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

TL;DR

This paper introduces a new class of low-complexity (5, 3) MDS codes for distributed storage that enable optimal repair bandwidth using interference alignment, constructed over a small finite field for practical efficiency.

Contribution

The paper presents a novel construction of (5, 3) MDS codes with minimal stripe size and finite field size, achieving optimal repair bandwidth with low computational complexity.

Findings

Constructed (5, 3) MDS codes over F4 with minimal stripe size.

Achieved optimal exact repair bandwidth for single node failures.

Codes are practical for real-world distributed storage systems.

Abstract

Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in 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 can retrieve 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) by downloading data segments from other surviving nodes. In this paper, we develop a new approach to construction of simple (5, 3) MDS codes. With judiciously block-designed generator matrices, we show that the proposed MDS codes have a minimum stripe size {\alpha} = 2 and can be constructed over a small (Galois) finite field F4 of only four elements, both facilitating low-complexity computations and implementations for data storage, retrieval and repair. In addition, with the proposed MDS codes, any single node failure can be repaired through interference alignment technique with a minimum data amount downloaded from the surviving nodes; i.e., the proposed codes ensure optimal exact-repair of any single node failure using the minimum bandwidth. The low-complexity and all-node-optimal-repair properties of the proposed MDS codes make them readily deployed for practical DSS.