Capacity of Energy Harvesting Binary Symmetric Channels With a $(\sigma ,\rho )$ -Power Constraint

Capacity of energy harvesting communications with deterministic energy arrival and finite battery size is investigated. An abstraction of the physical layer is considered, where binary sequences are transmitted through a binary symmetric channel, and a cost function is associated with the transmission of each symbol. Upper and lower bounds on the channel capacity are derived for the general case by studying the normalized exponent of the cardinality of the set of feasible input sequences. Several upper bounds on the exponent are proposed by studying supersets of the feasible set. Lower bounds are derived by applying the binary entropy-power inequality and by using specific signaling schemes based on a save-and-transmit strategy. Numerical results are presented for several values of the energy arrival rate and battery size, validating the usefulness of the capacity bounds established for the energy harvesting channels.