Approximate Secrecy Capacity of Gaussian Parallel Relay Networks

We consider a Gaussian relay network, which has to protect the message from a powerful eavesdropper, which has the possibility of listening to the transmitted signals on orthogonal channels. The secrecy capacity of the Gaussian network is approximated by considering the corresponding network in the deterministic discrete superposition model. Upper and lower bounds on the secrecy capacity are found in terms of the deterministic model, which are potentially easier to evaluate. We perform this evaluation for the particular topology of the parallel relay network, where the relays form a parallel layer between the source and the destination. By analyzing the deterministic model, we approximate the secrecy capacity within a constant gap. The approximation can be expressed just in terms of the channel gains of the network. It is therefore possible to deduct that the simple scheme of hiding the transmitted signals in noise is approximately optimal.