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The two-dimensional communication system (2DCS) is a novel technology that allows the surface physical as a communication medium for providing simultaneous power supply and data transmission to any device. However, how to carry out simultaneous power supply and data transmission in an efficient manner is still an open issue for 2DCS. In this paper, we propose a concurrent power supply and data transmission protocol based on the modifications of IEEE 802.15.4 MAC protocol standard, and then propose a generic rechargeable battery model by considering the features of 2DCS. Simulation results reveal that our proposed scheme highly improves the energy charging efficiency of 2DCS.