Transmitting Status Updates on Infinite Capacity Systems with Eavesdropper: Freshness Advantage of Legitimate...

We consider the scenario in which the source sends status updates, or packets, to the receiver through an infinite capacity transmitter, where the transmitted packets are subject to potential illegal eavesdropping. Time is discretized into identical time slots. In recent years, the age of information (AoI) metric, which was defined as the time has elapsed since the generation instant of the latest received packet, has been widely applied to characterize the freshness of obtained packets. Due to the presence of eavesdroppers, some packets may be eavesdropped during their transmissions, causing information leakages. To assess an infinite-capacity system's performance of securely transmitting status updates, in this paper, we define an AoI-related metric called the freshness advantage of the legitimate receiver, F, to be average instantaneous gap between eavesdropper's and legitimate receiver's AoI. For arbitrarily distributed packet interarrival times, and assuming that in each time slot with probabilities γd, γE, the transmitted packet is received by the legitimate receiver and the eavesdropper, we derive the explicit formula of F. The concise expression shows that F is fully determined by the average interarrival time and the ratio of γd to γE. For special cases where the interarrival time follows geometric distributions, we first determine the explicit distribution of instantaneous AoI gap. Then, given γd and γE, we derive the optimal packet generation rate p∗ that minimizes the combined performance Q, which is constructed as the average AoI minus the freshness advantage F. When imposing timeliness and security constraints at the same time, the feasible regions of p and γd such that both two required performances can be satisfied are depicted and discussed. Finally, we investigate the impacts of different parameters on F and show the tradeoffs between timeliness performance and security performance through numerical simulations.