Universally Typical Sets for Ergodic Sources of Multidimensional Data

Tyll Krüger, Guido Montúfar, Ruedi Seiler, and Rainer Siegmund-Schultze

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Submission date: 02. May. 2011
Pages: 17
published in: Kybernetika, 49 (2013) 6, p. 868-882 
Bibtex
MSC-Numbers: 94A24, 62D05
PACS-Numbers: 89.70.-a
Keywords and phrases: universal codes, ergodic theory, discrete samplings
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Abstract:

We lift important results of the theory of samples of discrete ergodic information sources to the multidimensional setting. We use the technique of packings and coverings with multidimensional windows in entropy estimation and universal lossless compression. In particular, we construct sequences of multidimensional array sets which, in the limit, build the generated samples of any ergodic source of entropy rate below an h₀ with probability 1 and whose cardinality grows at most at exponential rate h₀. Thereby we extrapolate mathematical framework relevant for universal source coding of multi-dimensionally correlated data.