Extracting Wyner's common randomness using polar codes

Abstract

Explicit construction of polar codes for the Gray-Wyner network is studied. We show that Wyner's common information plays an essential role in constructing polar codes for both lossless and lossy Gray-Wyner problems. For discrete sources, extracting Wyner's common randomness can be viewed as a lossy compression problem, which is accomplished by extending polar coding from a single source to a pair of sources with doubled alphabet size. We show that the lossless Gray-Wyner region can be achieved by an upgraded or degraded version of the common randomness. For joint Gaussian sources, we prove that extracting Wyner's common randomness is equivalent to lossy compression for a single Gaussian source, which implies that it can be extracted by a polar lattice for quantization.