Error exponents and test channel optimization for the Gaussian Wyner-Ziv problem

We consider the quadratic Gaussian Wyner-Ziv problem, i.e., the problem of lossy compression of a Gaussian source with Gaussian side information at the decoder and a quadratic distortion measure. Motivated by applications in video coding, we study how to minimize the probability that the distortion exceeds a given threshold, as opposed to the conventional approach of minimizing the average distortion. We obtain an achievable exponent for this problem, which is positive above the rate distortion function, and expose a tension in the choice of the test channel; the optimal test channel balances two competing error events.