Compressing Huffman Models on Large Alphabets

A naive storage of a Huffman model on a text of length n over an alphabet of size σ requires O(σlog n) bits. This can be reduced to σ logσ + O(σ) bits using canonical codes. This overhead over the entropy can be significant when σ is comparable to n, and it also dictates the amount of main memory required to compress or decompress. We design an encoding scheme that requires σlog log n+O(σ+log² n) bits in the worst case, and typically less, while supporting encoding and decoding of symbols in O(log log n) time. We show that our technique reduces the storage size of the model of state-of-the-art techniques to around 15% in various real-life sequences over large alphabets, while still offering reasonable compression/decompression times.