Generalized Optimal Storage Scaling via Network Coding

It is critical to support efficient scaling in distributed storage systems so as to meet increasing storage demands with new storage nodes. However, the scaling process incurs substantial scaling bandwidth due to reorganizing currently stored data to new storage nodes. Recent work has applied network coding to minimize scaling bandwidth for a special case where <tex>$(n,\ k)$</tex> MDS codes are scaled to <tex>$(n^{\prime}, k^{\prime})$</tex> MDS codes for <tex>$n^{\prime}-k^{\prime}=n-k$</tex>. In this paper, we extend the results and prove the minimum scaling bandwidth for a more general setting where <tex>$(n,\ k)$</tex> MDS codes are scaled to <tex>$(n^{\prime}, k^{\prime})$</tex> MDS codes for <tex>$n^{\prime} > n$</tex> and <tex>$k^{\prime}\geq k$</tex>. Furthermore, we present a family of MDS code construction that achieves optimal scaling from <tex>$(n,\ k)$</tex> to <tex>$(n^{\prime}, k^{\prime})$</tex> where <tex>$k=k^{\prime}$</tex>.