Explicit Construction of Minimum Storage Rack-Aware Regenerating Codes for All Parameters

We consider the rack-aware storage system where $n = \bar nu$ nodes are organized in $\bar n$ racks each containing u nodes, and any $k = \bar ku + {u_0}\left( {0 \leq {u_0} < u} \right)$ nodes can retrieve the original data file. More importantly, the cross-rack communication cost is much more expensive than the intra-rack communication cost, so that the latter is usually neglected in the system bandwidth. The MSRR (minimum storage rack-aware regenerating) code is an important variation of regenerating codes that achieves the optimal repair bandwidth for single node failures in the rack-aware model. However, explicit construction of MSRR codes for all parameters were not developed until Chen&Barg’s work. In this paper we present another explicit construction of MSRR codes for all parameters that improve Chen&Barg’s construction in two aspects: (1) The sub-packetization is reduced from ${\left( {\bar d - \bar k + 1} \right)^n}$to ${\left( {\bar d - \bar k + 1} \right)^{\left\lceil {\frac{{\bar n}}{{u - {u_0}}}} \right\rceil }}$ where $\bar d$ is the number of helper racks that participate in the repair process; (2) The field size is reduced to |F|>n which is almost half of the field used in Chen&Barg’s construction. Besides, our code keeps the same access level as Chen&Barg’s low-access construction.