Asymptotic construction of locally repairable codes with multiple recovering sets

Locally repairable codes have been extensively investigated due to practical applications in distributed and cloud storage systems in recent years. However, not much work on asymptotic behavior of locally repairable codes has been done. In particular, there is few result on constructive lower bound of asymptotic behavior of locally repairable codes with multiple recovering sets. In this paper, we construct some families of asymptotically good locally repairable codes with multiple recovering sets via automorphism groups of function fields of the Garcia-Stichtenoth towers. The main advantage of our construction is to allow more flexibility of localities

Increasing Availability in Distributed Storage Systems via Clustering

We introduce the Fixed Cluster Repair System (FCRS) as a novel architecture for Distributed Storage Systems (DSS), achieving a small repair bandwidth while guaranteeing a high availability. Specifically we partition the set of servers in a DSS into $s$ clusters and allow a failed server to choose any cluster other than its own as its repair group. Thereby, we guarantee an availability of $s-1$. We characterize the repair bandwidth vs. storage trade-off for the FCRS under functional repair and show that the minimum repair bandwidth can be improved by an asymptotic multiplicative factor of $2/3$ compared to the state of the art coding techniques that guarantee the same availability. We further introduce Cubic Codes designed to minimize the repair bandwidth of the FCRS under the exact repair model. We prove an asymptotic multiplicative improvement of $0.79$ in the minimum repair bandwidth compared to the existing exact repair coding techniques that achieve the same availability. We show that Cubic Codes are information-theoretically optimal for the FCRS with $2$ and $3$ complete clusters. Furthermore, under the repair-by-transfer model, Cubic Codes are optimal irrespective of the number of clusters