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Maximum-distance-separable (MDS) codes are a class of erasure codes that arewidely adopted to enhance the reliability of distributed storage systems (DSS).In (n, k) MDS coded DSS, the original data are stored into n distributed nodesin an efficient manner such that each storage node only contains a small amount(i.e., 1/k) of the data and a data collector connected to any k nodes canretrieve the entire data. On the other hand, a node failure can be repaired(i.e., stored data at the failed node can be successfully recovered) bydownloading data segments from other surviving nodes. In this paper, we developa new approach to construction of simple (5, 3) MDS codes. With judiciouslyblock-designed generator matrices, we show that the proposed MDS codes have aminimum stripe size {\alpha} = 2 and can be constructed over a small (Galois)finite field F4 of only four elements, both facilitating low-complexitycomputations and implementations for data storage, retrieval and repair. Inaddition, with the proposed MDS codes, any single node failure can be repairedthrough interference alignment technique with a minimum data amount downloadedfrom the surviving nodes; i.e., the proposed codes ensure optimal exact-repairof any single node failure using the minimum bandwidth. The low-complexity andall-node-optimal-repair properties of the proposed MDS codes make them readilydeployed for practical DSS.

A Novel Construction of Low-Complexity MDS Codes with Optimal Repair Capability for Distributed Storage Systems