Constant Composition Distribution Matching

TL;DR

This paper introduces a constant composition distribution matching method that efficiently transforms Bernoulli(1/2) bits into symbols with a target distribution, achieving optimal rate and minimal divergence asymptotically.

Contribution

It presents fixed-to-fixed length, invertible encoders and decoders based on constant composition and arithmetic coding with optimal asymptotic performance.

Findings

Achieves maximum rate equal to the entropy of the target distribution

Normalized divergence approaches zero as blocklength increases

Provides low-complexity, invertible encoding and decoding methods

Abstract

Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented. Asymptotically in the blocklength, the encoder achieves the maximum rate, namely the entropy of the desired distribution. Furthermore, the normalized divergence of the encoder output and the desired distribution goes to zero in the blocklength.