Progressive quantization in distributed average consensus

TL;DR

This paper introduces a progressive quantization scheme for distributed average consensus in sensor networks, reducing quantization intervals over iterations to improve accuracy with low communication rates.

Contribution

A novel progressive quantization method that adapts quantization intervals during consensus, with a recurrence relation for parameter computation based on network topology.

Findings

Effective consensus achieved at low communication rates

Quantization step size decreases exponentially over iterations

Simulation confirms improved accuracy with progressive quantization

Abstract

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 size of 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.