The Asymmetric Numeral Systems (ANS) algorithm (Duda et al, 2015) is perhaps the most practical way of getting near optimal compression ratios for independent and identically distributed random sequences of symbols from a known discrete probability distribution. Simplest example: a random sequence of 0’s and 1’s with probability p of getting a 1. Shannon’s entropy formula gives us the expected compression ratio for such a sequence, but realizing that compression ratio efficiently in a computer program is not such an easy task. ANS does the trick and is incorporated into several general purpose compression algorithms, but I wasn’t able to track down a simple, self-contained implementation that was reasonably performant.So I made simple_ans, a straightforward Python package that uses a small, yet efficient, kernel of C++ code (few hundred lines of code).
If you want it even simpler, there’s also a pure Python implementation in the repo (much slower though).
I hope you find it interesting and/or useful!