{"paper":{"title":"How to Quantize $n$ Outputs of a Binary Symmetric Channel to $n-1$ Bits?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Or Ordentlich, Wasim Huleihel","submitted_at":"2017-01-11T19:03:42Z","abstract_excerpt":"Suppose that $Y^n$ is obtained by observing a uniform Bernoulli random vector $X^n$ through a binary symmetric channel with crossover probability $\\alpha$. The \"most informative Boolean function\" conjecture postulates that the maximal mutual information between $Y^n$ and any Boolean function $\\mathrm{b}(X^n)$ is attained by a dictator function. In this paper, we consider the \"complementary\" case in which the Boolean function is replaced by $f:\\left\\{0,1\\right\\}^n\\to\\left\\{0,1\\right\\}^{n-1}$, namely, an $n-1$ bit quantizer, and show that $I(f(X^n);Y^n)\\leq (n-1)\\cdot\\left(1-h(\\alpha)\\right)$ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03119","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"}