Coding and Decoding for the Dynamic Decode and Forward Relay Protocol

We study the dynamic decode-and-forward (DDF) protocol for a single half-duplex relay, single-antenna channel with quasi-static fading. The DDF protocol is well known and has been analyzed in terms of the diversity-multiplexing tradeoff (DMT) in the infinite block length limit. We characterize the finite block length DMT and give new explicit code constructions. The finite block length analysis illuminates a few key aspects that have been neglected in the previous literature: 1) we show that one dominating cause of degradation with respect to the infinite block length regime is the event of decoding error at the relay; 2) we explicitly take into account the fact that the destination does not generally know a priori the relay decision time at which the relay switches from listening to transmit mode. Both of the above problems can be tackled by a careful design of the decoding algorithm. In particular, we introduce a decision rejection criterion at the relay based on Forney's decision rule (a variant of the Neyman-Pearson rule), such that the relay triggers transmission only when its decision is reliable. Also, we show that a receiver based on the generalized likelihood ratio test (GLRT) rule that jointly decodes the relay decision time and the information message achieves the optimal DMT. Our results show that no cyclic redundancy check (CRC) for error detection or additional protocol overhead to communicate the decision time are needed for DDF. Finally, we investigate the use of minimum mean-squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding at both the relay and the destination, and show that it provides near-optimal performance at moderate complexity.