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.
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