{"paper":{"title":"An Entropy Power Inequality for Discrete Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ehsan Nekouei, Karl Henrik Johansson, Mikael Skoglund","submitted_at":"2019-05-08T11:47:55Z","abstract_excerpt":"Let $\\mathsf{N}_{\\rm d}\\left[X\\right]=\\frac{1}{2\\pi {\\rm e}}{\\rm e}^{2\\mathsf{H}\\left[X\\right]}$ denote the entropy power of the discrete random variable $X$ where $\\mathsf{H}\\left[X\\right]$ denotes the discrete entropy of $X$. In this paper, we show that for two independent discrete random variables $X$ and $Y$, the entropy power inequality $\\mathsf{N}_{\\rm d}\\left[X\\right]+\\mathsf{N}_{\\rm d}\\left[Y\\right]\\leq 2 \\mathsf{N}_{\\rm d}\\left[X+Y\\right]$ holds and it can be tight. The basic idea behind the proof is to perturb the discrete random variables using suitably designed continuous random va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03015","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"}