### abstract

- The input-constrained binary erasure channel (BEC) with strictly causal feedback is studied. The channel input sequence must satisfy the (0, k)-runlength limited (RLL) constraint, i.e., no more than k consecutive zeros are allowed. The feedback capacity of this channel is derived for all k≥1 C fn (0, k) (ε) = max εH 2 (δ 0 )+Σ k-1 i=1 (ε i+1 H 2 )(δ i )Π i-1 m=0 δ m )/1+Σ k-1 i=0 (ε i+1 Π i m=0 δ m ) where ε is the erasure probability, ε=1-ε, H 2 (·) is the binary entropy function and the maximization is only over δ k-1 , while the other parameters δ 0 , ..., δ k-2 are simple functions of δ k-1 . A simple coding scheme is constructed for all k, establishing that the feedback capacity can be achieved using variable length zero-error coding. In addition, it is shown that non-causal knowledge of the erasures at the encoder does not increase the feedback capacity.