Gaussian wiretap channel with a batteryless energy harvesting transmitter

We study the Gaussian wiretap channel with an energy harvesting transmitter which does not have a battery to save energy. In the absence of a battery, the necessary transmission energy is maintained by an i.i.d. energy arrival process. We observe that this channel is an instance of the state-dependent wiretap channel with state available only to the transmitter causally, where the state is the available energy at the transmitter. We prove that the entire capacity-equivocation region can be obtained by single-letter Shannon strategies and its boundary is achieved by input distributions with support set of Lebesgue measure zero.