Detection under One-Bit Messaging over Adaptive Networks

TL;DR

This paper analyzes multi-agent networks performing binary decisions with one-bit messaging, deriving performance expressions and insights into the interplay between continuous adaptation and discrete communication constraints.

Contribution

It introduces a novel analytical framework for performance evaluation of networks with one-bit messaging, combining integral and Bernoulli convolution methods.

Findings

Derived approximate performance expressions that match simulations.

Revealed the impact of binary messaging on continuous adaptation.

Provided insights into the trade-offs between message quantization and network performance.

Abstract

This work studies the operation of multi-agent networks engaged in binary decision tasks, and derives performance expressions and performance operating curves under challenging conditions with some revealing insights. One of the main challenges in the analysis is that agents are only allowed to exchange one-bit messages, and the information at each agent therefore consists of both continuous and discrete components. Due to this mixed nature, the steady-state distribution of the state of each agent cannot be inferred from direct application of central limit arguments. Instead, the behavior of the continuous component is characterized in integral form by using a log-characteristic function, while the behavior of the discrete component is characterized by means of an asymmetric Bernoulli convolution. By exploiting these results, the article derives reliable approximate performance expressions for the network nodes that match well with the simulated results for a wide range of system parameters. The results also reveal an important interplay between continuous adaptation under constant step-size learning and the binary nature of the messages exchanged with neighbors.