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

arXiv: https://arxiv.org/abs/1905.08795 · HTML: https://mlsanity.com/paper/1905.08795/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2019.

## Built on by (most cited first, 11 of 11)

- [Generative AI for Physical Layer Communications: A Survey](https://mlsanity.com/paper/2312.05594/) (2023)
- [Autoregressive Belief Propagation for Decoding Block Codes](https://mlsanity.com/paper/2103.11780/) (2021)
- [Transformers are Provably Optimal In-context Estimators for Wireless Communications](https://mlsanity.com/paper/2311.00226/) (2023)
- [Blind Equalization and Channel Estimation in Coherent Optical Communications Using Variational Autoencoders](https://mlsanity.com/paper/2204.11776/) (2022)
- [Neural Decoding with Optimization of Node Activations](https://mlsanity.com/paper/2206.00786/) (2022)
- [Blind Channel Estimation and Joint Symbol Detection with Data-Driven Factor Graphs](https://mlsanity.com/paper/2401.12627/) (2024)
- [CMDNet: Learning a Probabilistic Relaxation of Discrete Variables for Soft Detection with Low Complexity](https://mlsanity.com/paper/2102.12756/) (2021)
- [Recovering AES Keys with a Deep Cold Boot Attack](https://mlsanity.com/paper/2106.04876/) (2021)
- [Online Optimization for Learning to Communicate over Time-Correlated Channels](https://mlsanity.com/paper/2409.00575/) (2024)
- [Recent Advances on Machine Learning-aided DSP for Short-reach and Long-haul Optical Communications](https://mlsanity.com/paper/2411.10101/) (2024)
- [Geometric Inductive Biases for Semi-Supervised Equalization: The Constellation-Aware Transformer](https://mlsanity.com/paper/2609.33695/) (2026)

## Abstract (arXiv)

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.