Tight upper bounds on the redundancy of optimal binary AIFV codes

Abstract

AIFV codes are lossless codes that generalize the class of instantaneous FV codes. The code uses multiple code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain better compression ratio than Huffman codes. Nevertheless, an upper bound on the redundancy of optimal binary AIFV codes is only known to be 1, the same as the bound of Huffman codes. In this paper, the upper bound is improved to 1/2, which is shown to be tight. Along with this, a tight upper bound on the redundancy of optimal binary AIFV codes is derived for the case p max ≥1/2, where p max is the probability of the most likely source symbol. This is the first theoretical work on the redundancy of optimal binary AIFV codes, suggesting superiority of the codes over Huffman codes.