Cooperative strategies for the half-duplex Gaussian parallel relay channel: Simultaneous relaying versus successive relaying

We consider the problem of cooperative communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise. Two protocols, i.e., Simultaneous and Successive relaying, associated with two possible relay orderings are proposed. The simultaneous relaying protocol is based on dynamic decode and forward (DDF) scheme. For the successive relaying protocol, a Non-Cooperative Coding based on dirty paper coding (DPC) is proposed. We also propose a general achievable rate based on the combination of the proposed simultaneous and successive relaying schemes. The optimum ordering of the relays and hence the capacity of the half-duplex Gaussian parallel relay channel in low and high SNR scenarios is derived. In low SNR scenario, we show that under certain conditions for the channel coefficients the ratio of the achievable rate of the simultaneous relaying protocol, based on the DDF scheme, to the cut-set bound of the half-duplex Gaussian parallel relay channel tends to 1. On the other hand, as SNR goes to infinity, we prove that successive relaying protocol, based on the DPC scheme, asymptotically achieves the capacity of the network.