Space-Efficient Huffman Codes Revisited

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