  This paper proposes a deep learning framework to design distributed
compression strategies in which distributed agents need to compress
high-dimensional observations of a source, then send the compressed bits via
bandwidth limited links to a fusion center for source reconstruction. Further,
we require the compression strategy to be progressive so that it can adapt to
the varying link bandwidths between the agents and the fusion center. Moreover,
to ensure scalability, we investigate strategies that depend only on the local
channel state information (CSI) at each agent. Toward this end, we use a
data-driven approach in which the progressive linear combination and uniform
quantization strategy at each agent are trained as a function of its local CSI.
To deal with the challenges of modeling the quantization operations (which
always produce zero gradients in the training of neural networks), we propose a
novel approach of exploiting the statistics of the batch training data to set
the dynamic ranges of the uniform quantizers. Numerically, we show that the
proposed distributed estimation strategy designed with only local CSI can
significantly reduce the signaling overhead and can achieve a lower
mean-squared error distortion for source reconstruction than state-of-the-art
designs that require global CSI at comparable overall communication cost.
