Lowest-density MDS array codes for reliable Smart Meter networks

In this paper we introduce a lowest density MDS array code which is applied to a Smart Meter network to introduce reliability. By treating the network as distributed storage with multiple sources, information can be exchanged between the nodes in the network allowing each node to store parity symbols relating to data from other nodes. A lowest density MDS array code is then applied to make the network robust against outages, ensuring low overhead and data transfers. We show the minimum amount of overhead required to be able to recover from r node erasures in an n node network and explicitly design an optimal array code with lowest density. In contrast to existing codes, this one has no restrictions on the number of nodes or erasures it can correct. Furthermore we consider incomplete networks where all nodes are not connected to each other. This limits the exchange of data for purposes of redundancy and we derive conditions on the minimum node degree that allow lowest density MDS codes to exist. We also present an explicit code design for incomplete networks that is capable of correcting two node failures.