Cache-Aided Variable-Length Coding with Perfect Privacy

TL;DR

This paper introduces a novel cache-aided variable-length coding scheme that ensures perfect privacy by combining privacy-aware compression with coded caching, addressing the challenge of private attribute leakage in correlated data.

Contribution

It proposes a new lossless coding scheme using two-part code construction and functional representation, enhancing privacy-preserving cache-aided delivery methods.

Findings

The proposed scheme achieves lower average code length compared to previous methods.

It guarantees perfect privacy by ensuring the delivered message is independent of private attributes.

The alternative coding approach based on minimum entropy coupling further improves efficiency.

Abstract

A cache-aided compression problem with perfect privacy is studied, where a server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits. The server is connected to $K$ users through a shared link, where each user has access to a local cache of size $MF$ bits. In the placement phase, the server fills the users$'$ caches without prior knowledge of their future demands, while the delivery phase takes place after the users send their demands to the server. We assume that each file $Y_i$ is arbitrarily correlated with a private attribute $X$, and an adversary is assumed to have access to the shared link. The users and the server have access to a shared secret key $W$. The goal is to design the cache contents and the delivered message $\cal C$ such that the average length of $\mathcal{C}$ is minimized, while satisfying: i. The response $\cal C$ does not disclose any information about $X$, i.e., $X$ and $\cal C$ are statistically independent yielding $I(X;\mathcal{C})=0$, which corresponds to the perfect privacy constraint; ii. User $i$ is able to decode its demand, $Y_{d_i}$, by using its local cache $Z_i$, delivered message $\cal C$, and the shared secret key $W$. Due to the correlation of database with the private attribute, existing codes for cache-aided delivery do not fulfill the perfect privacy constraint. Indeed, in this work, we propose a lossless variable-length coding scheme that combines privacy-aware compression with coded caching techniques. In particular, we use two-part code construction and Functional Representation Lemma. Furthermore, we propose an alternative coding scheme based on the minimum entropy coupling concept and a greedy entropy-based algorithm. We show that the proposed scheme improves the previous results obtained by Functional Representation Lemma.