A Communication Channel With Random Battery Recharges

Motivated by the recent emergence of energy harvesting and wirelessly powered transceivers, we study communication over a memoryless channel with a transmitter, whose battery is recharged at random or deterministic times known to the receiver. We characterize the capacity of this channel as the limit of an n-letter maximum mutual information rate under various assumptions: causal and noncausal transmitter knowledge of the battery recharges, with or without feedback from the receiver to the transmitter. While the resultant n-letter capacity expressions are not computable in the general case, we demonstrate their usefulness by focusing on two important special cases, namely, the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) channel, where they lead to some interesting, and somewhat surprising, insights. By focusing on the BEC, we show that output feedback can strictly increase the capacity of this channel, even though the channel is memoryless and the battery recharging process is independent over time. Interestingly, this provides a counter example to an old claim by Shannon stated without proof in his 1956 paper. On the other hand, by focusing on the AWGN channel, we are able to show that the capacity with noncausal knowledge of the battery recharging times at the transmitter is strictly larger than that with causal knowledge, even though the battery recharging process is independent over time and known to the receiver. The n-letter expressions can also be used to derive explicit upper and lower bounds on capacity. In particular, we derive simple upper and lower bounds on the capacity of the AWGN channel with random battery recharges, which are within 1.05 b/s/Hz of each other for all parameter values.