  We introduce a novel mechanism, called timid/bold coding, by which feedback
can be used to improve coding performance. For a certain class of DMCs, called
compound-dispersion channels, we show that timid/bold coding allows for an
improved second-order coding rate compared with coding without feedback. For
DMCs that are not compound dispersion, we show that feedback does not improve
the second-order coding rate. Thus we completely determine the class of DMCs
for which feedback improves the second-order coding rate. An upper bound on the
second-order coding rate is provided for compound-dispersion DMCs. We also show
that feedback does not improve the second-order coding rate for very noisy
DMCs. The main results are obtained by relating feedback codes to certain
controlled diffusions.
