{"paper":{"title":"Efficient Near-Optimal Codes for General Repeat Channels","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Francisco Pernice, Mary Wootters, Ray Li","submitted_at":"2022-01-30T07:47:08Z","abstract_excerpt":"Given a probability distribution $\\mathcal{D}$ over the non-negative integers, a $\\mathcal{D}$-repeat channel acts on an input symbol by repeating it a number of times distributed as $\\mathcal{D}$. For example, the binary deletion channel ($\\mathcal{D}=Bernoulli$) and the Poisson repeat channel ($\\mathcal{D}=Poisson$) are special cases. We say a $\\mathcal{D}$-repeat channel is square-integrable if $\\mathcal{D}$ has finite first and second moments. In this paper, we construct explicit codes for all square-integrable $\\mathcal{D}$-repeat channels with rate arbitrarily close to the capacity, that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.12746","kind":"arxiv","version":2},"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/2201.12746/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"}