The capacity to within a constant gap of the Gaussian half-duplex relay channel

This paper studies the Gaussian half duplex relay channel, where the relay node can not transmit and receive at the same time. The main contribution lies in showing that both Partial-Decode-Forward and Compress-Forward achieve the Cut-Set upper bound to within a constant gap regardless of the channel parameters. This provides a closed form characterization of the Generalized Degrees-of-Freedom (gDoF) of the channel, which for certain channel parameters is strictly smaller than the gDoF of the full duplex channel. Half duplex channels can convey information through the random switch between the receive and retransmit phases; this work shows numerically that random switch achieves larger rates compared to deterministic switch, which is usually considered in the literature.