Allerton 2015 Paper Abstract

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Paper ThA6.4

Hosseinitoushmanlouei, Maryamsadat (University of Hawaii at Manoa), Santhanam, Narayana Prasad (University of Hawaii)

Single Letter Characterization of Average-Case Strong Redundancy of Compressing Memoryless Sequences

Scheduled for presentation during the Regular Session "Information Theory and Source Coding" (ThA6), Thursday, October 1, 2015, 09:30−09:50, Visitor Center

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Information Theory, Source Coding and Compression

Abstract

We obtain a condition that is both necessary and sufficient to characterize strong universal compressibility (in the average sense) of sequences generated by iid sampling from a collection $cP$ of distributions over a countably infinite alphabet. Contrary to the worst case regret formulation of universal compression, finite single letter (average case) redundancy of $cP$ does not automatically imply that the expected redundancy of describing length-$n$ strings sampled iid from $cP$ grows sublinearly with $n$. Instead, we prove that asymptotic per-symbol redundancy of universally compressing length-$n$ iid sequences from $cP$ is characterized by how well the tails of their single letter marginals can be universally described, and we formalize the later as the tail-redundancy of $cP$.

 

 

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