Private Variable-Length Coding with Sequential Encoder
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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,…,d_K) corresponds to the demand vector. The goal is to design the delivered message 𝒞=(𝒞_1,…,𝒞_K) after the user send his demands to the encoder such that the average length of 𝒞 is minimized, while satisfying: i. The message C does not reveal any information about X, i.e., X and 𝒞 are independent, which corresponds to the perfect privacy constraint; ii. The user is able to decode its demands, Y_d_i, by using 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 𝒞 in an example. Finally, we study an application considering cache-aided networks.
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