On the excess distortion exponent of the quadratic-Gaussian Wyner-Ziv problem

An achievable excess distortion exponent for compression of a white Gaussian source by dithered lattice quantization is derived. We show that for a required distortion level close enough to the rate-distortion function, and in the high-rate limit, the exponent equals the optimal quadratic-Gaussian excess distortion exponent. Using this approach, no further loss is incurred by the presence of any source interference known at the decoder (“Wyner-Ziv side-information”). The derivation of this achievable exponent involves finding the exponent of the probability that a combination of a spherically-bounded vector and a Gaussian vector leaves the Voronoi cell of a good lattice.