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This paper studies the rate-distortion-perception (RDP) tradeoff for a Gaussian vector source coding problem where the goal is to compress the multi-component source subject to distortion and perception constraints. Specifically, the RDP setting with either the Kullback-Leibler (KL) divergence or Wasserstein-2 metric as the perception loss function is examined, and it is shown that for Gaussian vector sources, jointly Gaussian reconstructions are optimal. We further demonstrate that the optimal tradeoff can be expressed as an optimization problem, which can be explicitly solved. An interesting property of the optimal solution is as follows. Without the perception constraint, the traditional reverse water-filling solution for characterizing the rate-distortion (RD) tradeoff of a Gaussian vector source states that the optimal rate allocated to each component depends on a constant, called the water level. If the variance of a specific component is below the water level, it is assigned a zero compression rate. However, with active distortion and perception constraints, we show that the optimal rates allocated to the different components are always positive. Moreover, the water levels that determine the optimal rate allocation for different components are unequal. We further treat the special case of perceptually perfect reconstruction and study its RDP function in the high-distortion and low-distortion regimes to obtain insight to the structure of the optimal solution.

In the problem of quickest change detection, a change occurs at some unknown time in the distribution of a sequence of random vectors that are monitored in real time, and the goal is to detect this change as quickly as possible subject to a certain false alarm constraint. In this work we consider this problem in the presence of parametric uncertainty in the post-change regime and controlled sensing. That is, the post-change distribution contains an unknown parameter, and the distribution of each observation, before and after the change, is affected by a control action. In this context, in addition to a stopping rule that determines the time at which it is declared that the change has occurred, one also needs to determine a sequential control policy, which chooses the control action at each time based on the already collected observations. We formulate this problem mathematically using Lorden’s minimax criterion, and assuming that there are finitely many possible actions and post-change parameter values. We then propose a specific procedure for this problem that employs an adaptive CuSum statistic in which (i) the estimate of the parameter is based on a fixed number of the more recent observations, and (ii) each action is selected to maximize the Kullback-Leibler divergence of the next observation based on the current parameter estimate, apart from a small number of exploration times. We show that this procedure, which we call the Windowed Chernoff-CuSum (WCC), is first-order asymptotically optimal under Lorden’s minimax criterion, for every possible value of the unknown post-change parameter, as the mean time to false alarm goes to infinity. We also provide simulation results to illustrate the performance of the WCC procedure.

We study the problem of group testing with non-identical, independent priors. So far, the pooling strategies that have been proposed in the literature take the following approach: a hand-crafted test design along with a decoding strategy is proposed, and guarantees are provided on how many tests are sufficient in order to identify all infections in a population. In this paper, we take a different, yet perhaps more practical, approach: we fix the decoder and the number of tests, and we ask, given these, what is the best test design one could use? We explore this question for the Definite Non-Defectives (DND) decoder. We formulate a (non-convex) optimization problem, where the objective function is the expected number of errors for a particular design. We find approximate solutions via gradient descent, which we further optimize with informed initialization. We illustrate through simulations that our method can achieve significant performance improvement over traditional approaches.

We consider lossy compression of an information source when the decoder has lossless access to a correlated one. This setup, also known as the Wyner-Ziv problem, is a special case of distributed source coding. To this day, practical approaches for the Wyner-Ziv problem have neither been fully developed nor heavily investigated. We propose a data-driven method based on machine learning that leverages the universal function approximation capability of artificial neural networks. We find that our neural network-based compression scheme, based on variational vector quantization, recovers some principles of the optimum theoretical solution of the Wyner-Ziv setup, such as binning in the source space as well as optimal combination of the quantization index and side information, for exemplary sources. These behaviors emerge although no structure exploiting knowledge of the source distributions was imposed. Binning is a widely used tool in information theoretic proofs and methods, and to our knowledge, this is the first time it has been explicitly observed to emerge from data-driven learning.

In this paper, we study the computation of the rate-distortion-perception function (RDPF) for a multivariate Gaussian source assuming jointly Gaussian reconstruction under mean squared error (MSE) distortion and, respectively, Kullback–Leibler divergence, geometric Jensen-Shannon divergence, squared Hellinger distance, and squared Wasserstein-2 distance perception metrics. To this end, we first characterize the analytical bounds of the scalar Gaussian RDPF for the aforementioned divergence functions, also providing the RDPF-achieving forward “test-channel” realization. Focusing on the multivariate case, assuming jointly Gaussian reconstruction and tensorizable distortion and perception metrics, we establish that the optimal solution resides on the vector space spanned by the eigenvector of the source covariance matrix. Consequently, the multivariate optimization problem can be expressed as a function of the scalar Gaussian RDPFs of the source marginals, constrained by global distortion and perception levels. Leveraging this characterization, we design an alternating minimization scheme based on the block nonlinear Gauss–Seidel method, which optimally solves the problem while identifying the Gaussian RDPF-achieving realization. Furthermore, the associated algorithmic embodiment is provided, as well as the convergence and the rate of convergence characterization. Lastly, for the “perfect realism” regime, the analytical solution for the multivariate Gaussian RDPF is obtained. We corroborate our results with numerical simulations and draw connections to existing results.

In the popular federated learning scenarios, distributed nodes often represent and exch