When Does Feedback Improve the Second-Order Coding Rate in Discrete Memoryless Channels?

It is shown that feedback does not improve the second-order coding rate for a class of discrete memoryless channels which complements the class of channels for which feedback is known to improve the second-order coding rate. A refined achievability scheme is presented for the second-order rate when feedback helps. Moreover, for such channels an upper bound is derived on the achievable rate with feedback utilizing a novel proof technique.