Gaussian half-duplex relay channels: Generalized degrees of freedom and constant gap result

This paper considers the Gaussian relay channel where the relay node operates in half-duplex mode. The exact capacity of the linear deterministic approximation of the Gaussian channel at high SNR is derived first. This result is then used to inspire an achievable scheme valid for any SNR in the original channel. The scheme is quite simple: it uses successive decoding and does not incur in the typical delay of backward decoding. The achievable rate is then showed to be at most 3 bits away from the cut-set upper bound, which allows to analytically determine the generalized Degrees-of-Freedom of the channel. A closed form expression for the gDoF-optimal fraction of time the relay node transmits is found as well.