  We propose deep learning based communication methods for adaptive-bandwidth
transmission of images over wireless channels. We consider the scenario in
which images are transmitted progressively in layers over time or frequency,
and such layers can be aggregated by receivers in order to increase the quality
of their reconstructions. We investigate two scenarios, one in which the layers
are sent sequentially, and incrementally contribute to the refinement of a
reconstruction, and another in which the layers are independent and can be
retrieved in any order. Those scenarios correspond to the well known problems
of \textit{successive refinement} and \textit{multiple descriptions},
respectively, in the context of joint source-channel coding (JSCC). We propose
DeepJSCC-$l$, an innovative solution that uses convolutional autoencoders, and
present three architectures with different complexity trade-offs. To the best
of our knowledge, this is the first practical multiple-description JSCC scheme
developed and tested for practical information sources and channels. Numerical
results show that DeepJSCC-$l$ can learn to transmit the source progressively
with negligible losses in the end-to-end performance compared with a single
transmission. Moreover, DeepJSCC-$l$ has comparable performance with state of
the art digital progressive transmission schemes in the challenging low
signal-to-noise ratio (SNR) and small bandwidth regimes, with the additional
advantage of graceful degradation with channel SNR.
