  In order to satisfy the delay requirements of telecommunication systems, in
this paper, we present a cooperative network with the short packet transmission
in the Rayleigh fading channel. The desired relay can be implemented as a
two-way half-duplex (HD) or a two-way full-duplex (FD). Also, for more accurate
satisfaction and reduction of communication delays, sending and receiving with
short packets is considered. Effective capacity appropriately measures the
transmission rate under the delay constraint. Therefore, it is considered as a
performance evaluation criterion here. With a two-way relay, two nodes exchange
data with each other using a relay simultaneously. The priorities and
requirements of the two nodes are not necessarily the same. Therefore, to
increase performance, the system is modeled and solved as a multi-objective
problem. In this way, the available power in the network is divided between the
relay and two nodes, and the effective capacity of the two nodes is maximized.
Depending on the different conditions, the optimal amount of allocated power to
relay and nodes is calculated. However, due to the complexity and time
consuming calculations, an approximate method which speeds up the calculation
is presented. The approximated solution has a very close performance to the
optimal allocated power. Finally, various comparisons have been made in
different conditions between the performance of two-way HD and two-way FD
relays. The improvement of multi-objective power allocation has been shown,
especially when the relay is not located in the middle of two nodes.
