Distributed Average Consensus using Probabilistic Quantization

In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus, which is one of the quantization values. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios.