Cookies?
Library Header Image
LSE Research Online LSE Library Services

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

[img] Text (Compression of data streams down to their information content) - Accepted Version
Download (307kB)

Identification Number: 10.1109/TIT.2019.2896638

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 Sep 2019 23:08
URI: http://eprints.lse.ac.uk/id/eprint/100040

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics