same data availability and storage overhead, the proposed ABAS of GRCs can effectively reduce the GRBC compared to the traditional symmetric bandwidth allocation schemes

Node repair on connected graphs, Part II

We continue our study of regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the purpose of recovering the lost data. This information is moved across the network, and the cost of node repair is determined by the graphical distance from the helper nodes to the failed node. This problem was formulated in our recent work (IEEE IT Transactions, May 2022) where we showed that processing of the information at the intermediate nodes can yield savings in repair bandwidth over the direct forwarding of the data. While the previous paper was limited to the MSR case, here we extend our study to the case of general regenerating codes. We derive a lower bound on the repair bandwidth and formulate repair procedures with intermediate processing for several families of regenerating codes, with an emphasis on the recent constructions from multilinear algebra. We also consider the task of data retrieval for codes on graphs, deriving a lower bound on the communication bandwidth and showing that it can be attained at the MBR point of the storage-bandwidth tradeoff curve

Rack-aware minimum-storage regenerating codes with optimal access

We derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share the same rack. Furthermore, we construct a family of rack-aware minimum-storage regenerating (MSR) codes with the property that the number of symbols accessed for repairing a single failed node attains the bound with equality for all admissible parameters. Constructions of rack-aware optimal-access MSR codes were only known for limited parameters. We also present a family of Reed-Solomon (RS) codes that only require accessing a relatively small number of symbols to repair multiple failed nodes in a single rack. In particular, for certain code parameters, the RS construction attains the bound on the access complexity with equality and thus has optimal access