Lossy Compression with Privacy Constraints: Optimality of Polar Codes

TL;DR

This paper demonstrates that polar codes can achieve the optimal balance between data utility and privacy in lossy source coding with privacy constraints, providing a constructive method for the rate-distortion-equivocation tradeoff.

Contribution

It proves that polar codes, with possible time sharing, can attain the entire optimal rate-distortion-equivocation region for privacy-preserving lossy compression.

Findings

Polar codes achieve the optimal privacy-utility tradeoff.

Constructive scheme for the rate-distortion-equivocation region.

Applicable with or without time sharing.

Abstract

A lossy source coding problem with privacy constraint is studied in which two correlated discrete sources $X$ and $Y$ are compressed into a reconstruction $\hat{X}$ with some prescribed distortion $D$. In addition, a privacy constraint is specified as the equivocation between the lossy reconstruction $\hat{X}$ and $Y$. This models the situation where a certain amount of source information from one user is provided as utility (given by the fidelity of its reconstruction) to another user or the public, while some other correlated part of the source information $Y$ must be kept private. In this work, we show that polar codes are able, possibly with the aid of time sharing, to achieve any point in the optimal rate-distortion-equivocation region identified by Yamamoto, thus providing a constructive scheme that obtains the optimal tradeoff between utility and privacy in this framework.