  This paper considers a transmission control problem in network-coded two-way
relay channels (NC-TWRC), where the relay buffers random symbol arrivals from
two users, and the channels are assumed to be fading. The problem is modeled by
a discounted infinite horizon Markov decision process (MDP). The objective is
to find a transmission control policy that minimizes the symbol delay, buffer
overflow and transmission power consumption and error rate simultaneously and
in the long run. By using the concepts of submodularity, multimodularity and
L-natural convexity, we study the structure of the optimal policy searched by
dynamic programming (DP) algorithm. We show that the optimal transmission
policy is nondecreasing in queue occupancies or/and channel states under
certain conditions such as the chosen values of parameters in the MDP model,
channel modeling method, modulation scheme and the preservation of stochastic
dominance in the transitions of system states. The results derived in this
paper can be used to relieve the high complexity of DP and facilitate real-time
control.
