{"paper":{"title":"The Porosity of Additive Noise Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Tsachy Weissman, Vinith Misra","submitted_at":"2012-05-31T12:35:43Z","abstract_excerpt":"Consider a binary additive noise channel with noiseless feedback. When the noise is a stationary and ergodic process $\\mathbf{Z}$, the capacity is $1-\\mathbb{H}(\\mathbf{Z})$ ($\\mathbb{H}(\\cdot)$ denoting the entropy rate). It is shown analogously that when the noise is a deterministic sequence $z^\\infty$, the capacity under finite-state encoding and decoding is $1-\\bar{\\rho}(z^\\infty)$, where $\\bar{\\rho}(\\cdot)$ is Lempel and Ziv's finite-state compressibility. This quantity is termed the \\emph{porosity} $\\underline{\\sigma}(\\cdot)$ of an individual noise sequence. A sequence of schemes are pre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6974","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"}