Dynamic decode and forward for the multi-access relay channel with finite block length

The dynamic decode-and-forward (DDF) protocol for the multiple access relay channel (MARC) with quasi static fading is evaluated using the Zheng-Tse diversity-multiplexing tradeoff (DMT). We assume that there are two users, one half-duplex relay, and a common destination, each equipped with single antenna. For the Rayleigh fading channel, the DDF protocol is well known and has been analyzed in terms of the DMT with the infinite block length assumption by Azarian et al. However, to make the protocol feasible, the practical constraint of finite block length must be enforced, which may result in a loss in the DMT. Another practical effect not considered in the infinite block length DDF protocol is the possible decoding error at the relay. By carefully dealing with these practical issues due to finite block length, we characterize the finite block length DMT of the DDF protocol. We further consider the situation where the destination does not have a priori knowledge of the relay decision time at which the relay switches from listening to transmitting, and show that the optimal DMT is still achievable as if there is no decoding error at the relay. Therefore, the assumption of error-free decoding at the relay and additional protocol overhead to communicate the decision time are not needed for the DDF to achieve the optimal DMT.