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,infinity)-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 C-epsilon = max(0) (<= p <= 1) H-b(p)/p+1/1-epsilon, where epsilon is the erasure probability and H-b(-) 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.