Almost Instantaneous Fix-to-Variable Length Codes

TL;DR

This paper introduces almost instantaneous fixed-to-variable-length (AIFV) codes that improve compression efficiency over Huffman codes by allowing minimal decoding delay and using multiple code trees, applicable to binary and K-ary alphabets.

Contribution

The paper proposes AIFV codes with low decoding delay and demonstrates their optimality via 0-1 integer programming for binary and ternary cases.

Findings

AIFV codes achieve better average compression than Huffman codes.

Decoding delay is at most two bits for binary and one symbol for K-ary codes.

Optimal AIFV codes can be found through integer programming.

Abstract

We propose almost instantaneous fixed-to-variable-length (AIFV) codes such that two (resp. $K-1$) code trees are used if code symbols are binary (resp. $K$-ary for $K \geq 3$), and source symbols are assigned to incomplete internal nodes in addition to leaves. Although the AIFV codes are not instantaneous codes, they are devised such that the decoding delay is at most two bits (resp. one code symbol) in the case of binary (resp. $K$-ary) code alphabet. The AIFV code can attain better average compression rate than the Huffman code at the expenses of a little decoding delay and a little large memory size to store multiple code trees. We also show for the binary and ternary AIFV codes that the optimal AIFV code can be obtained by solving 0-1 integer programming problems.