Problems of robustness for universal coding schemes

Details Problems of robustness for universal coding schemes Problems of robustness for universal coding schemes

2008-06-27

arxiv.org/abs/0806.4572v1

Problems of Information Transmission, 39 (2003), pp. 32-46

Computer Science

Information Theory

23 pages

Scientific paper

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. A notion of deficiency of algorithmic randomness is used as a measure of disagreement between data sequence and probability measure. We prove that universal compressing schemes from a large class are non-robust 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 compressing algorithm can be violated. Lempel-Ziv compressing algorithms are robust on infinite sequences generated by ergodic Markov chains when the randomness deficiency of its initial fragments of length $n$ grows as $o(n)$.

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