{"paper":{"title":"Separating signal from noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CA","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Nir Lev, Ron Peled, Yuval Peres","submitted_at":"2013-12-24T15:38:45Z","abstract_excerpt":"Suppose that a sequence of numbers $x_n$ (a `signal') is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \\xi_n$, where $\\xi_n$ is a sequence of independent standard Gaussian random variables. Suppose further that the signal is known to come from some fixed space of possible signals. Is it possible to fully recover the transmitted signal from its noisy version? Is it possible to at least detect that a non-zero signal was transmitted?\n  In this paper we consider the case in which signals are infinite sequences and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6843","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":""},"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"}