Energy efficient scheduling in networks with correlated data

We consider a network of nodes measuring a correlated data field, and in which information measured by the nodes needs to reach a central location where the field is reconstructed. We consider the situation where, in order to save energy, the nodes employ a random ON/OFF schedule of being active. We analyze the tradeoff between the distortion of reconstruction of the field, given by the number of nodes not covered by active nodes, and the energy cost for gathering the data, given by the shortest path tree on the graph formed by the active nodes. This scenario is relevant in the design of energy efficient scheduling for sensor networks measuring correlated data. We show that in general there is an optimal probability defining the schedule which minimizes a cost function which considers jointly the distortion and the energy cost.