A multi-user private data compression problem is studied. A server has access to a database of $N$ files, $(Y_1,...,Y_N)$, each of size $F$ bits and is connected to an encoder. The encoder is connected through an unsecured link to a user. We assume that each file $Y_i$ is arbitrarily correlated with a private attribute $X$, which is assumed to be accessible by the encoder. Moreover, an adversary is assumed to have access to the link. The users and the encoder have access to a shared secret key $W$. We assume that at each time the user asks for a file $Y_{d_i}$, where $(d_1,\ldots,d_K)$ corresponds to the demand vector. The goal is to design the delivered message $\mathcal {C}=(\mathcal {C}_1,\ldots,\mathcal {C}_K)$ after the user send his demands to the encoder such that the average length of $\mathcal{C}$ is minimized, while satisfying: i. The message $\cal C$ does not reveal any information about $X$, i.e., $X$ and $\mathcal{C}$ are independent, which corresponds to the perfect privacy constraint; ii. The user is able to decode its demands, $Y_{d_i}$, by using $\cal C$, and the shared key $W$. Here, the encoder sequentially encode each demand $Y_{d_i}$ at time $i$, using the shared key and previous encoded messages. We propose a variable-length coding scheme that uses privacy-aware compression techniques. We study proposed upper and lower bounds on the average length of $\mathcal{C}$ in an example. Finally, we study an application considering cache-aided networks.

翻译：研究了多用户私有数据压缩问题。服务器拥有一个包含$N$个文件$(Y_1,...,Y_N)$的数据库，每个文件大小为$F$比特，并通过编码器连接。编码器通过不安全的链路连接到用户。我们假设每个文件$Y_i$与私有属性$X$任意相关，且编码器可访问该属性。此外，假设攻击者能够访问该链路。用户和编码器共享一个密钥$W$。我们假设每个时刻用户请求一个文件$Y_{d_i}$，其中$(d_1,\ldots,d_K)$对应于需求向量。目标是在用户向编码器发送其需求后，设计传递的消息$\mathcal {C}=(\mathcal {C}_1,\ldots,\mathcal {C}_K)$，使得$\mathcal{C}$的平均长度最小化，同时满足：i. 消息$\cal C$不泄露关于$X$的任何信息，即$X$和$\mathcal{C}$相互独立，这对应于完美隐私约束；ii. 用户能够通过$\cal C$和共享密钥$W$解码其需求$Y_{d_i}$。在此，编码器在时刻$i$使用共享密钥和先前编码的消息顺序编码每个需求$Y_{d_i}$。我们提出了一种利用隐私感知压缩技术的变长编码方案。通过实例研究了$\mathcal{C}$平均长度的上界和下界。最后，研究了考虑缓存辅助网络的应用。