Lossy network correlated data gathering with high-resolution coding

We consider a sensor network measuring correlated data, where the task is to gather all data from the network nodes to a sink. We consider the case where data at nodes is lossy coded with high-resolution, and the information measured by the nodes should be available at the sink within certain total and individual distortion bounds. First, we consider the problem of finding the optimal transmission structure and the rate-distortion allocations at the various spatially located nodes, such as to minimize the total power consumption cost of the network. We prove that the optimal transmission structure is the shortest path tree and that the problems of rate and distortion allocation separate in the high-resolution case, namely, we first find the distortion allocation as a function of the transmission structure, and then the rate allocation is computed. Then, we also study the case when the node positions can be chosen, by finding the optimal node placement when two different targets of interest are considered, namely total power minimization and network lifetime extension.