Distributed averaging on digital noisy networks

We consider a class of distributed algorithms for computing arithmetic averages (average consensus) over networks of agents connected through digital noisy broadcast channels. Our algorithms combine error-correcting codes with the classical linear consensus iterative algorithm, and do not require the agents to have knowledge of the global network structure. We improve the performance by introducing in the state-upadate a compensation for the quantization error, avoiding its accumulation. We prove almost sure convergence to state agreement, and we discuss the speed of convergence and the distance between the asymptotic value and the average of the initial values.