Construction of one special minimum storage regenerating code when α=2

Regenerating codes is one class of erasure codes for distributed storage. A [n, k, d, alpha, beta] regenerating code can recover the original message from any k out of n distributed storage nodes and repair any failed node from other arbitrary d nodes, alpha is the number of symbols stored in one node and beta is the number of symbols downloaded by a newcomer node. Minimum storage regenerating (MSR) code is a regenerating code attaining the minimal storage requirement. In this paper, we address the design of a special MSR code where alpha = 2 and the first fragment of a node stores original symbol (we call it hybrid systematic MSR code or HS-MSR code). We point out that there exists no exact-repair construction when k >= 5. A simple exact linear construction is given when k = 2. Furthermore, by relaxing the condition of connecting any d nodes, we investigate the properties of quasi-cyclic regenerating code and propose a unified construction such that when k 3, repairing process can be achieved with less repair bandwidth by repair-by-transfer form.