Fixed-to-Variable Length Distribution Matching

TL;DR

This paper introduces an efficient algorithm for fixed-to-variable length distribution matching that minimizes divergence from a target distribution, with divergence approaching zero for large block sizes, and relates it to Tunstall coding.

Contribution

An optimal fixed-to-variable length distribution matching algorithm is developed, improving approximation accuracy and establishing a connection to Tunstall coding.

Findings

Divergence per bit approaches zero as block length increases.

Algorithm efficiently finds optimal f2v codes.

Relation to Tunstall coding enhances understanding of distribution matching.

Abstract

Fixed-to-variable length (f2v) matchers are used to reversibly transform an input sequence of independent and uniformly distributed bits into an output sequence of bits that are (approximately) independent and distributed according to a target distribution. The degree of approximation is measured by the informational divergence between the output distribution and the target distribution. An algorithm is developed that efficiently finds optimal f2v codes. It is shown that by encoding the input bits blockwise, the informational divergence per bit approaches zero as the block length approaches infinity. A relation to data compression by Tunstall coding is established.