Capacity of the (1, ∞)-RLL input-constrained erasure channel with feedback

The input-constrained erasure channel with feedback is considered, where the input sequence contains no consecutive 1´s, i.e. the (1, ∞)-RLL constraint. The capacity is calculated using an equivalent dynamic program, which shows that the optimal average reward is equal to the capacity. The capacity can be expressed as Hb(p) C_ϵ = max_0≤p≤1(H_b(p))/(p+(1/1-ε)) , where ϵ is the erasure probability and Hb(·) is the binary entropy. This capacity also serves as an upper bound on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.