  We consider a multi-stage distributed detection scenario, where $n$ sensors
and a fusion center (FC) are deployed to accomplish a binary hypothesis test.
At each time stage, local sensors generate binary messages, assumed to be
spatially and temporally independent given the hypothesis, and then upload them
to the FC for global detection decision making. We suppose a one-bit memory is
available at the FC to store its decision history and focus on developing
iterative fusion schemes. We first visit the detection problem of performing
the Neyman-Pearson (N-P) test at each stage and give an optimal algorithm,
called the oracle algorithm, to solve it. Structural properties and limitation
of the fusion performance in the asymptotic regime are explored for the oracle
algorithm. We notice the computational inefficiency of the oracle fusion and
propose a low-complexity alternative, for which the likelihood ratio (LR) test
threshold is tuned in connection to the fusion decision history compressed in
the one-bit memory. The low-complexity algorithm greatly brings down the
computational complexity at each stage from $O(4^n)$ to $O(n)$. We show that
the proposed algorithm is capable of converging exponentially to the same
detection probability as that of the oracle one. Moreover, the rate of
convergence is shown to be asymptotically identical to that of the oracle
algorithm. Finally, numerical simulations and real-world experiments
demonstrate the effectiveness and efficiency of our distributed algorithm.
