Weighted Adaptive Coding

TL;DR

This paper introduces a new adaptive coding method that generalizes existing Huffman and arithmetic coding techniques, providing theoretical guarantees and empirical improvements over static and dynamic variants.

Contribution

It proposes a unified adaptive coding framework encompassing static and dynamic methods, including arithmetic coding, with proven performance bounds and empirical advantages.

Findings

The new method always performs at least as well as the best known dynamic variant.

Empirical results show improvements over static and dynamic Huffman and arithmetic coding.

The method remains effective even when encoding includes the model description.

Abstract

Huffman coding is known to be optimal, yet its dynamic version may be even more efficient in practice. A new variant of Huffman encoding has been proposed recently, that provably always performs better than static Huffman coding by at least $m-1$ bits, where $m$ denotes the size of the alphabet, and has a better worst case than the standard dynamic Huffman coding. This paper introduces a new generic coding method, extending the known static and dynamic variants and including them as special cases. In fact, the generalization is applicable to all statistical methods, including arithmetic coding. This leads then to the formalization of a new adaptive coding method, which is provably always at least as good as the best dynamic variant known to date. Moreover, we present empirical results that show improvements over static and dynamic Huffman and arithmetic coding achieved by the proposed method, even when the encoded file includes the model description.