Probability Approximation in Asymmetric Numeral Systems

Asymmetric Numeral Systems (ANS) are a family of entropy coders for information sources with a finite alphabet, and usually require approximating the source distribution to rational numbers to associate the source symbols with the internal states of ANS. In the range variant of ANS, each source symbol corresponds to a continuous interval of the state set. ANS assigns shorter codewords to states with smaller numbers and longer codewords to states with larger numbers. Therefore, it is not fair or valid to make the lengths of state intervals proportional to symbol probabilities. To overcome this problem, this paper proposes a new source approximation formula, and shows that it leads to an improvement of compression efficiency of ANS.