Decision Fusion with Unbalanced Priors under Synchronized Byzantine Attacks: A Message-Passing Approach

We consider a variant of the decision fusion problem in the presence of Byzantines where the two states of the system under observation are not equiprobable. In this setup, the Byzantines can not adopt a simple corruption strategy consisting in flipping the local decisions regardless of the estimated state of the system. Doing so, in fact, they would reveal their presence to the fusion center, since their reports would not follow the expected statistics. On its side, the fusion center can exploit the knowledge of the a-priori probabilities to improve its decision. In view of the above observations, we first introduce a new corruption strategy for the Byzantines, which permits them to make the statistics of their reports indistinguishable from those of the honest nodes. Then, we adopt the perspective of the fusion center and we propose a nearly-optimum, efficient, fusion strategy based on message passing, to face with the new attack. We do so in the most challenging scenario wherein the Byzantines are synchronised, i.e. they share a common source of randomness allowing them to submit wrong reports in a simultaneous way. We prove the validity of the proposed approach under several working conditions with regard to the percentage of byzantine nodes, the length of the observation window and the a priori-probabilities of the system states.