Diversity Multiplexing Tradeoff for Full-Duplex Relay Networks

Co-operative communication with relay assistance helps in enhancing the capacity of point to point links. The capacity of relay networks has been known to be upper bounded by the cut-set bound. Recently, the authors of [1] showed that it is possible to achieve the upper bound up to a constant additive gap, independent of the channel parameters. Presence of multiple relays provides multiple paths from the source to the destination. With no channel state information at the transmitter, these paths can be used to either obtain a high communication rate or a low probability of error. We can trade off one of these quantities for the other. This diversity multiplexing trade off has been studied extensively for MIMO systems. However, the trade off for full duplex Gaussian relay networks is not well understood. We shall study the diversity multiplexing trade off for multiple relay networks. This work provides a lower bound on the error probability at the destination as a function of the communication rate, assuming a finite time for communication. We see that if we choose block length corresponding to the optimal DMT for the min-cut, the probability of error is governed by one of the cuts with diversity gain less than the min-cut diversity gain. The error probability is exactly equal to the one obtained from the optimal DMT for the corresponding cut.