  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.
