  Rapid improvements in machine learning over the past decade are beginning to
have far-reaching effects. For communications, engineers with limited domain
expertise can now use off-the-shelf learning packages to design
high-performance systems based on simulations. Prior to the current revolution
in machine learning, the majority of communication engineers were quite aware
that system parameters (such as filter coefficients) could be learned using
stochastic gradient descent. It was not at all clear, however, that more
complicated parts of the system architecture could be learned as well. In this
paper, we discuss the application of machine-learning techniques to two
communications problems and focus on what can be learned from the resulting
systems. We were pleasantly surprised that the observed gains in one example
have a simple explanation that only became clear in hindsight. In essence, deep
learning discovered a simple and effective strategy that had not been
considered earlier.
