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In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless channel with the help of a relay. In this paper, the authors derive achievable rate regions for four new half-duplex protocols and compare these to four existing half-duplex protocols and outer bounds. In time, their protocols consist of either two or three phases. In the two phase protocols, both users simultaneously transmit during the first phase and the relay alone transmits during the second phase, while in the three phase protocol the two users sequentially transmit followed by a transmission from the relay.
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