  We propose a data-driven approach to explicitly learn the progressive
encoding of a continuous source, which is successively decoded with increasing
levels of quality and with the aid of correlated side information. This setup
refers to the successive refinement of the Wyner-Ziv coding problem. Assuming
ideal Slepian-Wolf coding, our approach employs recurrent neural networks
(RNNs) to learn layered encoders and decoders for the quadratic Gaussian case.
The models are trained by minimizing a variational bound on the rate-distortion
function of the successively refined Wyner-Ziv coding problem. We demonstrate
that RNNs can explicitly retrieve layered binning solutions akin to scalable
nested quantization. Moreover, the rate-distortion performance of the scheme is
on par with the corresponding monolithic Wyner-Ziv coding approach and is close
to the rate-distortion bound.
