This paper presents a perfectly secure matrix multiplication (PSMM) protocol for multiparty computation (MPC) of $\mathrm{A}^{\top}\mathrm{B}$ over finite fields. The proposed scheme guarantees correctness and information-theoretic privacy against threshold-bounded, semi-honest colluding agents, under explicit local storage constraints. Our scheme encodes submatrices as evaluations of sparse masking polynomials and combines coefficient alignment with Beaver-style randomness to ensure perfect secrecy. We demonstrate that any colluding set of parties below the security threshold observes uniformly random shares, and that the recovery threshold is optimal, matching existing information-theoretic limits. Building on this framework, we introduce a learning-augmented extension that integrates tensor-decomposition-based local block multiplication, capturing both classical and learned low-rank methods. We demonstrate that the proposed learning-based PSMM preserves privacy and recovery guarantees for MPC, while providing scalable computational efficiency gains (up to $80\%$) as the matrix dimensions grow.

In this work, we investigate low-complexity remote system state estimation over wireless multiple-input-multipleoutput (MIMO) channels without requiring prior knowledge of channel state information (CSI). We start by reviewing the conventional Kalman filtering-based state estimation algorithm, which typically relies on perfect CSI and incurs considerable computational complexity. To overcome the need for CSI, we introduce a novel semantic aggregation method, in which sensors transmit semantic measurement discrepancies to the remote state estimator through analog aggregation. To further reduce computational complexity, we introduce a constant-gain-based filtering algorithm that can be optimized offline using the constrained stochastic successive convex approximation (CSSCA) method. We derive a closed-form sufficient condition for the estimation stability of our proposed scheme via Lyapunov drift analysis. Numerical results showcase significant performance gains using the proposed scheme compared to several widely used methods.

We introduce a resource allocation framework for goal-oriented semantic networks, where participating agents assess system quality through subjective (e.g., context-dependent) perceptions. To accommodate this, our model accounts for agents whose preferences deviate from traditional expected utility theory (EUT), specifically incorporating cumulative prospect theory (CPT) preferences. We develop a comprehensive analytical framework that captures human-centric aspects of decision-making and risky choices under uncertainty, such as risk perception, loss aversion, and perceptual distortions in probability metrics. By identifying essential modifications in traditional resource allocation design principles required for agents with CPT preferences, we showcase the framework's relevance through its application to the problem of power allocation in multi-channel wireless communication systems.

Federated learning (FL) is a widely used and impactful distributed optimization framework that achieves consensus by averaging locally trained models. While effective, this approach may not align well with Bayesian inference, where the model space is more naturally represented as a distribution space. Taking an information-geometric perspective, we reinterpret FL aggregation as the problem of finding the barycenter of local posteriors using a predefined divergence metric, minimizing the average discrepancy across clients. This perspective provides a unifying framework that generalizes many existing methods and offers crisp insights into their theoretical underpinnings. We then propose BA-BFL, an algorithm that retains the convergence properties of Federated Averaging in non-convex settings. In non-independent and identically distributed scenarios, we conduct extensive comparisons with statistical aggregation techniques, showing that BA-BFL achieves performance comparable to state-of-the-art methods while also providing a geometric interpretation of the aggregation phase. Additionally, we extend our analysis to Hybrid Bayesian Deep Learning, exploring the impact of Bayesian layers on uncertainty quantification and model calibration.

In this paper, we investigate the rate-distortion-perception function (RDPF) of a source modeled as a Gaussian Process (GP) over a measure space$\Omega$, under mean squared error (MSE) distortion and squared Wasserstein-2 perception metrics. First, we show that the optimal reconstruction process is itself a GP, whose covariance operator shares the same set of eigenvectors as the source's covariance operator. This structural property, akin to the classical rate-distortion function (RDF), allows us to reformulate the RDPF problem in terms of the Karhunen-Loève (KL) transform coefficients of the involved GPs. Leveraging the similarities with the finite-dimensional Gaussian RDPF, we derive a tight analytical upper bound on the RDPF for GPs, which recovers the optimal solution in the “perfect realism” regime. Finally, for stationary GPs over the interval$[0, T]$with Lebesgue measure, we derive an upper bound on the rate and distortion for a fixed perceptual level and$T \rightarrow \infty$as a function of the spectral density of the source process. We complement our theoretical findings with relevant simulation studies.

