{"paper":{"title":"Bounds on the Feedback Capacity of the $(d,\\infty)$-RLL Input-Constrained Binary Erasure Channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Navin Kashyap, V. Arvind Rameshwar","submitted_at":"2021-01-21T14:33:58Z","abstract_excerpt":"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, i.e., 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 function $R(\\delta) = \\frac{h_b(\\delta)}{d\\delta + \\frac{1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.08638","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.08638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}