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Entropy 2009, 11(4), 634-642; doi:10.3390/e11040634

A Lower-Bound for the Maximin Redundancy in Pattern Coding

CNRS, Telecom ParisTech, Laboratoire Laboratoire Traitement et Communication de l’Information, 75013 Paris, France
Received: 1 September 2009 / Accepted: 20 October 2009 / Published: 22 October 2009
(This article belongs to the Special Issue Information and Entropy)
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We show that the maximin average redundancy in pattern coding is eventually larger than 1.84 (n/log n)1/3 for messages of length n. This improves recent results on pattern redundancy, although it does not fill the gap between known lower- and upper-bounds. The pattern of a string is obtained by replacing each symbol by the index of its first occurrence. The problem of pattern coding is of interest because strongly universal codes have been proved to exist for patterns while universal message coding is impossible for memoryless sources on an infinite alphabet. The proof uses fine combinatorial results on partitions with small summands.
Keywords: universal coding; pattern; minimax universal coding; pattern; minimax
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Garivier, A. A Lower-Bound for the Maximin Redundancy in Pattern Coding. Entropy 2009, 11, 634-642.

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