Results on the Rate-Equivocation Region of the Degraded Signal-Dependent Noise Wiretap Channel

This letter studies the rate-equivocation region of a degraded signal-dependent noise wiretap channel (SDGN-WC), where the noise is Gaussian. This signal-dependent noise occurs in optical wireless communication (OWC) settings based on intensity modulation and direct detection (IM-DD). In this setup, the transmitted signals are nonnegative and are restricted by an average optical power constraint. We consider the rate-equivocation region of the degraded SDGN-WC and through solving a convex optimization problem, we establish that the support set of the optimal distributions must be countably infinite. Our result implies that when the transmitted optical signals are restricted by an average optical power: 1) the secrecy capacity is achieved by a distribution which has a countably infinite support set; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a distribution having a countably infinite support set.