Poissonization and universal compression of envelope classes

Abstract

Poisson sampling is a method for eliminating dependence among symbols in a random sequence. It helps improve algorithm design, strengthen bounds, and simplify proofs. We relate the redundancy of fixed-length and Poisson-sampled sequences, use this result to derive a simple formula for the redundancy of general envelope classes, and apply this formula to obtain simple and tight bounds on the redundancy of power-law and exponential envelope classes, in particular answering a question posed in [1] about power-law envelopes.