  There have been significant research activities in recent years to automate
the design of channel encoders and decoders via deep learning. Due the
dimensionality challenge in channel coding, it is prohibitively complex to
design and train relatively large neural channel codes via deep learning
techniques. Consequently, most of the results in the literature are limited to
relatively short codes having less than 100 information bits. In this paper, we
construct ProductAEs, a computationally efficient family of deep-learning
driven (encoder, decoder) pairs, that aim at enabling the training of
relatively large channel codes (both encoders and decoders) with a manageable
training complexity. We build upon the ideas from classical product codes, and
propose constructing large neural codes using smaller code components. More
specifically, instead of directly training the encoder and decoder for a large
neural code of dimension $k$ and blocklength $n$, we provide a framework that
requires training neural encoders and decoders for the code parameters
$(n_1,k_1)$ and $(n_2,k_2)$ such that $n_1 n_2=n$ and $k_1 k_2=k$. Our training
results show significant gains, over all ranges of signal-to-noise ratio (SNR),
for a code of parameters $(225,100)$ and a moderate-length code of parameters
$(441,196)$, over polar codes under successive cancellation (SC) decoder.
Moreover, our results demonstrate meaningful gains over Turbo Autoencoder
(TurboAE) and state-of-the-art classical codes. This is the first work to
design product autoencoders and a pioneering work on training large channel
codes.
