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Reports (Research Report) Year : 1998

Analytic Variations on Redundancy Rates of Renewal Processes

Philippe Flajolet
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Wojtek Szpankowski
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Abstract

Csiszár and Shields have recently proved that the minimax redundancy for a class of renewal processes is $\Theta(\sqrt{n})$ where $n$ is the block length. This interesting result provides a first non-trivial bound on redundancy for a non-parametric family of processes. The present paper provides a precise estimate up to the constant term of the redundancy rate for such sources. The asymptotic expansion is derived by complex--analytic methods that include generating function representations, Mellin ransforms, singularity analysis and saddle point estimates. This work places itself within the framework of analytic information theory.
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Dates and versions

inria-00073130 , version 1 (24-05-2006)

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  • HAL Id : inria-00073130 , version 1

Cite

Philippe Flajolet, Wojtek Szpankowski. Analytic Variations on Redundancy Rates of Renewal Processes. [Research Report] RR-3553, INRIA. 1998. ⟨inria-00073130⟩
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