Secrecy Rate Pair Constraints for Secure Throughput

Physical layer security, which is an alternative to traditional cryptographic methods, has emerged as a promising candidate to protect wireless transmissions from an eavesdropper. An important measure of physical layer security is the secrecy outage: the event when the instantaneous secrecy capacity, which for the considered scenario is the difference between the capacity of the Alice (the transmitter) to Bob (the legitimate receiver) channel and the capacity of the Alice to Eve (the eavesdropper) channel, is below a target secrecy rate for which the system has been designed. In this paper, we argue that design under such an outage definition on a wireless channel is inadequate in some scenarios, as it treats very different error events with equal weight. In response, we propose that two conditions are met: the instantaneous capacity between the source and destination is above a target rate and the instantaneous capacity between the source and eavesdropper is held below a target rate. The two individual target rates form a secrecy rate pair. This also naturally splits the outage event into two regions with quite different costs: the eavesdropper's ability to decode the message (which is a security breach and must be avoided), and the destination's inability to decode the message (which simply requires a retransmission). We use our formulation to consider rate pair selection in hybrid ARQ systems and provide numerical results supporting this approach.