A Locally Differential Private Coding-Assisted Succinct Histogram Protocol

TL;DR

This paper introduces a practical local differential privacy protocol for succinct histograms using error-correcting codes, specifically polar codes with Gaussian perturbations, improving accuracy for low-frequency items.

Contribution

It is the first to apply polar codes with Gaussian perturbations in an LDP setting for succinct histograms, enhancing data utility and accuracy.

Findings

Outperforms prior methods in low-frequency item accuracy

Maintains similar overall frequency estimation accuracy

Uses polar codes with Gaussian-based perturbations for efficient soft decoding

Abstract

A succinct histogram captures frequent items and their frequencies across clients and has become increasingly important for large-scale, privacy-sensitive machine learning applications. To develop a rigorous framework to guarantee privacy for the succinct histogram problem, local differential privacy (LDP) has been utilized and shown promising results. To preserve data utility under LDP, which essentially works by intentionally adding noise to data, error-correcting codes naturally emerge as a promising tool for reliable information collection. This work presents the first practical $(\epsilon,\delta)$-LDP protocol for constructing succinct histograms using error-correcting codes. To this end, polar codes and their successive-cancellation list (SCL) decoding algorithms are leveraged as the underlying coding scheme. More specifically, our protocol introduces Gaussian-based perturbations to enable efficient soft decoding. Experiments demonstrate that our approach outperforms prior methods, particularly for items with low true frequencies, while maintaining similar frequency estimation accuracy.