The Capacity Of Two Way Relay Channel
  This paper investigates the capacity of a wireless two way relay channel in which two end nodes exchange information via a relay node. The capacity is defined in the information-theoretic sense as the maximum information exchange rate between the two end nodes. We give an upper bound of the capacity by applying the cut-set theorem. We prove that this upper bound can be approached in low SNR region using "separated" multiple access for uplinks from the end nodes to the relay in which the data from the end nodes are individually decoded at the relay; and network-coding broadcast for downlinks from the relay to the end nodes in which the relay mixes the information from end nodes before forwarding. We further prove that the capacity is approachable in high SNR region using physical-layer network coding (PNC) multiple access for uplinks, and network-coding broadcast for downlinks. From our proof and observations, we conjecture that the upper bound may be achieved with PNC in all SNR regions. 
Zhang Shengli, Soung Chang Liew