Successive relaying for the half-duplex parallel relay channel

We consider the problem of communication for a network composed of two half-duplex relays. A Successive relaying protocol in which the relays transmit their received messages successively to the destination is studied. A non-cooperative coding based on dirty paper coding (DPC) and a cooperative coding based on block Markov encoding (BME) are proposed and the optimum input distribution for the degraded case is derived. Furthermore, for the Gaussian case, we prove that the composite scheme of employing BME at one relay and DPC at another always achieves a better rate when compared to the cooperative scheme.