{"paper":{"title":"On the Zero-Error Capacity Threshold for Deletion Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ian A. Kash, Jonathan Ullman, Justin Thaler, Michael Mitzenmacher","submitted_at":"2011-01-31T23:41:41Z","abstract_excerpt":"We consider the zero-error capacity of deletion channels. Specifically, we consider the setting where we choose a codebook ${\\cal C}$ consisting of strings of $n$ bits, and our model of the channel corresponds to an adversary who may delete up to $pn$ of these bits for a constant $p$. Our goal is to decode correctly without error regardless of the actions of the adversary. We consider what values of $p$ allow non-zero capacity in this setting. We suggest multiple approaches, one of which makes use of the natural connection between this problem and the problem of finding the expected length of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0040","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"}