# Finite-Precision Implementation of Arithmetic Coding Based Distribution Matchers

## TL;DR

This paper explores finite-precision arithmetic implementation of distribution matchers, specifically CCDM, showing that rate-loss diminishes exponentially with increased precision bits, and establishes a relationship between rate and precision.

## Contribution

It provides an analysis of finite-precision arithmetic effects on CCDM, including rate-loss behavior and a derived relationship between rate and precision bits.

## Key findings

- Rate-loss decreases exponentially with more precision bits
- A quantitative relationship between CCDM rate and precision bits is established
- Finite-precision implementation is viable with controlled rate-loss

## Abstract

A distribution matcher (DM) encodes a binary input data sequence into a sequence of symbols with a desired target probability distribution. Several DMs, including shell mapping and constant-composition distribution matcher (CCDM), have been successfully employed for signal shaping, e.g., in optical-fiber or 5G. The CCDM, like many other DMs, is typically implemented by arithmetic coding (AC). In this work we implement AC based DMs using finite-precision arithmetic (FPA). An analysis of the implementation shows that FPA results in a rate-loss that shrinks exponentially with the number of precision bits. Moreover, a relationship between the CCDM rate and the number of precision bits is derived.