Towards Optimal Schemes for the Half-Duplex Two-Way Relay Channel

A restricted two-way communication problem in a small network is investigated. The network consists of three nodes, all having access to a common channel with half-duplex constraint. Two nodes want to establish a dialog while the third node can assist in the bi-directional transmission process. All nodes have agreed on a transmission protocol a priori and the problem is restricted to the dialog encoders not being allowed to establish a cooperation by the use of previous receive signals. The channel is referred to as the restricted half-duplex two-way relay channel. Here the channel is defined and an outer bound on the achievable rates is derived by the application of the Cut-set Theorem. This shows that the problem consists of six parts. By the use of random codes and suboptimal decoders an inner bound on the achievable rates with decoding at the relay is established. Restricting to this relaying strategy and fixed input distributions makes it possible to determine optimal transmission schemes with respect to maximizing a rate objective or to minimizing a cost objective by solving a small-scale linear program. Simulations for an AWGN-channel model then show that it is possible to simultaneously increase the communication rate of both dialog messages compared to two-way communication without relay.