{"paper":{"title":"Feedback Capacity and Coding for the $(0,k)$-RLL Input-Constrained BEC","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haim H. Permuter, Ori Peled, Oron Sabag","submitted_at":"2017-12-07T16:11:06Z","abstract_excerpt":"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 `$0$'s are allowed. The feedback capacity of this channel is derived for all $k\\geq 1$, and is given by $$C^\\mathrm{fb}_{(0,k)}(\\varepsilon) = \\max\\frac{\\overline{\\varepsilon}H_2(\\delta_0)+\\sum_{i=1}^{k-1}\\left(\\overline{\\varepsilon}^{i+1}H_2(\\delta_i)\\prod_{m=0}^{i-1}\\delta_m\\right)}{1+\\sum_{i=0}^{k-1}\\left(\\overline{\\varepsilon}^{i+1}\n  \\prod_{m=0}^{i}\\delta_m\\right)},$$ where $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02690","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}