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Entropy coding is the backbone data compression. Novel machine-learning basedcompression methods often use a new entropy coder called Asymmetric NumeralSystems (ANS) [Duda et al., 2015], which provides very close to optimalbitrates and simplifies [Townsend et al., 2019] advanced compression techniquessuch as bits-back coding. However, researchers with a background in machinelearning often struggle to understand how ANS works, which prevents them fromexploiting its full versatility. This paper is meant as an educational resourceto make ANS more approachable by presenting it from a new perspective of latentvariable models and the so-called bits-back trick. We guide the reader step bystep to a complete implementation of ANS in the Python programming language,which we then generalize for more advanced use cases. We also present andempirically evaluate an open-source library of various entropy coders designedfor both research and production use. Related teaching videos and problem setsare available online.

Understanding Entropy Coding With Asymmetric Numeral Systems (ANS): a Statistician's Perspective