This paper addresses energy harvesting systems, where the transmitter communicates using ON-OFF signaling i.e. in each slot it can either choose to transmit (ON) or stay silent (OFF). Two different communication models are introduced; in the first model an infinite-capacity battery is used and the system communicates on a binary-input memoryless channel, and the second model is a frame-based communication model where a random number of energy quanta is harvested in the beginning of each frame. For the slot-based communication model with an infinite-capacity battery, we have established the capacity and an optimal transmission scheme. For the frame-based communication model, we propose a transmission scheme based on reordering of energy quanta within a frame.
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