On the average-listsize capacity and the cutoff rate of discrete memoryless channels with feedback

We study the cutoff rate and the average-listsize capacity of discrete memoryless channels (DMCs) with feedback. We show that feedback can increase the average-listsize capacity but not the cutoff rate. For DMCs with positive zero-error capacity, we show that the average-listsize capacity with feedback is equal to the cutoff rate. For all other DMCs, we derive a lower bound on the average-listsize capacity with feedback. The bound is asymptotically tight for low-noise channels. We also show that a multi-letter version of Forney´s lower bound on the average-listsize capacity of DMCs without feedback is asymptotically tight.