Inventing Codes for Channels With Active Feedback via Deep Learning

Designing reliable codes for channels with feedback, which has significant theoretical and practical importance, is one of the long-standing open problems in coding theory. While there are numerous prior works on analytical codes for channels with feedback, the majority of them focus on channels with noiseless output feedback, where the optimal coding scheme is still unknown. For channels with noisy feedback, deriving analytical codes becomes even more challenging, and much less is known. Recently, it has been shown that deep learning can, in part, address these challenges and lead to the discovery of new codes for channels with noisy output feedback. Despite the success, there are three important open problems:
$(a)$
deep learning-based codes mainly focus on the passive feedback setup, which is shown to be worse than the active feedback setup;
$(b)$
deep learning-based codes are hard to interpret or analyze; and
$(c)$
they have not been successfully demonstrated in the over-the-air channels with feedback. We address these three challenges. First, we present a learning-based framework for designing codes for channels with active feedback. Second, we analyze the latent features of the learned codes to devise an analytical coding scheme. We show that the approximated analytical code is a non-trivial variation of the state-of-the-art codes, demonstrating that deep learning is a powerful tool for deriving a new analytical communication scheme for challenging communication scenarios. Finally, we demonstrate the over-the-air performance of our neural codes by building a wireless testbed that consists of two separate N200 USRPs operating as the transmitter and the receiver. To the best of our knowledge, this is the first over-the-air hardware implementation of neural codes for interactive channels.