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CapacityoftheTwo-HopHalf-DuplexRelayChannel.PDF
1 Capacity of the Two-Hop Half-Duplex Relay Channel Nikola Zlatanov, Vahid Jamali, and Robert Schober Abstract We derive the capacity of the two-hop half-duplex (HD) relay channel. This channel is comprised of a source, a HD relay, and a destination, and there is no direct link between the source and the destination. Hence, the source is forced to transmit its message to the destination via the HD relay. Since the relay is HD, it cannot transmit and receive at the same time. For the considered relay channel, we show that achieving the capacity requires the relay to switch between reception and transmission in a symbol-by-symbol manner. Moreover, to achieve the capacity, the relay sends information to the destination by transmitting information-carrying symbols and with the zero symbol resulting from the relay’s silence during reception. We derive simplified capacity expressions for the following two special cases: 1) The source-relay and relay-destination links are both binary-symmetric channels (BSCs); 2) The source-relay and relay-destination links are both additive white Gaussian noise (AWGN) channels. For these two cases, we numerically compare the capacity rate with the rate achieved by conventional relaying where the relay receives and transmits in a codeword-by-codeword fashion and switches between reception and transmission in a strictly alternating manner. Our numerical results show that the capacity rate is significantly larger than the rate achieved with conventional relaying, for both the BSC and the AWGN
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