Consensus method achieves exact average despite noisy network links
Exact Average Consensus under Noisy Communication Links: A Decentralized Gradient Perspective
Information Theory
Summary
When computers or devices try to agree on an average number by sharing information, noise in the communication can cause errors in the result. The authors found that traditional methods don't give the exact average but only an estimate with some error. They introduced a new approach that uses a kind of 'anchor' to keep each device's value close to its starting point, which helps cancel out the noise. This method ensures that all devices eventually agree exactly on the true average, even when communication is noisy.
What this means in practice
- •For network engineers: Design distributed systems that accurately aggregate sensor data despite unreliable communication links using the proposed anchoring consensus method.
- •For robotics system developers: Enable groups of robots to reliably share information and compute exact averages in noisy communication environments for coordinated tasks.
Authors
Yuhang Deng, Zheng Chen, Erik G. Larsson
Abstract
We study the distributed average consensus problem under persistent link-level disturbances modeled as a martingale difference sequence with uniformly bounded conditional second moments. Under such disturbances, the standard stochastic-approximation-based linear iteration with diminishing stepsizes drives the network to consensus on an unbiased random variable with non-vanishing variance instead of the exact initial average. To understand and resolve this limitation, we develop an anchoring-based mechanism derived from a decentralized gradient descent formulation and study the effect of incorporating a decaying anchoring term that continuously pulls each agent state toward its initial value. This perspective provides an intuitive interpretation of how state anchoring counteracts disturbance accumulation. Under standard summability conditions, we prove that the resulting algorithm achieves exact average consensus almost surely. Furthermore, this decentralized gradient perspective offers a unifying framework for several related methods and an interpretable design principle for exact average consensus under persistent disturbances.