An unified form of exact-MSR codes via product-matrix framework

Regenerating code represents a class of erasure codes applicable to distributed storage systems. An [n, k, d] regenerating code admits the recovery of the message from any k out of the n encoded fragments, and the recovery of an erasure fragment from other arbitrary d valid fragments, for k ≤ d ≤ n - 1. Minimum Storage Regenerating (MSR) code is the regenerating code attaining the minimal storage requirement. By product-matrix framework, the [n, k, d ≥ 2k-2] exact-MSR code is presented by Rashmi et al. This paper presents a novel version of exact-MSR codes for the same set of parameters. As compared with previous works, the major contributions of work include: i). An approach is proposed to directly include the d > 2k - 2 Exact-MSR codes in the product-matrix representation; ii). The required size of the finite field is reduced to n from n(d - k +1). The proposed coding techniques further improve the practicability of Exact-MSR codes.