  A restricted two-way communication problem in a small fully-connected 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. We propose a transmission protocol which takes into account all possible
transmit-receive configurations of the network and performs partial decoding of
the messages at the relay as well as sequential decoding at the dialog nodes.
By the use of random codes and suboptimal decoders, two inner bound on the
achievable rates are derived. Restricting to the suggested strategies and fixed
input distributions it is argued to be possible to determine optimal
transmission schemes with respect to various reasonable objectives at low
complexity. In comparison to two-way communication without relay, simulations
for an AWGN channel model then show that it is possible to simultaneously
increase the communication rates of both dialog messages and to outperform
relaying strategies that ignore an available direct path.
