# UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA

Krüger T, Montufar G, Seiler R, Siegmund-Schultze R (2013)
KYBERNETIKA 49(6): 868-882.

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Journal Article | Published | English

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We lift important results about universally typical sets, typically sampled sets, and empirical entropy estimation in the theory of samplings of discrete ergodic information sources from the usual one-dimensional discrete-time setting to a multidimensional lattice setting. We use techniques of packings and coverings with multidimensional windows to 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 one and whose cardinality grows at most at exponential rate h(0).
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Krüger T, Montufar G, Seiler R, Siegmund-Schultze R. UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA. KYBERNETIKA. 2013;49(6):868-882.
Krüger, T., Montufar, G., Seiler, R., & Siegmund-Schultze, R. (2013). UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA. KYBERNETIKA, 49(6), 868-882.
Krüger, T., Montufar, G., Seiler, R., and Siegmund-Schultze, R. (2013). UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA. KYBERNETIKA 49, 868-882.
Krüger, T., et al., 2013. UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA. KYBERNETIKA, 49(6), p 868-882.
T. Krüger, et al., “UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA”, KYBERNETIKA, vol. 49, 2013, pp. 868-882.
Krüger, T., Montufar, G., Seiler, R., Siegmund-Schultze, R.: UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA. KYBERNETIKA. 49, 868-882 (2013).
Krüger, Tyll, Montufar, Guido, Seiler, Ruedi, and Siegmund-Schultze, Rainer. “UNIVERSALLY TYPICAL SETS FOR ERGODIC SOURCES OF MULTIDIMENSIONAL DATA”. KYBERNETIKA 49.6 (2013): 868-882.
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