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Journal of Mathematical Physics

Bounds for Certain Thermodynamic Averages

A. Brooks Harris

Published May 1, 1967• 24 citations
Publisher

Abstract

Upper and lower bounds for thermodynamic averages of the form 〈{A, A†}〉 are presented.
DOI
10.1063/1.1705312

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This paper investigates the physical-layer security for an indoor visible light communication network consisting of a transmitter, a legitimate receiver, and an eavesdropper. Both the main channel and the wiretapping channel have non-negative inputs, which are corrupted by additive white Gaussian noises. Considering the illumination requirement and the physical characteristics of lighting source, the input is also constrained in both its average and peak optical intensities. Two scenarios are investigated: one is only with an average optical intensity constraint and the other is with both average and peak optical intensity constraints. Based on the information theory, closed-form expressions of the upper and lower bounds on secrecy capacity for the two scenarios are derived. Numerical results show that the upper and lower bounds on secrecy capacity are tight, which validates the derived closed-form expressions. Moreover, the asymptotic behaviors in the high signal-to-noise ratio (SNR) regime are analyzed from the theoretical aspects. At high SNR, when only considering the average optical intensity constraint, a small performance gap exists between the asymptotic upper and lower bounds on secrecy capacity. When considering both average and peak optical intensity constraints, the asymptotic upper and lower bounds on secrecy capacity coincide with each other. These conclusions are also confirmed by numerical results.