# Unsupervised Linear and Nonlinear Channel Equalization and Decoding using Variational Autoencoders

## TL;DR

This paper introduces a novel unsupervised approach using variational autoencoders for blind linear and nonlinear channel equalization and decoding, achieving improved error rates and faster channel acquisition without pilot symbols.

## Contribution

It presents the first application of VAEs for blind channel equalization and decoding, with a method that outperforms existing techniques like EM and constant modulus in accuracy and efficiency.

## Key findings

- Significant error rate improvements over traditional blind equalization methods.
- Faster channel acquisition due to the VAE approach.
- Reduced computational complexity compared to EM, especially for larger channels.

## Abstract

A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equalization methods such as constant modulus, thus enabling faster channel acquisition. The VAE equalizer uses a convolutional neural network with a small number of free parameters. These results are extended to blind equalization over a noisy nonlinear ISI channel with unknown parameters. We then consider coded communication using low-density parity-check (LDPC) codes transmitted over a noisy linear or nonlinear ISI channel. The goal is to reconstruct the transmitted message from the channel observations corresponding to a transmitted codeword, without using pilot symbols. We demonstrate improvements compared to the expectation maximization (EM) algorithm using turbo equalization. Furthermore, unlike EM, the computational complexity of our method does not have exponential dependence on the size of the channel impulse response.