Practical Design of Probabilistic Constellation Shaping for Physical Layer Security in Visible Light Communications

TL;DR

This paper proposes a practical probabilistic constellation shaping method for physical layer security in visible light communications, optimizing constellation distributions to enhance secrecy capacity and BER performance under various channel knowledge scenarios.

Contribution

It introduces a novel PCS design for VLC that accounts for reliability, flickering, and symmetry constraints, using a convex-concave procedure for non-convex optimization.

Findings

PCS outperforms uniform signaling across all optical power levels.

The proposed method maintains security and reliability even with unknown eavesdropper CSI.

Insights into optimal constellation distribution relative to emitted optical power.

Abstract

This paper studies a practical design of probabilistic constellation shaping (PCS) for physical layer security in visible light communications (VLC). In particular, we consider a wiretap VLC channel employing a probabilistically shaped $M$-ary pulse amplitude modulation (PAM) constellation. Considering the requirements for reliability of the legitimate user's channel, flickering-free transmission, and symmetric constellation distribution, the optimal constellation distributions to maximize modulation-constrained secrecy capacity or the bit error rate (BER) of eavesdropper's channel are investigated for both scenarios of known and unknown eavesdropper's channel state information (CSI). To formulate the constraint on the channel reliability, tractable closed-form expressions for the upper bound and approximate BER of $M$-ary PAM under an arbitrary symbol probability are derived. The design problem is shown to be non-convex due to the non-convex BER constraint. By proving that the upper bound BER is a concave function of the constellation distribution, a suboptimal solution based on the convex-concave procedure (CCCP) is presented. Our findings reveal that while the uniform signaling can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in the entire region of the optical power. Some insights into the optimal constellation distribution with respect to the emitted optical power are also discussed.