  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.
