The paper considers the input-constrained binary erasure channel (BEC) with causal,
noiseless feedback. The channel input sequence respects the (d,∞)-runlength limited (RLL)
constraint, ie, any pair of successive 1s must be separated by at least d 0s. We derive upper
and lower bounds on the feedback capacity of this channel, given by single parameter
maximization problems that differ exclusively in the domain of maximization. The results of
Sabag et al.(2016) show that our bounds are tight for the case when d=1. For the case when …

The paper considers the input-constrained binary erasure channel (BEC) with causal,
noiseless feedback. The channel input sequence respects the $(d,\infty) $-runlength limited
(RLL) constraint, ie, any pair of successive $1 $ s must be separated by at least $ d $ $0 $ s.
We derive upper and lower bounds on the feedback capacity of this channel, for all $ d\geq
1$, given by: $\max\limits_ {\delta\in [0,\frac {1}{d+ 1}]} R (\delta)\leq C^{\text {fb}} _
{(d\infty)}(\epsilon)\leq\max\limits_ {\delta\in [0,\frac {1}{1+ d\epsilon}]} R (\delta) $, where the …