Can half-duplex be simply derived from full-duplex communications?

We consider a discrete memoryless channel between two users and a destination in half-duplex mode implemented by time division. Each transmission block of length n is divided into 3 time slots with variable durations. During the first two time slots, each user alternatively transmits and receives, while during the last time slot, they both transmit to the destination. Even though within each time slot, the channel is similar to a (possibly degraded) broadcast or multiple access channel with known capacity, the capacity of the half-duplex channel cannot be simply derived from these components because of the possibility for joint decoding at the destination over all 3 time slots. We analyze achievable rate regions obtained by superposition encoding, partial decode-forward relaying at each user and two different decoding techniques at the destination. In the first technique, the destination performs separate decoding in each time slot, while in the second one, it performs joint decoding over all 3 time slots. Numerical results for the Gaussian channel show that joint decoding achieves a strictly larger rate region than separate decoding, and both approach the performance of the full-duplex cooperative scheme by Willem et al. as the inter-user channel quality increases.