  We study the behavior of the belief-propagation (BP) algorithm affected by
erroneous data exchange in a wireless sensor network (WSN). The WSN conducts a
distributed binary hypothesis test where the joint statistical behavior of the
sensor observations is modeled by a Markov random field whose parameters are
used to build the BP messages exchanged between the sensing nodes. Through
linearization of the BP message-update rule, we analyze the behavior of the
resulting erroneous decision variables and derive closed-form relationships
that describe the impact of stochastic errors on the performance of the BP
algorithm. We then develop a decentralized distributed optimization framework
to enhance the system performance by mitigating the impact of errors via a
distributed linear data-fusion scheme. Finally, we compare the results of the
proposed analysis with the existing works and visualize, via computer
simulations, the performance gain obtained by the proposed optimization.
