The partial side information problem with additional reconstructions

We consider a quadratic Gaussian distributed lossy source coding setup with an additional constraint of identical reconstructions between the encoder and the decoder. The setup consists of two correlated Gaussian sources,wherein one of them has to be reconstructed to be within some distortion constraint and match with a corresponding reconstruction at the encoder, while the other source acts as coded side information. We study the tradeoff between the rates of two encoders for a given distortion constraint on the reconstruction. An explicit characterization of this trade-off is the main result of the paper. We also give close inner and outer bounds for the discrete memoryless version of the problem.