Space-Efficient Huffman Codes Revisited

Abstract

Canonical Huffman code is an optimal prefix-free compression code whose codewords enumerated in the lexicographical order form a list of binary words in non-decreasing lengths. Gagie et al. ( 2015) gave a representation of this coding capable to encode or decode a symbol in constant worst case time. It uses σ lg ℓmax + o(σ) + O(ℓ 2 max ) bits of space, where σ and ℓmax are the alphabet size and maximum codeword length, respectively. We refine their representation to reduce the space complexity to σ lg ℓmax(1 + o(1)) bits while preserving the constant encode and decode times. Our algorithmic idea can be applied to any canonical code.