{"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/compression-of-data-streams-down-to-their","title":"Compression of data streams down to their information content","arxiv_id":"1710.02092","date":"2017-10-05","proceeding":null,"authors":["George Barmpalias","Andrew Lewis-Pye"],"abstract":"According to Kolmogorov complexity, every finite binary string is compressible to a shortest code -- its information content -- from which it is effectively recoverable. We investigate the extent to which this holds for infinite binary sequences (streams). We devise a new coding method which uniformly codes every stream $X$ into an algorithmically random stream $Y$, in such a way that the first $n$ bits of $X$ are recoverable from the first $I(X\\upharpoonright_n)$ bits of $Y$, where $I$ is any partial computable information content measure which is defined on all prefixes of $X$, and where $X\\upharpoonright_n$ is the initial segment of $X$ of length $n$. As a consequence, if $g$ is any computable upper bound on the initial segment prefix-free complexity of $X$, then $X$ is computable from an algorithmically random $Y$ with oracle-use at most $g$. Alternatively (making no use of such a computable bound $g$) one can achieve an oracle-use bounded above by $K(X\\upharpoonright_n)+\\log n$. This provides a strong analogue of Shannon's source coding theorem for algorithmic information theory.","url_abs":"http://arxiv.org/abs/1710.02092v4","url_pdf":"http://arxiv.org/pdf/1710.02092v4.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":"compression-of-data-streams-down-to-their","repo_url":"https://github.com/bob7/Kraft-Chaitin-codes","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}