{"paper":{"title":"An Improved Upper Bound for the Most Informative Boolean Function Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ofer Shayevitz, Omri Weinstein, Or Ordentlich","submitted_at":"2015-05-21T17:16:00Z","abstract_excerpt":"Suppose $X$ is a uniformly distributed $n$-dimensional binary vector and $Y$ is obtained by passing $X$ through a binary symmetric channel with crossover probability $\\alpha$. A recent conjecture by Courtade and Kumar postulates that $I(f(X);Y)\\leq 1-h(\\alpha)$ for any Boolean function $f$. So far, the best known upper bound was $I(f(X);Y)\\leq (1-2\\alpha)^2$. In this paper, we derive a new upper bound that holds for all balanced functions, and improves upon the best known bound for all $\\tfrac{1}{3}<\\alpha<\\tfrac{1}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05794","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"}