Stochastic distributed consensus with quantized data and input noise

This paper studies the problem of distributed average consensus with input noise and the quantized data. We assume the network, which is expressed by a first-order difference equation. We suppose that the topologies of the network are fixed, and noise is added after encoding and furthermore, some conditions are derived to achieve convergence. However, the weight in our approach is forced to satisfy a persistence condition, and assume that the quantization level is bounded, we prove that there is a stochastic final state for each agent to approach. Furthermore, the rate of convergence of the mean consensus and the statistic properties, such as unbiasedness and mean square error are analyzed in detail. Interestingly, the tradeoff between the convergence rate and the mean square error are found, then a numerical study is also illustrated.