We consider the joint optimization of sensor placement and transmission structure for data gathering, where a given number of nodes need to be placed in a field such that the sensed data can be reconstructed at a sink within specified distortion bounds while minimizing the energy consumed for communication. We assume that the nodes use either joint entropy coding based on explicit communication...

We deal with centralized and distributed rate-constrained estimation of random signal vectors using a network of wireless sensors communicating with a fusion center. Specifically, we determine lower and upper bounds for the Distortion-Rate (D-R) function. The lower bound is obtained by considering centralized estimation with a single-sensor setup, for which we determine the D-R function in clos...

We introduce a quantitative version of Property A in order to estimate the Lp-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to be useful to yield upper bounds on the Lpdistortion of finite metric spaces. Namely, we obtain new optimal results for finite subsets of homogeneous Riemanni...

The problem of data privacy is to verify that confidential information stored in an information system is not provided to unauthorized users and, therefore, personal and other sensitive data remain private. One way to guarantee this is to distort a knowledge base such that it does not reveal sensitive information. In the present paper we will give a definition of the problem of knowledge base d...

Given a space Y in X, a cycle in Y may be filled with a chain in two ways: either by restricting the chain to Y or by allowing it to be anywhere in X. When the pair (G, H) acts on (X, Y ), we define the k–volume distortion function of H in G to measure the large-scale difference between the volumes of such fillings. We show that these functions are quasi-isometry invariants, and thus independen...

The characterization of the set of achievable rate and distortion values for scalable source coding is extended to additionally account for error exponents, namely, the negative normalized asymptotic log likelihood of error events at different layers. The “error” at each layer is defined as the event that the source block is not reproduced within the prespecified fidelity at the corresponding d...

Motivated by many practical scenarios, in this paper we study fundamental limits to performance of sensor networks for a class of linear sensing models under a fixed SNR regime. Under a linear observation model the information about a signal X ∈ Rn is acquired as projections onto a set of m vectors. We extend this set-up in several ways to address problems of detection, classification and estim...

A new class of lower bounds to rate-distortion functions ofstationary processes with memory and single-letter vector-valued distor-tion measures is derived. This class is shown to include or imply all otherwell-known lower bounds to rates of such sources and distortion measures.The derivation is based on the definition and properties of the conditionalratedistortion function...