The capacity of channels with feedback

Abstract

In this paper, we introduce a general framework for treating channels with memory and feedback. First, we prove a general feedback channel coding theorem based on Massey's concept of directed information. Second, we present coding results for Markov channels. This requires determining appropriate sufficient statistics at the encoder and decoder. We give a recursive characterization of these sufficient statistics. Third, a dynamic programming framework for computing the capacity of Markov channels is presented. Fourth, it is shown that the average cost optimality equation (ACOE) can be viewed as an implicit single-letter characterization of the capacity. Fifth, scenarios with simple sufficient statistics are described. Sixth, error exponents for channels with feedback are presented.