Capacity of the Ising channel with feedback

In this paper we consider the Ising channel, which is a channel with memory. We formulate a dynamic program that characterizes the capacity of the Ising channel with feedback and solve it numerically using the value iteration algorithm. We then establish analytically that the feedback capacity is the expression C = (2H(a)/3+a) ≈ 0.575522 where a is a particular root of a fourth-degree polynomial and, simultaneously, is the value that maximizes (2H(z)/3+z) over 0 ≤ z ≤ 1, where H(z) is the binary entropy function.