A dynamic programming algorithm to construct optimal code trees of AIFV codes

Binary AIFV (almost instantaneous fixed-to-variable length) codes, which uses two code trees, can attain better compression rates than binary Huffman codes. Although the optimal binary AIFV codes can be constructed by combining an iterative algorithm to improve a parameter and an integer programming (IP) to derive the optimal code trees for a given parameter, the complexity of the IP problem is NP hard in general. In this paper, we propose a dynamic programming algorithm, which can be used instead of the above IP. The proposed dynamic programming algorithm works with O(n
⁵
) time and O(n
³
) space for source alphabet size n.