A Generic Transformation to Enable Optimal Repair in MDS Codes for Distributed Storage Systems

Abstract

We propose a generic transformation that can convert any nonbinary $(n=k+r,k)$ maximum distance separable (MDS) code into another $(n,k)$ MDS code over the same field such that 1) some arbitrarily chosen $r$ nodes have the optimal repair bandwidth and the optimal rebuilding access, 2) for the remaining $k$ nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved, 3) the sub-packetization level is increased only by a factor of $r$. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary $(n,k)$ scalar MDS code can be converted into an $(n,k)$ MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.

This paper has been published in IEEE Transactions on Information Theory

References in corpus (1)

• Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction

Cited by in corpus (8)

• A Systematic Construction of MDS Codes With Small Sub-packetization Level and Near-Optimal Repair Bandwidth
• Cascade Codes For Distributed Storage Systems
• Towards Practical Private Information Retrieval from MDS Array Codes
• MSR Codes with Linear Field Size and Smallest Sub-packetization for Any Number of Helper Nodes
• A Generic Transformation for Optimal Node Repair in MDS Array Codes over ${\mathbf{F}}_2$
• Constructing MSR codes with subpacketization $2^{n/3}$ for $k+1$ helper nodes
• PMDS Array Codes With Small Sub-packetization, Small Repair Bandwidth/Rebuilding Access
• Constructing $(h,d)$ cooperative MSR codes with sub-packetization $(d-k+h)(d-k+1{)}^{\lceil n/2\rceil }$