{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/encoding-of-probability-distributions-for","title":"Encoding of probability distributions for Asymmetric Numeral Systems","arxiv_id":"2106.06438","date":"2021-06-11","proceeding":null,"authors":["Jarek Duda"],"abstract":"Many data compressors regularly encode probability distributions for entropy coding - requiring minimal description length type of optimizations. Canonical prefix/Huffman coding usually just writes lengths of bit sequences, this way approximating probabilities with powers-of-2. Operating on more accurate probabilities usually allows for better compression ratios, and is possible e.g. using arithmetic coding and Asymmetric Numeral Systems family. Especially the multiplication-free tabled variant of the latter (tANS) builds automaton often replacing Huffman coding due to better compression at similar computational cost - e.g. in popular Facebook Zstandard and Apple LZFSE compressors. There is discussed encoding of probability distributions for such applications, especially using Pyramid Vector Quantizer(PVQ)-based approach with deformation, bucket approximation, prefix trees, improving accuracy with additional bits, also tuned symbol spread for tANS.","url_abs":"https://arxiv.org/abs/2106.06438v4","url_pdf":"https://arxiv.org/pdf/2106.06438v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"encoding-of-probability-distributions-for","repo_url":"https://github.com/JarekDuda/AsymmetricNumeralSystemsToolkit","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}