Polar Codes and Polar Lattices for the Heegard-Berger Problem

TL;DR

This paper introduces explicit polar code and lattice constructions to achieve the rate-distortion function in the Heegard-Berger problem for binary and Gaussian sources, combining source and channel coding techniques.

Contribution

It presents novel nested polar code and lattice schemes tailored for the Heegard-Berger problem, extending polar coding applications to complex source coding scenarios.

Findings

Achieves the rate-distortion function for binary sources with side information.

Constructs polar lattices for Gaussian sources and side information.

Demonstrates the effectiveness of nested polar structures in source coding.

Abstract

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 the 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.