This paper studies the degraded optical wiretap channel with an input-dependent Gaussian noise when the channel input is only constrained by nonnegativity and average-intensity constraints. We consider the rate-equivocation region of this wiretap channel and through solving a convex optimization problem, we establish that discrete input distributions with an infinite number of mass points exhaust the entire rate-equivocation region of the degraded OWC-IDGN with non-negativity and average-intensity constraints. This result implies that when nonnegativity and average-intensity constraints are imposed on the channel input: 1) the secrecy-capacity-achieving input distribution of the degraded OWC-IDGN is discrete with an unbounded support, i.e., the support set of the optimal distribution is countably infinite; 2) the channel capacity (the case with no secrecy constraints) is also achieved by a discrete distribution with an unbounded support set.
Soltani, M., & Rezki, Z. (2020). New Results on The Rate-Equivocation Region of The Optical Wiretap Channel with Input-Dependent Gaussian Noise with an Average-Intensity Constraint. 2020 Information Theory and Applications Workshop (ITA). doi:10.1109/ita50056.2020.9245013
This work has been supported by the King Abdullah University of Science and Technology (KAUST), under a competitive research grant (CRG) OSR-2016-CRG5-2958-01.