The majority of works in distributed storage networks assume a simple network model with a collection of identical storage nodes with the same communication cost between the nodes. In this paper, we consider a realistic multi-rack distributed data storage network and present a code design framework for this model. Considering the cheaper data transmission within the racks, our code construction method is able to locally repair the nodes failure within the same rack by using only the survived nodes in the same rack. However, in the case of severe failure patterns when the information content of the survived nodes is not sufficient to repair the failures, other racks will participate in the repair process. By employing the criteria of our multi-rack storage code, we establish a linear programming bound on the size of the code in order to maximize the code rate.

Locally repairable codes are used in distributed storage networks to minimise the number of survived nodes required to repair a failed node. However, the robustness of these codes is a main concern since locally repair procedure may fail when there are multiple node failures. This paper proposes a new class of robust locally repairable codes which guarantees that a failed node can be repaired locally even when there are multiple node failures. Upper bound on the size of robust locally repairable codes using linear programming tools are obtained and examples of robust locally repairable codes attaining these bounds are constructed.

In practical distributed storage networks, data centres house hundreds of racks, each of which contains several storage nodes. However, the majority of works in distributed storage assume a simple network model with a collection of identical storage nodes with same communication cost between the nodes. In this paper, we consider a more realistic rack model of storage network and present a code design framework for this model. Using our code construction method, node failures within a rack can be repaired locally by survived nodes in the same rack or by the other survived racks when the information content of the same rack is not sufficient to repair the failed nodes.