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We consider the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. In particular, we exploit the increasing correlation between the exchanged values throughout the iterations of the consensus algorithm in order to design a novel quantization scheme, particularly efficient at low bit rates. We implement a low complexity, uniform quantizer in each sensor, where refined quantization is achieved by progressively reducing the quantization intervals with 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. Finally, simulation results demonstrate the effectiveness of the progressive quantization scheme that leads to the consensus solution even at low communication rate.