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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2011

Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes

Résumé

This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope classes with exponent $\alpha$. The minimax redundancy of exponentially decreasing envelope classes is proved to be equivalent to $\frac{1}{4 \alpha \log e} \log^2 n$. Then a coding strategy is proposed, with a Bayes redundancy equivalent to the maximin redundancy. At last, an adaptive algorithm is provided, whose redundancy is equivalent to the minimax redundancy
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Dates et versions

hal-00284638 , version 1 (03-06-2008)
hal-00284638 , version 2 (24-03-2010)

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Dominique Bontemps. Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes. IEEE Transactions on Information Theory, 2011, 57 (3), pp.1466 - 1478. ⟨10.1109/TIT.2010.2103831⟩. ⟨hal-00284638v2⟩
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