Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes

Details Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes

2008-06-03

arxiv.org/abs/0806.0562v2

IEEE Transactions on Information Theory 57, 3 (2011) 1466 - 1478

Computer Science

Information Theory

Scientific paper

10.1109/TIT.2010.2103831

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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