  We derive expressions for the achievable rate region of a collaborative
coding scheme in a two-transmitter, two-receiver Pairwise Collaborative Network
(PCN) where one transmitter and receiver pair, namely relay pair, assists the
other pair, namely the source pair, by partially decoding and forwarding the
transmitted message to the intended receiver. The relay pair provides such
assistance while handling a private message. We assume that users can use the
past channel outputs and can transmit and receive at the same time and in the
same frequency band. In this collaborative scheme, the transmitter of the
source pair splits its information into two independent parts. Ironically, the
relay pair employs the decode and forward coding to assist the source pair in
delivering a part of its message and re-encodes the decoded message along with
private message, which is intended to the receiver of the relay pair, and
broadcasts the results. The receiver of the relay pair decodes both messages,
retrieves the private message, re-encodes and transmits the decoded massage to
the intended destination. We also characterize the achievable rate region for
Gaussian PCN. Finally, we provide numerical results to study the rate trade off
for the involved pairs. Numerical result shows that the collaboration offers
gain when the channel gain between the users of the relay pair are strong. It
also shows that if the channel conditions between transmitters or between the
receivers of the relay and source pairs are poor, such a collaboration is not
beneficial.
