Encoding of probability distributions for Asymmetric Numeral Systems

Many data compressors regularly encode probability distributions for entropy coding requiring minimal description length type of optimizations. Canonical prefix/Huffman coding usually just writes lengths of bit sequences, this way approximating probabilities with powers-of-2. Operating on more accurate probabilities usually allows for better compression ratios, and is possible e.g. using arithmetic coding and Asymmetric Numeral Systems family. Especially the multiplication-free tabled variant of the latter (tANS) builds automaton often replacing Huffman coding due to better compression at similar computational cost e.g. in popular Facebook Zstandard and Apple LZFSE compressors. There is discussed encoding of probability distributions for such applications, especially using Pyramid Vector Quantizer(PVQ)based approach with deformation, also tuned symbol spread for tANS.