Capacity and Coding for the Ising Channel With Feedback

The Ising channel, which was introduced in 1990, is a channel with memory that models intersymbol 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 = (2H_b(a)/3+a) ≈ 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≤x≤1 (2H_b(x)/3+x). Finally, an error-free, capacity-achieving coding scheme is provided together with the outlining of a strong connection between the DP results and the coding scheme.