109 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
Private Variable-Length Coding with Non-zero Leakage
A private compression design problem is studied, where an encoder observes
useful data , wishes to compress it using variable length code and
communicates it through an unsecured channel. Since is correlated with
private data , the encoder uses a private compression mechanism to design
encoded message and sends it over the channel. An adversary is assumed
to have access to the output of the encoder, i.e., , and tries to
estimate . Furthermore, it is assumed that both encoder and decoder have
access to a shared secret key . In this work, we generalize the perfect
privacy (secrecy) assumption and consider a non-zero leakage between the
private data and encoded message . The design goal is to encode
message with minimum possible average length that satisfies
non-perfect privacy constraints. We find upper and lower bounds on the average
length of the encoded message using different privacy metrics and study them in
special cases. For the achievability we use two-part construction coding and
extended versions of Functional Representation Lemma. Lastly, in an example we
show that the bounds can be asymptotically tight.Comment: arXiv admin note: text overlap with arXiv:2306.1318
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
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