137 research outputs found
The Optimal Mechanism in Differential Privacy
We derive the optimal -differentially private mechanism for single
real-valued query function under a very general utility-maximization (or
cost-minimization) framework. The class of noise probability distributions in
the optimal mechanism has {\em staircase-shaped} probability density functions
which are symmetric (around the origin), monotonically decreasing and
geometrically decaying. The staircase mechanism can be viewed as a {\em
geometric mixture of uniform probability distributions}, providing a simple
algorithmic description for the mechanism. Furthermore, the staircase mechanism
naturally generalizes to discrete query output settings as well as more
abstract settings. We explicitly derive the optimal noise probability
distributions with minimum expectation of noise amplitude and power. Comparing
the optimal performances with those of the Laplacian mechanism, we show that in
the high privacy regime ( is small), Laplacian mechanism is
asymptotically optimal as ; in the low privacy regime
( is large), the minimum expectation of noise amplitude and minimum
noise power are and as , while the expectation of
noise amplitude and power using the Laplacian mechanism are
and , where is
the sensitivity of the query function. We conclude that the gains are more
pronounced in the low privacy regime.Comment: 40 pages, 5 figures. Part of this work was presented in DIMACS
Workshop on Recent Work on Differential Privacy across Computer Science,
October 24 - 26, 201
Interference Channels with Destination Cooperation
Interference is a fundamental feature of the wireless channel. To better
understand the role of cooperation in interference management, the two-user
Gaussian interference channel where the destination nodes can cooperate by
virtue of being able to both transmit and receive is studied. The sum-capacity
of this channel is characterized up to a constant number of bits. The coding
scheme employed builds up on the superposition scheme of Han and Kobayashi
(1981) for two-user interference channels without cooperation. New upperbounds
to the sum-capacity are also derived.Comment: revised based on reviewers' comment
Capacity of Fading Gaussian Channel with an Energy Harvesting Sensor Node
Network life time maximization is becoming an important design goal in
wireless sensor networks. Energy harvesting has recently become a preferred
choice for achieving this goal as it provides near perpetual operation. We
study such a sensor node with an energy harvesting source and compare various
architectures by which the harvested energy is used. We find its Shannon
capacity when it is transmitting its observations over a fading AWGN channel
with perfect/no channel state information provided at the transmitter. We
obtain an achievable rate when there are inefficiencies in energy storage and
the capacity when energy is spent in activities other than transmission.Comment: 6 Pages, To be presented at IEEE GLOBECOM 201
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