Improving Achievability of Cache-Aided Private Variable-Length Coding with Zero Leakage

TL;DR

The paper addresses cache-aided private content delivery under a perfect privacy constraint where a private attribute $X$ is correlated with the database, and an adversary observes the delivered code. It proposes a novel two-part achievability that combines a one-time-pad encoding of $X$ with a greedy entropy-based encoder aligned with minimum entropy coupling to create the remaining message $U$, achieving $I(\\mathcal{C};X)=0$ while enabling reliable decoding at the users. The authors derive upper bounds on the average delivery length $\\mathbb{L}(P_{XY_1\\cdot Y_N},T)$, giving explicit bounds for $|\\mathcal{X}|=2$ and $|\\mathcal{X}|>2$ with constant gaps, and show how the new scheme improves upon previous results. They further tighten bounds in two special cases using common information theory, demonstrating favorable behavior when the private data is large, and provide numerical illustrations to highlight reduced leakage and shorter transmissions.

Abstract

A statistical cache-aided compression problem with a privacy constraint is studied, where a server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is linked through a shared channel to $K$ users, where each has access to a local cache memory of size $MF$ bits. During the placement phase, the server fills the users' caches without prior knowledge of their demands, while the delivery phase takes place after the users send their demands to the server. We assume that each file in database $Y_i$ is arbitrarily correlated with a private attribute $X$, and an adversary is assumed to have access to the shared channel. The users and the server have access to a shared 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 reveal any information about $X$, i.e., $I(X;\mathcal{C})=0$; ii. User $i$ can decode its demand, $Y_{d_i}$, by using the shared key $W$, $\cal C$, and its local cache $Z_i$. In a previous work, we have proposed a variable-length coding scheme that combines privacy-aware compression with coded caching techniques. In this paper, we propose a new achievability scheme using minimum entropy coupling concept and a greedy entropy-based algorithm. We show that the proposed scheme improves the previous results. Moreover, considering two special cases we improve the obtained bounds using the common information concept.

Figures (4)

• Figure 1: In this work a server wants to send a response over a shared link to satisfy users' demands, where the database is correlated with the private data. In the delivery phase, we hide the information about $X$ using one-time-pad coding and send the rest of response using a greedy entropy-based algorithm proposed in kocaoglu2017entropic.
• Figure 2: Encoder design: illustration of the achievability scheme of Theorem \ref{['th1']}. Two-part code construction is used to produce the response of the server, $\mathcal{C}$. The server sends $\cal C$ over the channel, which is independent of $X$.
• Figure 3: Illustration of the decoding process for the achievability scheme of Theorem \ref{['th1']}.
• Figure 4: In this work, we use two-part construction coding strategy to send codewords over the channels. We hide the information of $X$ using one-time-pad coding and we then use the solution of $h_0(P_{X\mathcal{C}'})=g_0(P_{X\mathcal{C}'})$ to construct $U$.

Theorems & Definitions (19)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Theorem 1
• Theorem 2
• Remark 5
• Remark 6
• Theorem 3
• proof