In this paper, we investigate the problem of distributionally robust source coding, i.e., source coding under uncertainty in the source distribution, discussing both the coding and computational aspects of the problem. We propose two extensions of the so-called Strong Functional Representation Lemma (SFRL), considering the cases where, for a fixed conditional distribution, the marginal inducing the joint coupling belongs to either a finite set of distributions or a Kullback-Leibler divergence sphere (KL-Sphere) centered at a fixed nominal distribution. Using these extensions, we derive distributionally robust coding schemes for both the one-shot and asymptotic regimes, generalizing previous results in the literature. Focusing on the case where the source distribution belongs to a given KL-Sphere, we derive an implicit characterization of the points attaining the robust rate-distortion function (R-RDF), which we later exploit to implement a novel algorithm for computing the R-RDF. Finally, we characterize the analytical expression of the R-RDF for Bernoulli sources, providing a theoretical benchmark to evaluate the estimation performance of the proposed algorithm.

We study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint belonging to the family off-divergences. In this setting, the RDPF forms a convex programming problem for which we characterize optimal parametric solutions. We employ the developed solutions in an alternating minimization scheme, namely Optimal Alternating Minimization (OAM), for which we provide convergence guarantees. Nevertheless, the OAM scheme does not lead to a direct implementation of a generalized Blahut-Arimoto (BA) type of algorithm due to implicit equations in the iteration’s structure. To overcome this difficulty, we propose two alternative minimization approaches whose applicability depends on the smoothness of the used perception metric: a Newton-based Alternating Minimization (NAM) scheme, relying on Newton’s root-finding method for the approximation of the optimal solution of the iteration, and a Relaxed Alternating Minimization (RAM) scheme, based on relaxing the OAM iterates. We show, by deriving necessary and sufficient conditions, that both schemes guarantee convergence to a globally optimal solution. We also provide sufficient conditions on the distortion and perception constraints, which guarantee that the proposed algorithms converge exponentially fast in the number of iteration steps. We corroborate our theoretical results with numerical simulations and establish connections with existing results.

In this paper, we propose a generic method for computing the rate-distortion-perception function (RDPF) of a multivariate Gaussian source under tensorizable distortion and perception metrics. Through the assumption of a jointly Gaussian reconstruction, we establish that the optimal solution of the RDPF belongs to 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. Utilizing this result, we devise an alternating minimization scheme based on the block nonlinear Gauss-Seidel method. This scheme solves optimally the optimization problem while identifying the optimal stage-wise distortion and perception levels. Furthermore, the associated algorithmic embodiment is provided, along with the convergence and the rate of convergence characterization. Lastly, in the regime of “perfect realism”, we provide the analytical solution for the multivariate Gaussian RDPF. We corroborate our findings with numerical simulations and draw connections to existing results.

We present a new method to estimate the rate-distortion-perception function in the perfect realism regime (PR-RDPF), for multivariate continuous sources subject to a single-letter average distortion constraint. The proposed approach is not only able to solve the specific problem but also two related problems: the entropic optimal transport (EOT) and the output-constrained rate-distortion function (OC-RDF), of which the PR-RDPF represents a special case. Using copula distributions, we show that the OC-RDF can be cast as an$I$-projection problem on a convex set, based on which we develop a parametric solution of the optimal projection proving that its parameters can be estimated, up to an arbitrary precision, via the solution of a convex program. Subsequently, we propose an iterative scheme via gradient methods to estimate the convex program. Lastly, we characterize a Shannon lower bound (SLB) for the PR-RDPF under a mean squared error (MSE) distortion constraint. We support our theoretical findings with numerical examples by assessing the estimation performance of our iterative scheme using the PR-RDPF with the obtained SLB for various sources.

In this paper, we study the computation of the rate-distortion-perception function (RDPF) for discrete memoryless sources subject to a single-letter average distortion constraint and a perception constraint that belongs to the family of f-divergences. For that, we leverage the fact that RDPF, assuming mild regularity conditions on the perception constraint, forms a convex programming problem. We first develop parametric characterizations of the optimal solution and utilize them in an alternating minimization approach for which we prove convergence guarantees. The resulting structure of the iterations of the alternating minimization approach renders the implementation of a generalized Blahut-Arimoto (BA) type of algorithm infeasible. To overcome this difficulty, we propose a relaxed formulation of the structure of the iterations in the alternating minimization approach, which allows for the implementation of an approximate iterative scheme. This approximation is shown, via the derivation of necessary and sufficient conditions, to guarantee convergence to a globally optimal solution. We also provide sufficient conditions on the distortion and the perception constraints which guarantee that our algorithm converges exponentially fast. We corroborate our theoretical results with numerical simulations, and we draw connections with existing results.

