LIBRARIES

In this thesis, I explore via two formulations the impact of communication constraints on distributed computation. In both formulations, nodes make partial observations of an underlying source. They communicate in order to compute a given function of all the measurements in the network, to within a desired level of error. Such computation in networks arises in various contexts, like wireless and sensor networks, consensus and belief propagation with bit constraints, and estimation of a slowly evolving process. By utilizing Information Theoretic formulations and tools, I obtain code- or algorithm-independent lower bounds that capture fundamental limits imposed by the communication network. In the first formulation, each node samples a component of a source whose values belong to a field of order q. The nodes utilize their knowledge of the joint probability mass function of the components together with the function to be computed to efficiently compress their messages, which are then broadcast. The question is: how many bits per sample are necessary and sufficient for each node to broadcast in order for the probability of decoding error to approach zero as the number of samples grows