Saved in:
| Main Author: | |
|---|---|
| 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.