Correcting one error in channels with feedback

We address the problem of correcting a single error in an arbitrary discrete memoryless channel with error-free instantaneous feedback. For the case of a one-time feedback, we propose a method for constructing optimal transmission strategies. The obtained result allows us to prove that for a binary channel, two feedbacks are sufficient to transmit the same number of messages as in the case of complete feedback. We also apply the developed techniques to a binary asymmetric channel to construct transmission strategies for small lengths.