Reliable digital communication is a primary workhorse of the modern information age. The disciplines of communication, coding, and information theories drive the innovation by designing efficient codes that allow transmissions to be robustly and efficiently decoded. Progress in near optimal codes is made by individual human ingenuity over the decades, and breakthroughs have been, befittingly, sporadic and spread over several decades. Deep learning is a part of daily life where its successes can be attributed to a lack of a (mathematical) generative model. Deep learning empirically fits neural network models to the data, and the result has been extremely potent. In yet other applications, the data is generated by a simple model and performance criterion mathematically precise and training/test samples infinitely abundant, but the space of algorithmic choices is enormous (example: chess). Deep learning has recently shown strong promise in these problems too (example: alphazero). The latter scenario is a good description of communication theory. The mathematical models underlying canonical communication channels allow one to sample an unlimited amount of data to train and test the communication algorithms ((encoder, decoder) pairs) and the metric of bit (or block) error rate allows for mathematically precise evaluation. Motivated by the successes of deep learning in mathematically well defined and extremely challenging tasks of chess, Go, and protein folding, we posit that deep learning methods can play a crucial role in solving core goals of coding theory: designing new (encoder, decoder) pairs that improve state of the art performance over canonical channel models. This manuscript surveys recent advances towards demonstrating this hypothesis, by focusing on strengthening a specific family of coding methods - sequential codes (convolutional codes) and codes that use them as basic building blocks (Turbo codes) - via deep learning methods. New state of the art results are derived on several canonical channels, including the AWGN channel with feedback.
