Distributed Consensus Algorithms in Sensor Networks: Quantized Data

The paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures simultaneously. We consider two versions of the algorithm: unbounded quantizers (algorithm QC) and bounded quantizers (algorithm QCF). To achieve consensus, dither (small noise) is added to the sensor states before quantization. We show by stochastic approximation techniques that consensus is asymptotically achieved with probability one to a finite random variable. For the QC algorithm we show that the mean-squared error (m.s.e.) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate. For the QCF algorithm we study the tradeoffs between how far away is this limiting random variable from the desired average, the consensus convergence rate, the quantizer parameters, and the network topology. We cast these tradeoff issues as an optimal quantizer design that we solve. A numerical study illustrates the design tradeoffs.