Capacity of the energy harvesting channel with energy arrival information at the receiver

We determine the capacity of a discrete memoryless communication channel with an energy harvesting transmitter and the energy arrival information available at the receiver as well as the transmitter. We obtain an n-letter capacity expression and prove that the capacity is achieved by an encoding scheme that depends only on the current battery state. Moreover, the capacity is invariant to the non-causal knowledge of energy arrivals. Finally, we show that the capacity expression is equivalently the maximum directed mutual information and that the channel output feedback does not increase the capacity in this case. We obtain upper and lower bounds on the capacity and numerically evaluate them for comparison.