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Distributed Average Consensus With Quantization Refinement

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4 Author(s)
Thanou, D. ; Ecole Polytechnique Fédérale de Lausanne (EPFL), Signal Processing Laboratory-LTS4, Lausanne, Switzerland ; Kokiopoulou, E. ; Pu, Y. ; Frossard, P.

We consider the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. We propose a novel quantization scheme that exploits the increasing correlation between the values exchanged by the sensors throughout the iterations of the consensus algorithm. A low complexity, uniform quantizer is implemented in each sensor, and refined quantization is achieved by progressively reducing the quantization intervals during the convergence of the consensus algorithm. We propose a recurrence relation for computing the quantization parameters that depend on the network topology and the communication rate. We further show that the recurrence relation can lead to a simple exponential model for the quantization step size over the iterations, whose parameters can be computed a priori. Finally, simulation results demonstrate the effectiveness of the progressive quantization scheme that leads to the consensus solution even at low communication rate.

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Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 1 )