In this paper, we prove a new achievable rate region for the two-phase two-way relay channel under half-duplex constraints. The points in the region are achieved by a combination of a compress-and-forward strategy at the relay node (potentially including partial decoding) with a kind of joint decoding at the receivers. For some channels, the achievable rate region presented in this paper is shown to be a proper superset of a rate region proven in some recent papers where a separate decoding was assumed.

We consider the broadcast phase of a three-node network, where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient two-phase decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node. Then the relay node decodes the messages and broadcasts a re-encoded composition of them in the second phase. We consider Gaussian MIMO channels and determine the capacity region for the second phase which we call the Gaussian MIMO bidirectional broadcast channel.

In this paper, we state a new achievable rate region for the two-phase two-way relay channel with a half-duplex relay node. The new region is obtained using a partial-decode-and-forward protocol, which is a superposition of both, decode-and-forward and compress-and-forward. It contains the achievable rate regions of [1] and [2] as special cases.

In a three-node network bidirectional communication between two nodes can be enabled by a half-duplex relay node with a decode-and-forward protocol. In the first phase, the messages of two nodes are transmitted to the relay node. In the second phase a re-encoded composition is broadcasted by the relay node. In this work the capacity region of the broadcast phase in terms of the maximal probability of error is determined. It is characterized by the mutual informations of the separate channels coupled by the common input.

In our previous work we determined the weak capacity region for the broadcast phase of two-phase bidirectional relay channel. It turned out that the set of achievable rates obtained by optimizing over the two communication phases exceeds that obtained by using the network coding principle, i.e. by applying XOR to the decoded messages. In this paper we supplement our result by a proof of the strong converse with respect to the maximum error probability to the coding theorem for the broadcast phase. This result implies that the capacity region of that phase remains constant for a certain range of values of average error parameters [epsiv1,epsiv2].