{"paper":{"title":"Capacity of Random Channels with Large Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"David Sutter, John Lygeros, Tobias Sutter","submitted_at":"2015-03-13T15:32:42Z","abstract_excerpt":"We consider discrete memoryless channels with input alphabet size $n$ and output alphabet size $m$, where $m=$ceil$(\\gamma n)$ for some constant $\\gamma>0$. The channel transition matrix consists of entries that, before being normalised, are independent and identically distributed nonnegative random variables $V$ and such that $E[(V \\log V)^2]<\\infty$. We prove that in the limit as $n\\to \\infty$ the capacity of such a channel converges to $Ent(V) / E[V]$ almost surely and in $L^2$, where $Ent(V):= E[V\\log V]-E[V] \\log E[V]$ denotes the entropy of $V$. We further show that, under slightly diffe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04108","kind":"arxiv","version":3},"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"}