Generalized Bayes Estimates for Transmission in Channels with Feedback

A method of transmission in memoryless channels with noiseless feedback is considered, generalizing certain transmission methods described in [J. P. M. Schalkwijk and T. Kailath, IEEE Trans. Inf. Theory, 1966, vol. 12, no. 2, pp. 172–182; J. P. M. Schalkwijk, IEEE Trans. Inf. Theory, 1966, vol. 12, no. 2, pp. 183–189; K. Sh. Zigangirov, Probl. Peredachi Inf., 1967, vol. 3, no. 2, pp. 98–101]. The case in which the average power of the transmitted signals is small is investigated in detail (on the assumption of a certain noise regularity). In this extreme case the proposed transmission method makes it possible to obtain an arbitrarily small error probability for transmission rates whose upper bound coincides asymptotically with the channel carrying capacity.