Achieving Full Secrecy Rate with Low Packet Delays: An Optimal Control Approach

We consider a single-user, single-hop wireless communication system, in which data packets arrive at a data queue to be transmitted to a receiver over a block fading channel, privately from an eavesdropper. We assume that the eavesdropper listens to the transmitter over another independently fading channel and that the transmitter only has knowledge of the distribution of the eavesdropper´s channel. We propose a joint secrecy rate, transmission, and admission controller based on a simple index policy that only relies on the distribution of the eavesdropper´s channel rate. Given any arrival sample path, we show that our controller achieves the maximum possible data admission rate, while keeping the data queue stable as well as meeting an upper bound on the rate of secrecy outage, i.e., the fraction of data packets that are in part or fully decodable by the eavesdropper. While the solution is not unique, i.e., there are other schemes that can achieve the aforementioned performance, we show that our scheme also achieves a low queuing delay for the data packets enqueued at the data queue by striking the correct balance between direct secrecy encoding for data bits and secret key generation and utilization. To obtain this result, our transmission controller makes use of the secret key queue to smooth out the variations in the achievable secrecy rate of the associated fading wiretap channel.