  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 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 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.
