Simplifying Computation of Diversity-Multiplexing Trade-off of Full-duplex Diamond Relay Channels

For the most relay networks with fading channels, it is practicable to devise communication schemes that are optimal in terms of diversity multiplexing trade-off (DMT). Characterizing the DMT of a general -relay is an ongoing challenging problem. In this paper, we show that to compute DMT of a diamond relay channel one has to solve an optimization problem. Direct computation of DMT of a diamond network with relays requires solving optimization problems (an optimization for each cut in the network). Solving that many optimization problems in networks with many relays is not practical. We demonstrate that for any -relay full-duplex diamond channel, if all the exponential orders of the average signal to ratios of links in the network are greater than the multiplexing gain, then computing DMT of such network is equivalent to minimizing a submodular function and can be carried out in polynomial time.