Optical Wiretap Channel With Input-Dependent Gaussian Noise Under Peak- and Average-Intensity Constraints

• Published in: IEEE transactions on information theory Vol. 64; no. 10; pp. 6878 - 6893
• Main Authors: Soltani, Morteza, Rezki, Zouheir
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic properties; Gaussian noise; high-intensity regime; input-dependent Gaussian noise; intensity modulation and direct detection; low-intensity regime; Luminous intensity; Optical fiber communication; Optical noise; Optical receivers; Optical transmitters; Optical wiretap channel; peak- and average-intensity constraints; Random noise; Signal strength; Wireless communication; Wireless communications; Wiretapping
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2018.2851225

This paper studies the optical wiretap channel with input-dependent Gaussian noise, in which the main distortion is caused by an additive Gaussian noise whose variance depends on the current signal strength. Subject to nonnegativity and peak-intensity constraints on the channel input, we first present a practical optical wireless communication scenario for which the considered wiretap channel is stochastically degraded. We then study the secrecy-capacity-achieving input distribution of this wiretap channel and prove it to be discrete with a finite number of mass points, one of them located at the origin. Moreover, we show that the entire rate-equivocation region of this wiretap channel is also obtained by discrete input distributions with a finite support. Similar to the case of the Gaussian wiretap channel under a peak-power constraint, here too, we observe that under nonnegativity and peak-intensity constraints, there is a tradeoff between the secrecy capacity and the capacity in the sense that both may not be achieved simultaneously. Furthermore, we prove the optimality of discrete input distributions in the presence of an additional average intensity constraint. Finally, we shed light on the asymptotic behavior of the secrecy capacity in the low- and high-intensity regimes. In the low-intensity regime, the secrecy capacity scales quadratically with the peak-intensity constraint. On the other hand, in the high-intensity regime, the secrecy capacity does not scale with the constraint.