{"paper":{"title":"Finite-Length Scaling of Polar Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kasra Alishahi, Rudiger Urbanke, S. Hamed Hassani","submitted_at":"2013-04-17T11:53:42Z","abstract_excerpt":"Consider a binary-input memoryless output-symmetric channel $W$. Such a channel has a capacity, call it $I(W)$, and for any $R<I(W)$ and strictly positive constant $P_{\\rm e}$ we know that we can construct a coding scheme that allows transmission at rate $R$ with an error probability not exceeding $P_{\\rm e}$. Assume now that we let the rate $R$ tend to $I(W)$ and we ask how we have to \"scale\" the blocklength $N$ in order to keep the error probability fixed to $P_{\\rm e}$. We refer to this as the \"finite-length scaling\" behavior. This question was addressed by Strassen as well as Polyanskiy, P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4778","kind":"arxiv","version":4},"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"}