Better Than Optimal Huffman Coding?

Huffman coding is known to be optimal, yet its dynamic version may yield smaller compressed files. The best known bound is that the number of bits used by dynamic Huffman coding in order to encode a message of n characters is at most larger by n bits than the number of bits required by static Huffman coding. In particular, dynamic Huffman coding can also generate a larger encoded file than the static variant, though in practice the file might often, but not always, be smaller. We propose here a new dynamic Huffman encoding approach, that provably always performs at least as good as static Huffman coding, and may be better than the standard dynamic Huffman coding for certain files.