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

Structured Optimal Transmission Control in Network-coded Two-way Relay Channels