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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&#x2265;1 Cfn(0, k)(&#x03B5;) = max &#x03B5;H2(&#x03B4;0)+&#x03A3;k-1i=1(&#x03B5;i+1H2)(&#x03B4;i)&#x03A0;i-1m=0&#x03B4;m)/1+&#x03A3;k-1i=0(&#x03B5;i+1&#x03A0;im=0&#x03B4;m) where &#x03B5; is the erasure probability, &#x03B5;=1-&#x03B5;, H2(&#x00B7;) is the binary entropy function and the maximization is only over &#x03B4;k-1, while the other parameters &#x03B4;0, ..., &#x03B4;k-2 are simple functions of &#x03B4;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.

Feedback capacity and coding for the (0, k)-RLL input-constrained BEC