{"paper":{"title":"Codes for Tasks and R\\'enyi Entropy Rate","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amos Lapidoth, Christoph Bunte","submitted_at":"2013-12-13T09:09:01Z","abstract_excerpt":"A task is randomly drawn from a finite set of tasks and is described using a fixed number of bits. All the tasks that share its description must be performed. Upper and lower bounds on the minimum $\\rho$-th moment of the number of performed tasks are derived. The key is an analog of the Kraft Inequality for partitions of finite sets. When a sequence of tasks is produced by a source of a given R\\'enyi entropy rate of order $1/(1+\\rho)$ and $n$ tasks are jointly described using $nR$ bits, it is shown that for $R$ larger than the R\\'enyi entropy rate, the $\\rho$-th moment of the ratio of performe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3735","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"}