Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes

Dominique Bontemps (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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

Mots clés: Data compression; Universal coding; Infinite countable alphabets; Redundancy; Bayes; Adaptive compression.; Adaptive compression

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Dominique Bontemps. Universal Coding on Infinite Alphabets: Exponentially Decreasing Envelopes. 2008. ⟨hal-00284638v1⟩