Energy harvesting communication using limited battery with efficiency

We consider an energy harvesting point-to-point communication system where the transmitter is powered by an energy arrival process and is equipped with a finite battery of size B_max, which has limited efficiencies for storing energy into the battery and withdrawing energy from the battery. We assume a discrete i.i.d. energy arrival process where at each time step, energy of size A_i is harvested with probability p_i, ∀i ∈ {1, 2;..., K}, independent of the other time steps. We provide upper and lower bounds on the information-theoretic capacity of this channel. These bounds are within a constant gap for K = 2 and a special case (with perfect battery efficiencies) for K = 3.