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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">successive refinement</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple descriptions</i> , respectively, in the context of joint source-channel coding (JSCC). We propose DeepJSCC- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula> , 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- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula> can learn to transmit the source progressively with negligible losses in the end-to-end performance compared with a single transmission. Moreover, DeepJSCC- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l$ </tex-math></inline-formula> 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.
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