Polar Codes for a Quadratic-Gaussian Wyner-Ziv Problem

In this work, we study the performance of polar codes for lossy compression of a Gaussian source with a side information at decoder; known as the quadratic-Gaussian Wyner-Ziv problem. First we extend the binary polar codes to q-ary for the Wyner-Ziv problem. We show that the nested q- ary polar codes are optimal for this case. Then we present two polar coding schemes for the Gaussian Wyner-Ziv problem. In the first scheme, we achieve a rate above the Wyner-Ziv rate-distortion function with a gap of 0.5 bits compared with the optimal rate. This scheme utilizes a successive cancellation decoder and is optimal in weak side-information cases when the decoder side-information noise variance is extremely higher than the source variance, referred to as low signal-to-noise ratios (SNRs). In the second scheme, we achieve the optimal rate in strong side-information cases, i.e., at high SNRs. The decoder utilizes an estimator to achieve the optimal distortion. Thus, with both schemes, we can achieve the optimal rate depending on the quality of side information at the decoder.