# Deep Learning-Based Quantization of L-Values for Gray-Coded Modulation

## TL;DR

This paper introduces a deep learning-based quantization method for L-values in Gray-coded modulation, achieving significant memory reduction with minimal performance loss and demonstrating universality across different channel models.

## Contribution

A novel autoencoder-based quantization scheme for L-values that reduces memory footprint and is adaptable across various channel conditions without retraining.

## Key findings

- Reduces memory by up to 50% compared to state-of-the-art methods.
- Maintains performance loss below 0.1 dB with less than two bits per L-value.
- Demonstrates universal applicability across different channel models without retraining.

## Abstract

In this work, a deep learning-based quantization scheme for log-likelihood ratio (L-value) storage is introduced. We analyze the dependency between the average magnitude of different L-values from the same quadrature amplitude modulation (QAM) symbol and show they follow a consistent ordering. Based on this we design a deep autoencoder that jointly compresses and separately reconstructs each L-value, allowing the use of a weighted loss function that aims to more accurately reconstructs low magnitude inputs. Our method is shown to be competitive with state-of-the-art maximum mutual information quantization schemes, reducing the required memory footprint by a ratio of up to two and a loss of performance smaller than 0.1 dB with less than two effective bits per L-value or smaller than 0.04 dB with 2.25 effective bits. We experimentally show that our proposed method is a universal compression scheme in the sense that after training on an LDPC-coded Rayleigh fading scenario we can reuse the same network without further training on other channel models and codes while preserving the same performance benefits.