Encoding of probability distributions for Asymmetric Numeral Systems

TL;DR

This paper explores advanced methods for encoding probability distributions in entropy coding, focusing on Asymmetric Numeral Systems and related techniques to improve compression efficiency and accuracy.

Contribution

It introduces novel encoding strategies for probability distributions in ANS, including PVQ-based approaches, deformation, bucket approximation, and symbol spread tuning.

Findings

Enhanced probability encoding accuracy for ANS

Improved compression ratios in practical codecs

Effective use of PVQ and deformation techniques

Abstract

Many data compressors regularly encode probability distributions for entropy coding - requiring minimal description length type of optimizations. Canonical prefix/Huffman coding usually just writes lengths of bit sequences, this way approximating probabilities with powers-of-2. Operating on more accurate probabilities usually allows for better compression ratios, and is possible e.g. using arithmetic coding and Asymmetric Numeral Systems family. Especially the multiplication-free tabled variant of the latter (tANS) builds automaton often replacing Huffman coding due to better compression at similar computational cost - e.g. in popular Facebook Zstandard and Apple LZFSE compressors. There is discussed encoding of probability distributions for such applications, especially using Pyramid Vector Quantizer(PVQ)-based approach with deformation, bucket approximation, prefix trees, improving accuracy with additional bits, also tuned symbol spread for tANS.