Space-efficient Huffman codes revisited

A canonical Huffman code is an optimal prefix-free compression whose codewords enumerated in the lexicographical order form a list of binary words non-decreasing lengths. Gagie et al. (2015) gave representation this coding capable encoding and decoding symbol constant worst-case time. It uses σlg⁡ℓmax+o(σ)+O(ℓmax2) bits space, where σ ℓmax are alphabet size maximum codeword length, respectively. We refine their to reduce space complexity σlg⁡ℓmax(1+o(1)) while preserving encode decode times. Our algorithmic idea can be applied any code.