Unsupervised Linear and Nonlinear Channel Equalization and Decoding using Variational Autoencoders

A new approach for blind channel equalization and decoding, using variational autoencoders (VAEs), 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 approximated 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 fully 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 substantial improvements compared to expectation maximization (EM) using turbo equalization. Furthermore, in our simulations we demonstrate a relatively small gap between the performance of the new unsupervised equalization method and that of the fully channel informed (non-blind) turbo equalizer.