A private cache-aided compression problem is studied, where a server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is connected through a shared link to $K$ users, each equipped with a local cache of size $MF$ bits. In the placement phase, the server fills the users$'$ caches without knowing their 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 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., $X$ and $\cal C$ are independent, which corresponds to the perfect privacy constraint; ii. User $i$ is able to decode its demand, $Y_{d_i}$, by using $\cal C$, its local cache $Z_i$, and the shared key $W$. Since the database is correlated with $X$, existing codes for cache-aided delivery do not satisfy the perfect privacy condition. Indeed, we propose a 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. Finally, we extend the results to the case, where $X$ and $\mathcal{C}$ can be correlated, i.e., non-zero leakage is allowed.

翻译：针对私有缓存辅助压缩问题展开研究：服务器可访问包含N个文件(Y_1,...,Y_N)的数据库，每个文件大小为F比特，通过共享链路连接K个用户，每个用户配备MF比特本地缓存。在存储阶段，服务器在未知用户需求的情况下填充用户缓存；交付阶段则在用户向服务器发送需求后进行。假设每个文件Y_i与私有属性X任意相关，且攻击者可访问共享链路。用户与服务器共享密钥W。目标是在满足以下约束条件下设计缓存内容与交付消息C，使得C平均长度最小化：i.响应C不泄露任何X信息，即X与C独立（完美隐私约束）；ii.用户i可通过C、本地缓存Z_i及共享密钥W解码其需求Y_{d_i}。由于数据库与X相关，现有缓存辅助编码方案无法满足完美隐私条件。为此，本文提出结合隐私感知压缩与编码缓存技术的变长编码方案，具体采用两部分编码结构与函数表示引理。最后，将结果扩展至允许X与C相关（即非零泄漏）的场景。