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Adaptive compression against a countable alphabet

By Dominique Bontemps, Stephane Boucheron and Elisabeth Gassiat

Abstract

International audienceThis paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the collection of such classes. The analysis builds on the tight characterization of universal redundancy rate in terms of metric entropy by Haussler and Opper (1997) and on a careful analysis of the performance of the AC-coding algorithm. The latter relies on non-asymptotic bounds for maxima of samples from discrete distributions with finite and non-decreasing hazard rate

Topics: adaptive compression, countable alphabets, lossless data compression, minimax, redundancy, universal coding, [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]
Publisher: DMTCS
Year: 2012
OAI identifier: oai:HAL:hal-01197243v1
Provided by: Hal-Diderot

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