Diversity-Multiplexing Tradeoff of Network Coding with Bidirectional Random Relaying

Abstract: This paper develops a diversity-multiplexing tradeoff (DMT) over a bidirectional random relay set in a wireless network where the distribution of all nodes is a stationary Poisson point process. This is a nontrivial extension of the DMT because it requires consideration of the cooperation (or lack thereof) of relay nodes, the traffic pattern and the time allocation between the forward and reverse traffic directions. We then use this tradeoff to compare the DMTs of traditional time-division multihop (TDMH) and network coding (NC). Our main results are the derivations of the DMT for both TDMH and NC. This shows, surprisingly, that if relay nodes collaborate NC does not always have a better DMT than TDMH since it is difficult to simultaneously achieve bidirectional transmit diversity for both source nodes. In fact, for certain traffic patterns NC can have a worse DMT due to suboptimal time allocation between the forward and reverse transmission directions.