  We consider a class of Gaussian layered networks where a source communicates
with a destination through $L$ intermediate relay layers with $N$ nodes in each
layer in the presence of a single eavesdropper which can overhear the
transmissions of the nodes in any one layer. The problem of maximum secrecy
rate achievable with analog network coding for a unicast communication over
such layered wireless relay networks with directed links is considered. A relay
node performing analog network coding scales and forwards the signals received
at its input. The key contribution of this work is a lemma that provides the
globally optimal set of scaling factors for the nodes that maximizes the
end-to-end secrecy rate for a class of layered networks. We also show that in
the high-SNR regime, ANC achieves secrecy rates within a constant gap of the
cutset upper bound on the secrecy capacity. To the best of our knowledge, this
work offers the first characterization of the performance of secure ANC in
multi-layered networks in the presence of an eavesdropper.
