Distributed consensus over network with noisy links

We consider a distributed consensus problem where a set of agents want to agree on a common value through local computations and communications. We assume that agents communicate over a network with time-varying topology and noisy communication links. We are interested in the case when the link noise is independent in time, and it has zero mean and bounded variance. We present and study an iterative algorithm with a diminishing stepsize. We show that the algorithm converges in expectation and almost surely to a “random” consensus, and we characterize the statistics of the consensus. In particular, we give the expected value of the consensus and provide an upper bound on its variance.