# A Message Passing Approach for Decision Fusion in Adversarial Multi-Sensor Networks

## TL;DR

This paper introduces a message passing algorithm for decision fusion in adversarial multi-sensor networks, achieving near-optimal performance with reduced complexity, effective for both independent and dependent system states, and robust against malicious nodes.

## Contribution

It proposes a computationally efficient message passing approach for decision fusion in adversarial settings, extending effectiveness to dependent system states and long observation windows.

## Key findings

- The proposed scheme performs close to the optimal fusion rule for small observation windows.
- It outperforms prior suboptimal schemes when using long observation windows.
- Byzantine nodes may aim to minimize mutual information rather than always flipping decisions.

## Abstract

We consider a simple, yet widely studied, set-up in which a Fusion Center (FC) is asked to make a binary decision about a sequence of system states by relying on the possibly corrupted decisions provided by byzantine nodes, i.e. nodes which deliberately alter the result of the local decision to induce an error at the fusion center. When independent states are considered, the optimum fusion rule over a batch of observations has already been derived, however its complexity prevents its use in conjunction with large observation windows. In this paper, we propose a near-optimal algorithm based on message passing that greatly reduces the computational burden of the optimum fusion rule. In addition, the proposed algorithm retains very good performance also in the case of dependent system states. By first focusing on the case of small observation windows, we use numerical simulations to show that the proposed scheme introduces a negligible increase of the decision error probability compared to the optimum fusion rule. We then analyse the performance of the new scheme when the FC make its decision by relying on long observation windows. We do so by considering both the case of independent and Markovian system states and show that the obtained performance are superior to those obtained with prior suboptimal schemes. As an additional result, we confirm the previous finding that, in some cases, it is preferable for the byzantine nodes to minimise the mutual information between the sequence system states and the reports submitted to the FC, rather than always flipping the local decision.