On the Capacity of the Two-Hop Half-Duplex Relay Channel

Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be evaluated straightforwardly is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel based on a simplified converse. Compared to previous results, this capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve the capacity, the relay does not only send information to the destination by transmitting information-carrying symbols but also with the zero symbols resulting from the relay's silence during reception. As examples, we compute the capacities of the two-hop HD relay channel for the cases when the source-relay and relay-destination links are both binary-symmetric channels (BSCs) and additive white Gaussian noise (AWGN) channels, respectively, and numerically compare the capacities with the rates 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 capacities of the two-hop HD relay channel for BSC and AWGN links are significantly larger than the rates achieved with conventional relaying.