Asymmetric numeral systems (2014)

I once found a really great article explaining arithmetic encoding¹, and I felt I understood what was going on and managed to re-implement the article's example from MS-DOS-era C to modern Python, but when I tried to use it for anything else it didn't work and I wasn't smart enough to debug it.

The claim that asymmetric numeral systems are simpler than arithmetic encoding is quite interesting, but as a working programmer, I have difficulty with the academic language and mathematical generality used in papers like this. Does anybody have a more approachable explanation of what's going on?

¹: http://marknelson.us/1991/02/01/arithmetic-coding-statistica...

It points to even older paper for ANS: http://arxiv.org/abs/0710.3861

The more recent one is: http://arxiv.org/abs/1311.2540

The first one is about kind of multidimensional analogue of Fibonacci coding ( https://en.wikipedia.org/wiki/Fibonacci_coding )- on a lattice, such that there cannot be two neighboring '1's. It also uses an interesting concept of Maximal Entropy Random Walk.