  The design of codes for communicating reliably over a statistically well
defined channel is an important endeavor involving deep mathematical research
and wide-ranging practical applications. In this work, we present the first
family of codes obtained via deep learning, which significantly beats
state-of-the-art codes designed over several decades of research. The
communication channel under consideration is the Gaussian noise channel with
feedback, whose study was initiated by Shannon; feedback is known theoretically
to improve reliability of communication, but no practical codes that do so have
ever been successfully constructed.
  We break this logjam by integrating information theoretic insights
harmoniously with recurrent-neural-network based encoders and decoders to
create novel codes that outperform known codes by 3 orders of magnitude in
reliability. We also demonstrate several desirable properties of the codes: (a)
generalization to larger block lengths, (b) composability with known codes, (c)
adaptation to practical constraints. This result also has broader ramifications
for coding theory: even when the channel has a clear mathematical model, deep
learning methodologies, when combined with channel-specific
information-theoretic insights, can potentially beat state-of-the-art codes
constructed over decades of mathematical research.
