Analytic Variations on Redundancy Rates of Renewal Processes
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.