The Wyner-Ziv Problem with Noisy Side-Information at the Encoder

In the problem of lossy source coding with side-information, it is well known (Wyner and Ziv 1976) that knowledge of the side-information at the encoder improves the rate-distortion trade-off for binary sources and the Hamming distortion measure. We consider a scenario where the encoder has access to a noisy version of the binary side-information. We evaluate the rate-distortion function for this scenario and characterize it as an optimization problem over four parameters. When the sources are Gaussian and the distortion measure is the squared error, it is known that encoder side-information does not improve the rate-distortion trade-off. However, knowing the side-information at the encoder greatly reduces the coding complexity. We investigate the question whether the knowledge of noisy side-information can improve the coding complexity for such sources. However, our results suggest that this is not the case.