RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Probl. Peredachi Inf.: Year: Volume: Issue: Page: Find

 Probl. Peredachi Inf., 2003, Volume 39, Issue 1, Pages 36–52 (Mi ppi156)

Problems of Robustness for Universal Coding Schemes

V. V. V'yugin

Abstract: The Lempel–Ziv universal coding scheme is asymptotically optimal for the class of all stationary ergodic sources. A problem of robustness of this property under small violations of ergodicity is studied. The notion of deficiency of algorithmic randomness is used as a measure of disagreement between data sequence and probability measure. We prove that universal compression schemes from a large class are nonrobust in the following sense: If the randomness deficiency grows arbitrarily slowly on initial fragments of an infinite sequence, then the property of asymptotic optimality of any universal compression algorithm can be violated. Lempel–Ziv compression algorithms are robust on infinite sequences generated by ergodic Markov chains when the randomness deficiency of their initial fragments of length $n$ grows as $o(n)$.

Full text: PDF file (2147 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2003, 39:1, 32–46

Bibliographic databases:

UDC: 621.391.1:519.2

Citation: V. V. V'yugin, “Problems of Robustness for Universal Coding Schemes”, Probl. Peredachi Inf., 39:1 (2003), 36–52; Problems Inform. Transmission, 39:1 (2003), 32–46

Citation in format AMSBIB
\Bibitem{Vyu03} \by V.~V.~V'yugin \paper Problems of Robustness for Universal Coding Schemes \jour Probl. Peredachi Inf. \yr 2003 \vol 39 \issue 1 \pages 36--52 \mathnet{http://mi.mathnet.ru/ppi156} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2101343} \zmath{https://zbmath.org/?q=an:1077.94010} \transl \jour Problems Inform. Transmission \yr 2003 \vol 39 \issue 1 \pages 32--46 \crossref{https://doi.org/10.1023/A:1023626414365} 

• http://mi.mathnet.ru/eng/ppi156
• http://mi.mathnet.ru/eng/ppi/v39/i1/p36

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V'yugin V., “On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic Randomness”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011, 1514–1518
2. Uspensky V.A., V'yugin V.V., “Development of the algorithmic information theory in Russia”, Journal of Communications Technology and Electronics, 56:6 (2011), 739–747
•  Number of views: This page: 451 Full text: 112 References: 42