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We study the problem of joint information and energy transfer in a binarytwo-hop channel with an energy harvesting relay. We consider a finite batterysize at the relay and energy loss in transmitting energy. In other words, to beable to send an energy-contained symbol, the relay must receive multipleenergy-contained symbols. Thus, we face a kind of channel with memory. We modelthe energy saved in the battery as the channel state with the challenge thatthe receiver does not know the channel state. We propose two differentachievable schemes, the first one is based on state-dependent superpositioncoding and the second one is based on the equivalent timing channel approach.Both of our schemes are based on block Markov coding and backward decodingtechniques. Due to these two approaches, we find achievable rates with asingle-letter expression for the model.

Achievable Rates for Binary Two-hop Channel with Energy Harvesting Relay and Finite Battery