21,128 research outputs found
The Capacity of Private Computation
We introduce the problem of private computation, comprised of distributed
and non-colluding servers, independent datasets, and a user who wants to
compute a function of the datasets privately, i.e., without revealing which
function he wants to compute, to any individual server. This private
computation problem is a strict generalization of the private information
retrieval (PIR) problem, obtained by expanding the PIR message set (which
consists of only independent messages) to also include functions of those
messages. The capacity of private computation, , is defined as the maximum
number of bits of the desired function that can be retrieved per bit of total
download from all servers. We characterize the capacity of private computation,
for servers and independent datasets that are replicated at each
server, when the functions to be computed are arbitrary linear combinations of
the datasets. Surprisingly, the capacity,
, matches the capacity of PIR with
servers and messages. Thus, allowing arbitrary linear computations does
not reduce the communication rate compared to pure dataset retrieval. The same
insight is shown to hold even for arbitrary non-linear computations when the
number of datasets
Blind Interference Alignment for Private Information Retrieval
Blind interference alignment (BIA) refers to interference alignment schemes
that are designed only based on channel coherence pattern knowledge at the
transmitters (the "blind" transmitters do not know the exact channel values).
Private information retrieval (PIR) refers to the problem where a user
retrieves one out of K messages from N non-communicating databases (each holds
all K messages) without revealing anything about the identity of the desired
message index to any individual database. In this paper, we identify an
intriguing connection between PIR and BIA. Inspired by this connection, we
characterize the information theoretic optimal download cost of PIR, when we
have K = 2 messages and the number of databases, N, is arbitrary
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