  This paper analyzes the throughput of industrial communication networks under
a secrecy constraint. The proposed scenario is composed by sensors that measure
some relevant information of the plant that is first processed by aggregator
node and then sent to the control unit. The sensor measurements, their
communication with the aggregetor and the information processing are all
assumed perfect. To reach the control unit, the message may travel through
relay nodes, forming a multi-hop, wireless link. At every hop, eavesdropper
nodes attempt to acquire the messages transmitted through the legitimate link.
The communication design problem posed here is how to maximize the multi-hop
throughput from the aggregator to the control unit by finding the best
combination of relay positions (i.e. hop length: short or long) and coding
rates (i.e. high or low spectral efficiency) so that the secrecy constraint is
satisfied. Using a stochastic-geometry approach, we show that the optimal
choice of coding rate depends only on the path- loss exponent and is normally
high while greater number of shorter hops are preferable to smaller number of
longer hops. For the scenarios of interest, we prove that the optimal
throughput subject to the secrecy constraint achieves the unconstrained optimal
performance if a feasible solution exists.
