Optimal encoders maximizing directed information of channels with memory and feedback: Stochastic control and dynamic programming

Abstract

This paper is concerned with the stochastic control formulation of the capacity of channel with memory and feedback. The pay-off is the directed information from the source sequence to the channel output sequence, while the objective is to find the optimal encoder which maximizes this quantity. By invoking a change of measure technique this problem is re- formulated in terms of controlling the a posteriori probability via the choice of the encoder strategies to maximize the directed information. A principle of optimality is derived and a dynamic programming equation is obtained which describe how the optimal encoder strategy should be selected. Further, a generalization of posterior matching scheme is presented. © 2011 IFAC.