Distributed Average Consensus With Dithered Quantization

Abstract

In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth/power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean square error performance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimum-length interval containing the node values. We reveal that the length of this interval is a monotonically non-increasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios.

Distributed averaging on digital noisy networks

“…As this assumption is clearly not met by digital communication, the community has been studying how to adapt such algorithms to realistic digital networks. A few papers have considered the issue of quantization, i.e., limited precision in communications, and provided results on the precision which can be achieved in approximating the average when using static uniform quantizers [9], [1], or designed effective quantization schemes to achieve arbitrary precision (based on adaptive [14] or logarithmic [3] quantizers). On the other hand, in the literature we find mainly two approaches to the issue of noisy communication.…”

Distributed parameter estimation in unreliable sensor networks via broadcast gossip algorithms

“…where r = (x ij − π k )/∆, we refer to [12] to make further relevant comments. It is easy to see that when the variable is exactly equal to a quantization centroid, there is zero probability of choosing another centroid.…”

“…sequence of uniformly distributed random variables on [−∆/2, ∆/2]. As pointed out in [12], probabilistic quantization is equivalent to a "dithered quantization" method [2]. It has been shown by Schuchman that the subtractive dithering process yields error signal values that are statistically independent from each other and the input.…”

Distributed inference in wireless sensor networks

“…For example, the ring-network structure has been considered [86][87][88] for in-network information processing, where the sensors are organized in a cycle and process the information by passing the estimates along the cycle. Consensus-based approaches for distributed estimation have been discussed [14,[89][90][91][92]. In addition, specific approaches to distributed estimation of diffusive sources have been studied [15,93,94].…”