Semi-Supervised Channel Equalization Using Variational Autoencoders

We present methods for semi-supervised learning (SSL) from few pilots over nonlinear channels using variational autoencoders. These channels, which are unknown at the receiver, may have finite memory (intersymbol interference). The loss function we use for SSL incorporates both the labeled (pilot) symbols and unlabeled (payload) symbols. We demonstrate a very significant reduction in the number of pilot symbols required for reliable inference over the channel when applying SSL to train a variational autoencoder, compared to standard supervised learning of a neural network decoder using only pilot data information.