Capacity of remotely powered communication

Motivated by recent developments in wireless power transfer, we study communication with a remotely powered transmitter. We propose an information-theoretic model where a charger can dynamically decide on how much power to transfer to the transmitter based on its side information regarding the communication, while the transmitter needs to dynamically adopt its coding strategy to its instantaneous energy state, which in turn depends on the actions previously taken by the charger. We characterize the capacity as n-letter mutual information rate under various levels of side information available at the charger. In some special cases, motivated by different settings of practical interest, we simplify these expressions to single-letter form, or provide an algorithm to efficiently compute capacity using dynamic programming. Our results provide some surprising insights on how side information at the charger can be used to increase the overall capacity of the system.