Universally Typical Sets for Ergodic Sources of Multidimensional Data

Details Universally Typical Sets for Ergodic Sources of Multidimensional Data Universally Typical Sets for Ergodic Sources of Multidimensional Data

2011-05-02

arxiv.org/abs/1105.0393v2

Computer Science

Information Theory

15 pages, spelling of an author's name was corrected: Kr\"uger -> Krueger

Scientific paper

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 $h_{0}$ with probability 1 and whose cardinality grows at most at exponential rate $h_{0}$. Thereby we extrapolate mathematical framework relevant for universal source coding of multi-dimensionally correlated data.

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