{"paper":{"title":"High-resolution scalar quantization with R\\'enyi entropy constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Tamas Linder, Wolfgang Kreitmeier","submitted_at":"2010-08-10T15:56:17Z","abstract_excerpt":"We consider optimal scalar quantization with $r$th power distortion and constrained R\\'enyi entropy of order $\\alpha$. For sources with an absolutely continuous distribution the high rate asymptotics of the quantizer distortion has long been known for $\\alpha=0$ (fixed-rate quantization) and $\\al pha=1$ (entropy-constrained quantization). For a large class of absolutely continuous source distributions we determine the sharp asymptotics of the optimal quantization distortion for $\\alpha\\in [-\\infty,0)\\cup (0,1)$. The achievability proof is based on finding (asymptotically) optimal quantizers vi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1744","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"}