# Lossless Compression with Asymmetric Numeral Systems

During my undergraduate days, one of the most interesting courses I took was on
coding and compression. Here was a course that combined algorithms,
probability and secret messages, what's not to like? 1 I ended up not going
down that career path, at least partially because communications systems had
its heyday around the 2000s with companies like Nortel and Blackberry and its
predecessors (some like to joke that all the major theoretical breakthroughs
were done by Shannon and his discovery of information theory around 1950). Fortunately, I
eventually wound up studying industrial applications of classical AI techniques
and then machine learning, which has really grown like crazy in the last 10
years or so. Which is exactly why I was so surprised that a *new* and *better*
method of lossless compression was developed in 2009 *after* I finished my
undergraduate degree when I was well into my PhD. It's a bit mind boggling that
something as well-studied as entropy-based lossless compression still had
(have?) totally new methods to discover, but I digress.

In this post, I'm going to write about a relatively new entropy based encoding
method called Asymmetrical Numeral Systems (ANS) developed by Jaroslaw (Jarek)
Duda [2]. If you've ever heard of Arithmetic Coding (probably best known for
its use in JPEG compression), ANS runs in a very similar vein. It can
generate codes that are close to the theoretical compression limit
(similar to Arithmetic coding) but is *much* more efficient. It's been used in
modern compression algorithms since 2014 including compressors developed
by Facebook, Apple and Google [3]. As usual, I'm going to go over some
background, some math, some examples to help with intuition, and finally some
experiments with a toy ANS implementation I wrote. I hope you're as
excited as I am, let's begin!