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 $σ\lg \ell_{\text{max}} + o(σ) + O(\ell_{\text{max}}^2)$ bits of space, where $σ$ and $\ell_{\text{max}}$ are the alphabet size and maximum codeword length, respectively. We refine their representation to reduce the space complexity to $σ\lg \ell_{\text{max}} (1 + o(1))$ bits while preserving the constant encode and decode times. Our algorithmic idea can be applied to any canonical code.