Compression of data streams down to their information content

Barmpalias, George and Lewis-Pye, Andrew (2019) Compression of data streams down to their information content. IEEE Transactions on Information Theory, 65 (7). pp. 4471-4485. ISSN 0018-9448

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Abstract

According to the 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 the infinite binary sequences (streams). We devise a new coding method that 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 that 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 the oracle-use bounded above by K(X \upharpoonright -{n})+\log n. This provides a strong analogue of Shannon's source coding theorem for the algorithmic information theory.

Item Type:	Article
Additional Information:	© 2019 IEEE
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	07 Feb 2019 11:30
Last Modified:	12 Dec 2024 01:40
URI:	http://eprints.lse.ac.uk/id/eprint/100040

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