Private Variable-Length Coding with Sequential Encoder

A multi-user private data compression problem is studied. A server has access to a database of $N$ files, $(Y_{1},\ldots,\ Y_{N})$, 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: $\mathbf{i}$. The message $\mathcal{C}$ 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 $\mathcal{C}$, 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.