{"paper":{"title":"Coded trace reconstruction in a constant number of traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS","math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Bruce Spang, Joshua Brakensiek, Ray Li","submitted_at":"2019-08-12T04:27:12Z","abstract_excerpt":"The coded trace reconstruction problem asks to construct a code $C\\subset \\{0,1\\}^n$ such that any $x\\in C$ is recoverable from independent outputs (\"traces\") of $x$ from a binary deletion channel (BDC). We present binary codes of rate $1-\\varepsilon$ that are efficiently recoverable from ${\\exp(O_q(\\log^{1/3}(\\frac{1}{\\varepsilon})))}$ (a constant independent of $n$) traces of a $\\operatorname{BDC}_q$ for any constant deletion probability $q\\in(0,1)$. We also show that, for rate $1-\\varepsilon$ binary codes, $\\tilde \\Omega(\\log^{5/2}(1/\\varepsilon))$ traces are required. The results follow fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03996","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/1908.03996/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"}