{"paper":{"title":"Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Jesper Nederlof, Mikko Koivisto, Per Austrin, Petteri Kaski","submitted_at":"2016-05-02T12:58:13Z","abstract_excerpt":"Two sets $A, B \\subseteq \\{0, 1\\}^n$ form a Uniquely Decodable Code Pair (UDCP) if every pair $a \\in A$, $b \\in B$ yields a distinct sum $a+b$, where the addition is over $\\mathbb{Z}^n$. We show that every UDCP $A, B$, with $|A| = 2^{(1-\\epsilon)n}$ and $|B| = 2^{\\beta n}$, satisfies $\\beta \\leq 0.4228 +\\sqrt{\\epsilon}$. For sufficiently small $\\epsilon$, this bound significantly improves previous bounds by Urbanke and Li~[Information Theory Workshop '98] and Ordentlich and Shayevitz~[2014, arXiv:1412.8415], which upper bound $\\beta$ by $0.4921$ and $0.4798$, respectively, as $\\epsilon$ approa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00462","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"}