Secrecy rate closed-form expressions for the SISO VLC wiretap channel with discrete input signaling

We study in this letter the secrecy performance of a degraded single-input single-output visible-light communication wiretap channel. It has been shown in the literature that the secrecy capacity-achieving input distribution for this system is discrete with a finite support set. However, neither the secrecy capacity nor its achieving distribution has been derived in closed-form. In this letter, we derive in closed-form the achievable secrecy rate as a function of the discrete input distribution. We propose a class of discrete input distributions in an effort to enhance the achievable secrecy rate and approach the secrecy capacity. We also derive expressions for the achievable secrecy rate for different scenarios including the one in which the locations of the terminals are randomly located. We provide several examples that demonstrate the accuracy of the derived expressions and show the substantial secrecy rate improvements provided by the proposed scheme over existing ones.