Unsupervised Linear and Nonlinear Channel Equalization and Decoding Using Variational Autoencoders

Avi Caciularu, David Burshtein

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish
Article number9080094
Pages (from-to)1003-1018
Number of pages16
JournalIEEE Transactions on Cognitive Communications and Networking
Issue number3
StatePublished - Sep 2020
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received May 21, 2019; revised December 31, 2019 and April 12, 2020; accepted April 21, 2020. Date of publication April 28, 2020; date of current version September 9, 2020. This research was supported by the Israel Science Foundation (grant no. 1868/18), and by the Yitzhak and Chaya Weinstein Research Institute for Signal Processing. The associate editor coordinating the review of this article and approving it for publication was C. Regazzoni. (Corresponding author: Avi Caciularu.) Avi Caciularu was with the School of Electrical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel. He is now with the Department of Computer Science, Bar-Ilan University, Ramat Gan 5290002, Israel (e-mail: avi.c33@gmail.com).

Publisher Copyright:
© 2015 IEEE.


  • Blind equalizers
  • belief propagation
  • convolutional neural networks
  • deep learning
  • maximum likelihood estimation


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