Capacity of the energy harvesting channel with a finite battery
We consider an energy harvesting channel, in which the transmitter is powered by an exogenous stochastic energy arrival process, which can be stored in a battery of finite size. We provide an n-letter expression for the capacity of this channel under various assumptions on the availability of energy arrival information: causal and noncausal knowledge of the energy arrivals at the transmitter with and without knowledge at the receiver. We then proceed to deriving lower and upper bounds on the capacity that are easier to compute and are within a constant gap of each other. In particular, we show that the power control problem for energy-harvesting communication, extensively studied in the communication theory literature over the recent years, provides an upper bound on the true information-theoretic capacity of the channel. For example, the offline power control problem provides an upper bound on the information-theoretic capacity with noncausal knowledge of the energy arrivals at the transmitter and the receiver, while the online problem is an upper bound on the capacity with causal information. Perhaps more surprisingly, we also show that given an optimal power control policy there is a natural way to construct an explicit scheme which achieves a rate within a constant gap of the upper bound for any i.i.d. energy harvesting process and any battery size. This shows that these two different formulations of the energy-harvesting communication problem, so far studied in isolation, are strongly coupled; solving the power control problem is almost sufficient to solve the information-theoretic problem.