On the stationary distribution of asymmetric numeral systems

The Asymmetric Numeral Systems (ANS) are a family of entropy coders for information sources with a finite alphabet, developed by J. Duda as an alternative to arithmetic coding. We have already proposed an approximation formula to the stationary distribution of the states in a special version (ABS) of ANS. We show that our previous result in ABS, which deals only with binary sources, can be applied to ANS as it is. The previous approximation holds regardless of the alphabet size or source parameters. We prove in a similar way to our previous one that the rate of ANS asymptotically attains the source entropy.