105 research outputs found
Lossy Source Coding with Reconstruction Privacy
We consider the problem of lossy source coding with side information under a
privacy constraint that the reconstruction sequence at a decoder should be kept
secret to a certain extent from another terminal such as an eavesdropper, a
sender, or a helper. We are interested in how the reconstruction privacy
constraint at a particular terminal affects the rate-distortion tradeoff. In
this work, we allow the decoder to use a random mapping, and give inner and
outer bounds to the rate-distortion-equivocation region for different cases
where the side information is available non-causally and causally at the
decoder. In the special case where each reconstruction symbol depends only on
the source description and current side information symbol, the complete
rate-distortion-equivocation region is provided. A binary example illustrating
a new tradeoff due to the new privacy constraint, and a gain from the use of a
stochastic decoder is given.Comment: 22 pages, added proofs, to be presented at ISIT 201
Source Coding Problems with Conditionally Less Noisy Side Information
A computable expression for the rate-distortion (RD) function proposed by
Heegard and Berger has eluded information theory for nearly three decades.
Heegard and Berger's single-letter achievability bound is well known to be
optimal for \emph{physically degraded} side information; however, it is not
known whether the bound is optimal for arbitrarily correlated side information
(general discrete memoryless sources). In this paper, we consider a new setup
in which the side information at one receiver is \emph{conditionally less
noisy} than the side information at the other. The new setup includes degraded
side information as a special case, and it is motivated by the literature on
degraded and less noisy broadcast channels. Our key contribution is a converse
proving the optimality of Heegard and Berger's achievability bound in a new
setting. The converse rests upon a certain \emph{single-letterization} lemma,
which we prove using an information theoretic telescoping identity {recently
presented by Kramer}. We also generalise the above ideas to two different
successive-refinement problems
New Privacy Mechanism Design With Direct Access to the Private Data
The design of a statistical signal processing privacy problem is studied
where the private data is assumed to be observable. In this work, an agent
observes useful data , which is correlated with private data , and wants
to disclose the useful information to a user. A statistical privacy mechanism
is employed to generate data based on that maximizes the revealed
information about while satisfying a privacy criterion. To this end, we use
extended versions of the Functional Representation Lemma and Strong Functional
Representation Lemma and combine them with a simple observation which we call
separation technique. New lower bounds on privacy-utility trade-off are derived
and we show that they can improve the previous bounds. We study the obtained
bounds in different scenarios and compare them with previous results.Comment: arXiv admin note: substantial text overlap with arXiv:2201.08738,
arXiv:2212.1247
Multi-User Privacy Mechanism Design with Non-zero Leakage
A privacy mechanism design problem is studied through the lens of information
theory. In this work, an agent observes useful data that is
correlated with private data which is assumed to be also
accessible by the agent. Here, we consider users where user demands a
sub-vector of , denoted by . The agent wishes to disclose to
user . Since is correlated with it can not be disclosed
directly. A privacy mechanism is designed to generate disclosed data which
maximizes a linear combinations of the users utilities while satisfying a
bounded privacy constraint in terms of mutual information. In a similar work it
has been assumed that is a deterministic function of , however in
this work we let and be arbitrarily correlated. First, an upper
bound on the privacy-utility trade-off is obtained by using a specific
transformation, Functional Representation Lemma and Strong Functional
Representaion Lemma, then we show that the upper bound can be decomposed into
parallel problems. Next, lower bounds on privacy-utility trade-off are
derived using Functional Representation Lemma and Strong Functional
Representaion Lemma. The upper bound is tight within a constant and the lower
bounds assert that the disclosed data is independent of all
except one which we allocate the maximum allowed leakage to it. Finally, the
obtained bounds are studied in special cases.Comment: arXiv admin note: text overlap with arXiv:2205.04881,
arXiv:2201.0873
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