# Arithmetic Coding Based Multi-Composition Codes for Bit-Level Distribution Matching

## TL;DR

This paper introduces multi-composition codes and an arithmetic coding scheme to enhance distribution matching efficiency, especially for short message lengths, outperforming constant-composition methods in rate and divergence.

## Contribution

It proposes a novel multi-composition coding approach with an efficient arithmetic coding scheme, improving performance over traditional CCDM for short blocks.

## Key findings

- MCDM encodes more data than CCDM.
- Lower KL divergence achieved with MCDM.
- Enhanced performance for short block messages.

## Abstract

A distribution matcher (DM) encodes a binary input data sequence into a sequence of symbols (codeword) with desired target probability distribution. The set of the output codewords constitutes a codebook (or code) of a DM. Constant-composition DM (CCDM) uses arithmetic coding to efficiently encode data into codewords from a constant-composition (CC) codebook. The CC constraint limits the size of the codebook, and hence the coding rate of the CCDM. The performance of CCDM degrades with decreasing output length. To improve the performance for short transmission blocks we present a class of multi-composition (MC) codes and an efficient arithmetic coding scheme for encoding and decoding. The resulting multi-composition DM (MCDM) is able to encode more data into distribution matched codewords than the CCDM and achieves lower KL divergence, especially for short block messages.