  The Ising channel, which was introduced in 1990, is a channel with memory
that models Inter-Symbol interference. In this paper we consider the Ising
channel with feedback and find the capacity of the channel together with a
capacity-achieving coding scheme. To calculate the channel capacity, an
equivalent dynamic programming (DP) problem is formulated and solved. Using the
DP solution, we establish that the feedback capacity is the expression
$C=(\frac{2H_b(a)}{3+a})\approx 0.575522$ where $a$ is a particular root of a
fourth-degree polynomial and $H_b(x)$ denotes the binary entropy function.
Simultaneously, $a=\arg \max_{0\leq x \leq 1} (\frac{2H_b(x)}{3+x})$. Finally,
a simple, error-free, capacity-achieving coding scheme is provided together
with outlining a strong connection between the DP results and the coding
scheme.
