  We consider wireless transmission of images in the presence of channel output
feedback. From a Shannon theoretic perspective feedback does not improve the
asymptotic end-to-end performance, and separate source coding followed by
capacity-achieving channel coding, which ignores the feedback signal, achieves
the optimal performance. It is well known that separation is not optimal in the
practical finite blocklength regime; however, there are no known practical
joint source-channel coding (JSCC) schemes that can exploit the feedback signal
and surpass the performance of separation-based schemes. Inspired by the recent
success of deep learning methods for JSCC, we investigate how noiseless or
noisy channel output feedback can be incorporated into the transmission system
to improve the reconstruction quality at the receiver. We introduce an
autoencoder-based JSCC scheme, which we call DeepJSCC-f, that exploits the
channel output feedback, and provides considerable improvements in terms of the
end-to-end reconstruction quality for fixed-length transmission, or in terms of
the average delay for variable-length transmission. To the best of our
knowledge, this is the first practical JSCC scheme that can fully exploit
channel output feedback, demonstrating yet another setting in which modern
machine learning techniques can enable the design of new and efficient
communication methods that surpass the performance of traditional structured
coding-based designs.
