# Private Status Updating with Erasures: A Case for Retransmission Without Resampling

## TL;DR

This paper explores a privacy-aware status updating system over erasure channels, demonstrating that retransmitting stale updates without resampling can enhance privacy while managing age-of-information.

## Contribution

It introduces a novel approach combining waiting times and retransmissions of stale updates to balance privacy and freshness in AoI systems.

## Key findings

- Retransmitting stale updates can improve privacy under certain conditions.
- Waiting times can be optimized to balance privacy and AoI.
- Stale update retransmission is beneficial without resampling in specific scenarios.

## Abstract

A status updating system is considered in which a source updates a destination over an erasure channel. The utility of the updates is measured through a function of their age-of-information (AoI), which assesses their freshness. Correlated with the status updates is another process that needs to be kept private from the destination. Privacy is measured through a leakage function that depends on the amount and time of the status updates received: stale updates are more private than fresh ones. Different from most of the current AoI literature, a post-sampling waiting time is introduced in order to provide a privacy cover at the expense of AoI. More importantly, it is also shown that, depending on the leakage budget and the channel statistics, it can be useful to retransmit stale status updates following erasure events without resampling fresh ones.