Universal Sampling Rate Distortion

We examine the coordinated and universal rate-efficient sampling of a subset of correlated discrete memoryless sources followed by lossy compression of the sampled sources. The goal is to reconstruct a predesignated subset of sources within a specified level of distortion. The combined sampling mechanism and rate distortion code are universal in that they are devised to perform robustly without exact knowledge of the underlying joint probability distribution of the sources. In Bayesian as well as nonBayesian settings, single-letter characterizations are provided for the universal sampling rate distortion function for fixed-set sampling, independent random sampling and memoryless random sampling. It is illustrated how these sampling mechanisms are successively better. Our achievability proofs bring forth new schemes for joint source distribution-learning and lossy compression

Information Rates of Densely Sampled Gaussian Data

With mean-squared error D as a goal, it is well known that one may approach the rate-distortion function R(D) of a nonbandlimited, continuous-time Gaussian source by sampling at a sufficiently high rate, applying the Karhunen-Loeve transform to sufficiently long blocks, and then independently coding the transform coefficients of each type. Motivated by the question of the efficiency of dense sensor networks for sampling, encoding and reconstructing spatial random fields, this paper studies the following three cases. In the first, we consider a centralized encoding setup with a sample-transform-quantize scheme where the quantization is assumed to be optimal. In the second, we consider a distributed setup, where a spatio-temporal source is sampled and distributively encoded to be reconstructed at a receiver. We show that with ideal distributed lossy coding, dense sensor networks can efficiently sense and convey a field, in contrast to the negative result obtained by Marco et al. for encoders based on time- and space-invariant scalar quantization and ideal Slepian-Wolf distributed lossless coding. In the third, we consider a centralized setup, with a sample-and-transform coding scheme in which ideal coding of coefficients is replaced by coding with some specified family of quantizers. It is shown that when the sampling rate is large, the operational rate-distortion function of such a scheme comes within a finite constant of that of the first case