Saved in:
Bibliographic Details
Main Author: Szewczyk, Kamila
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.00579
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • Range coders and ANS replace empirical probabilities with integer frequencies summing to a fixed $M$; the resulting per-symbol code-length redundancy is exactly the KL divergence of the empirical distribution from the quantized one. Existing normalizers (Giesen, Bloom, Collet) are heuristic or only partially marginal-optimal. We give three provably KL-optimal algorithms: a bottom-up archetype, a bidirectional exchange repair of Bloom's heap correction, and a top-down window method that runs in $\mathcal{O}(r)$, asymptotically optimal in $r$, where $r$ is the number of positive-count symbols.