A simple class of capacity-achieving strategies for discrete memoryless channels with feedback

A class of multiple-repetition strategies is presented for discrete memoryless channels with noiseless feedback. This extends results obtained by Schalkwijk (1971) to nonbinary, asymmetric memoryless channels. An interesting characterization of the attainability of a rate is presented in terms of a generating polynomial, from which follows that for each strategy in our class, there exists a discrete memoryless channel such that capacity can be achieved on this channel.