Time and power allocation for the Gaussian wiretap channel with feedback of secret keys

This paper solves the time and power allocation problem for the simplest feedback scheme for the Gaussian wiretap channel, which is based on the transmission of random secret keys to be used in a one time pad manner. Specifically, the optimal transmission powers at Alice and Bob, as well as the time sharing factor between the feedback and feedforward channels, are given by the solution of a non-convex optimization problem, which is found by means of the golden section algorithm and the sequential solution of several convex optimization problems. Additionally, an specific and highly efficient procedure for the solution of the inner convex optimization problems is provided, which avoids the need for general purpose optimization packages. Finally, several simulation results illustrate the potential secrecy gains achievable with a feedback scheme as simple as the one considered in this paper.