Perfect Privacy and Strong Stationary Times for Markovian Sources

TL;DR

This paper investigates privacy-preserving data sharing from Markov sources using redaction mechanisms, establishing connections with strong stationary times and demonstrating mechanisms that optimize utility while maintaining perfect privacy.

Contribution

It introduces a novel link between perfect privacy and window-based redaction schemes, and shows that optimal mechanisms can redact a constant number of data points regardless of data length.

Findings

Redaction up to a strong stationary time preserves privacy.

Optimal mechanisms achieve minimal distortion with constant redacted points.

Both mechanisms are equivalent and effective for Markovian data.

Abstract

We consider the problem of sharing correlated data under a perfect information-theoretic privacy constraint. We focus on redaction (erasure) mechanisms, in which data are either withheld or released unchanged, and measure utility by the average cardinality of the released set, equivalently, the expected Hamming distortion. Assuming the data are generated by a finite time-homogeneous Markov chain, we study the protection of the initial state while maximizing the amount of shared data. We establish a connection between perfect privacy and window-based redaction schemes, showing that erasing data up to a strong stationary time preserves privacy under suitable conditions. We further study an optimal sequential redaction mechanism and prove that it admits an equivalent window interpretation. Interestingly, we show that both mechanisms achieve the optimal distortion while redacting only a constant average number of data points, independent of the data length~$N$.