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

This paper proposes a practical design of probabilistic constellation shaping (PCS) for physical layer security in visible light communications. In particular, the M-ary PAM symbol distribution is optimized to maximize the secrecy capacity given constraints on the legitimate user's bit error rate (BER) and flickering mitigation. For this purpose, an approximate closed-form expression for the BER of M-ary PAM under an arbitrary symbol probability is derived and the issue of flickering caused by the channel-dependent solution is described. The design problem is shown to be non-convex due to the non-convex BER constraint. Thus, a suboptimal solution based on successive convex approximation (SCA) is presented. Our findings reveal that while the uniform signaling and PCS design without BER constraint can only satisfy the BER constraint when the optical power is beyond a certain value, the proposed PCS design works in all regions of the optical power. Some insights into the optimal symbol distribution with respect to the optical power are also discussed.