Universal lossless compression via multilevel pattern matching

@article{Kieffer2000UniversalLC,
  title={Universal lossless compression via multilevel pattern matching},
  author={John C. Kieffer and En-hui Yang and G. Nelson and Pamela C. Cosman},
  journal={IEEE Trans. Inf. Theory},
  year={2000},
  volume={46},
  pages={1227-1245},
  url={https://api.semanticscholar.org/CorpusID:8191526}
}
A O(1/log n) maximal redundancy/sample upper bound is established for the multilevel pattern matching code with respect to any class of finite state sources of uniformly bounded complexity in processing a finite-alphabet data string of length n.
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36 References

Grammar-based codes: A new class of universal lossless source codes

It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet.

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It is demonstrated that for unifilar or Markov sources, the redundancy of encoding the first n letters of the source output with the Lempel-Ziv incremental parsing rule, the Welch modification, or a new variant is O((ln n)/sup -1/), and the exact form of convergence is upper-bound.

Compression of individual sequences via variable-rate coding

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Universal codeword sets and representations of the integers

An application is the construction of a uniformly universal sequence of codes for countable memoryless sources, in which the n th code has a ratio of average codeword length to source rate bounded by a function of n for all sources with positive rate.

Redundancy of MPM data compression system

    J. KiefferE. Yang
    Computer Science
    Proceedings. 1998 IEEE International Symposium on…
  • 1998
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