  End-to-end learning of communication systems enables joint optimization of
transmitter and receiver, implemented as deep neural network-based
autoencoders, over any type of channel and for an arbitrary performance metric.
Recently, an alternating training procedure was proposed which eliminates the
need for an explicit channel model. However, this approach requires feedback of
real-valued losses from the receiver to the transmitter during training. In
this paper, we first show that alternating training works even with a noisy
feedback channel. Then, we design a system that learns to transmit real numbers
over an unknown channel without a preexisting feedback link. Once trained, this
feedback system can be used to communicate losses during alternating training
of autoencoders. Evaluations over additive white Gaussian noise and Rayleigh
block-fading channels show that end-to-end communication systems trained using
the proposed feedback system achieve the same performance as when trained with
a perfect feedback link.
