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 tabled variant of the latter (tANS) often replaces Huffman coding due to better compression at similar computational cost - e.g. in Facebook Zstandard and Apple LZFSE popular compressors. There is discussed encoding of probability distributions for this kind of applications, especially using Pyramid Vector Quantizer(PVQ)-based approach with deformation, also tuned symbol spread for tANS.