Polar Codes and Polar Lattices for the Heegard–Berger Problem

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for doubly symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting a quantization polar lattice and a capacity-achieving polar lattice for the additive white Gaussian noise channel.