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 byrelying on the possibly corrupted decisions provided by byzantine nodes, i.e.nodes which deliberately alter the result of the local decision to induce anerror at the fusion center. When independent states are considered, the optimumfusion rule over a batch of observations has already been derived, however itscomplexity prevents its use in conjunction with large observation windows. In this paper, we propose a near-optimal algorithm based on message passingthat greatly reduces the computational burden of the optimum fusion rule. Inaddition, the proposed algorithm retains very good performance also in the caseof dependent system states. By first focusing on the case of small observationwindows, we use numerical simulations to show that the proposed schemeintroduces a negligible increase of the decision error probability compared tothe optimum fusion rule. We then analyse the performance of the new scheme whenthe FC make its decision by relying on long observation windows. We do so byconsidering both the case of independent and Markovian system states and showthat the obtained performance are superior to those obtained with priorsuboptimal schemes. As an additional result, we confirm the previous findingthat, in some cases, it is preferable for the byzantine nodes to minimise themutual information between the sequence system states and the reports submittedto the FC, rather than always flipping the local decision.
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