Corpus ID: 13442919

Universally typical sets for ergodic sources of multidimensional data

@article{Krger2013UniversallyTS,
  title={Universally typical sets for ergodic sources of multidimensional data},
  author={T. Kr{\"u}ger and Guido Mont{\'u}far and R. Seiler and R. Siegmund-Schultze},
  journal={Kybernetika},
  year={2013},
  volume={49},
  pages={868-882}
}
  • T. Krüger, Guido Montúfar, +1 author R. Siegmund-Schultze
  • Published 2013
  • Mathematics, Computer Science
  • Kybernetika
  • 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… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 28 REFERENCES
    Compression of two-dimensional data
    • 186
    • PDF
    Compression of individual sequences via variable-rate coding
    • 3,327
    • PDF
    The Shannon-McMillan theorem for ergodic quantum lattice systems
    • 52
    • PDF
    A universal algorithm for sequential data compression
    • 5,143
    • PDF
    How Sampling Reveals a Process
    • 109
    The Shannon-McMillan-Breiman theorem for a class of amenable groups
    • 102
    • Highly Influential
    Pointwise theorems for amenable groups
    • 264
    • PDF
    The Ergodic Theory of Discrete Sample Paths
    • 309
    • Highly Influential
    • PDF
    A Mathematical Theory of Communication
    • 43,162
    • Highly Influential
    • PDF
    Elements of Information Theory
    • 38,856
    • PDF