Nested linear/lattice codes for Wyner-Ziv encoding

We construct structured codes for lossy compression with uncoded side information at the decoder. These codes aim at achieving the optimal performance, given by the Wyner-Ziv (1976) rate-distortion function, for two typical settings. For binary symmetric source/side-information, we show that a pair of nested linear binary codes, each individually "good" in the classical sense, approaches the WZ-function relative to the Hamming distortion measure. For the quadratic Gaussian case we show a similar result at high SNR, using a pair of nested lattices and their associated lattice-decoding functions.