# Deep Log-Likelihood Ratio Quantization

## TL;DR

This paper introduces a deep autoencoder-based method for lossy compression and quantization of log-likelihood ratios in communication systems, achieving significant compression with minimal performance loss.

## Contribution

It proposes a novel deep learning approach that models quantization effects differentiably, enabling efficient compression of LLRs in fading communication channels.

## Key findings

- Achieves nearly threefold compression of LLRs for a standard LDPC code.
- Maintains performance within 0.1 dB of scalar quantization methods.
- Demonstrates effectiveness in a single-input single-output fading setting.

## Abstract

In this work, a deep learning-based method for log-likelihood ratio (LLR) lossy compression and quantization is proposed, with emphasis on a single-input single-output uncorrelated fading communication setting. A deep autoencoder network is trained to compress, quantize and reconstruct the bit log-likelihood ratios corresponding to a single transmitted symbol. Specifically, the encoder maps to a latent space with dimension equal to the number of sufficient statistics required to recover the inputs - equal to three in this case - while the decoder aims to reconstruct a noisy version of the latent representation with the purpose of modeling quantization effects in a differentiable way. Simulation results show that, when applied to a standard rate-1/2 low-density parity-check (LDPC) code, a finite precision compression factor of nearly three times is achieved when storing an entire codeword, with an incurred loss of performance lower than 0.1 dB compared to straightforward scalar quantization of the log-likelihood ratios.