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

Stabilization of Linear Systems Over Gaussian Networks

The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes operate subject to an average transmit power constraint and they can cooperate to communicate the observations of the plant's state to the remote controller. The communication links between all nodes are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The sufficient conditions are in general obtained using delay-free linear policies and the necessary conditions are obtained using information theoretic tools. Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have been identified. For the case with noisy multi-dimensional sources controlled over scalar channels, it is shown that linear time varying policies lead to minimum capacity requirements, meeting the fundamental lower bound. For the case with noiseless sources and parallel channels, non-linear policies which meet the lower bound have been identified

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 $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A statistical privacy mechanism is employed to generate data $U$ based on $(X,Y)$ that maximizes the revealed information about $Y$ 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