# Probabilistically Shaped Multi-Level Coding with Polar Codes for Fading Channels

## TL;DR

This paper introduces a probabilistic shaping method for multi-level coding with polar codes that improves performance over fading channels by shaping a single bit-level, reducing shaping loss without increasing decoding complexity.

## Contribution

It proposes a novel probabilistic shaping scheme for MLC with polar codes, using a precoder to shape one bit-level, enhancing performance on fading channels.

## Key findings

- Performance gains over BICM- and MLC-based polar codes without shaping
- Shaping a single bit-level effectively compensates for shaping loss
- Implementation achieves improved error rates on Rayleigh fading channels

## Abstract

A probabilistic shaping method for multi-level coding (MLC) is presented, where the transmitted symbols are forced to have a shaped non-uniform distribution. It is shown that shaping only a single bit-level suffices to compensate for most of the shaping loss on the fading channels. A polar code based implementation of the proposed scheme is presented, where shaping is performed by using a precoder at the transmitter without increasing the decoding complexity. Simulation results show that performance improvements can be obtained compared to BICM- and MLC-based polar coding without shaping on Rayleigh fading channels.