We consider a remote source coding problem subject to a distortion function. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, f-separable distortion measure and study its implications on the characterization of the minimum achievable rates (also called f-separable indirect rate distortion function (iRDF)) under both excess and average distortion constraints. First, we provide a single-letter characterization of the optimal rates subject to an excess distortion using properties of the f-separable distortion. Our main result is a single-letter characterization of the f-separable iRDF subject to an average distortion constraint. As a consequence of the previous results, we also show a series of equalities that hold using either indirect or classical RDF under f-separable excess or average distortions. We corroborate our results with two application examples in which new closed-form solutions are derived, and based on these, we also recover known special cases.

A new variation of the classical point-to-point joint source-channel coding (JSCC) is studied here, which is relevant for identifying goal-oriented semantic aspects of a transmitted source message over a noisy channel in the presence of multiple distortion constraints. For this new formulation, coined goal-oriented JSCC, we first introduce optimality criteria followed by necessary and sufficient conditions for global optimality. The focus of our main theoretical results is on investigating the implications of a special subclass of block codes, namely, the single-letter codes, via a theorem in which we provide necessary and sufficient conditions for the probabilistic matching of a noisy source message with a noisy channel. We corroborate our theoretical results with two examples, in which goal-oriented single-letter codes and uncoded transmission perform optimally. Our results further highlight the important role of multiple fidelity constraints in goal-oriented communications.

We study a variant of a robust description source coding framework, which is a relevant model for goal-oriented semantic information transmission, via its corresponding characterization. Considering two individual single-letter separable distortion constraints and input and output data acting as the intrinsic and extrinsic message, respectively, we first derive a lower bound on the optimal rates of the problem, as well as necessary and sufficient conditions for this bound to be tight. Subsequently, we prove a general result that provides in parametric form the optimal solution of the characterization of this problem. Capitalizing on these results, we examine the structure of the solution for one case study of general binary alphabets under Hamming distortions and solve in closed form a special case. We also solve another general binary alphabet case where a Hamming and an erasure distortion coexist, as a means to highlight the importance of selecting the type of the distortion constraint in goal-oriented semantic communication. Furthermore, we develop a goal-oriented Blahut-Arimoto (BA) algorithm, which can be used for the computation of any finite alphabet intrinsic or extrinsic message under individual distortion criteria. Finally, we revisit the problem for multidimensional independent and identically distributed ($\mathop {\mathrm {i.i.d.}}$) jointly Gaussian processes with individual mean-square error (MSE) distortion constraints, providing new insights that have previously been overlooked. This work reveals the cardinal role of context-dependent fidelity criteria in goal-oriented semantic communication.

A variant of a robust description source coding framework motivated by goal-oriented semantic information transmission is studied here. Considering two individual distortion constraints and input and output data that takes values in finite sets, we prove new bounds and structural properties for these bounds to be tight with respect to the information theoretic characterization of the problem. Then, we derive a general result that provides in parametric form the various cases of optimal solutions of this problem. Capitalizing on these results, we examine the structure of the solution for one case study of general binary alphabets under Hamming distortions and solve in closed form a special case. We also solve another general binary alphabet case where Hamming and erasure distortion are used, as a means to highlight the importance of selecting the type of the distortion constraint in the problem.

Power consumption is a major challenge for a massive deployment of wireless sensors in Internet of Things (IoT) networks. This article studies the use of analog joint source-channel coding (AJSCC) mappings in low-power sensing schemes. In particular, we propose a noveltriangularmapping geometry as a low-complexity dimension reduction mapping. The proposed triangular mapping is employed for analog compression of multiple sensor readings into one signal and, thus, limits the need for power-hungry analog-to-digital conversion and processing at the sensing nodes. A comprehensive performance analysis of the proposed triangular mapping in terms of the mean squared error (MSE) performance is provided analytically and verified numerically. The problem of mapping adaptation to different source distributions is also studied. Moreover, the proposed triangular mapping is adopted in an energy scheduling problem in which the sensing nodes schedule their use of the received powers at different time instants and adjust the mapping parameters accordingly with the goal of minimizing the sum distortion at the receiver. We present a fast low-complexity algorithm for optimal energy scheduling and verify its performance in comparison with commercial convex optimization solvers. It is shown that the proposed mapping provides a very good MSE performance compared to the AJSCC benchmarks despite having a much lower complexity circuit implementation.

In this study, Nash and Stackelberg equilibria of single-stage and multi-stage quadratic signaling games between an encoder and a decoder are investigated. In the considered setup, the objective functions of the encoder and the decoder are misaligned, there is a noisy channel between the encoder and the decoder, the encoder has a soft power constraint, and the decoder has also noisy observation of the source to be estimated. We show that there exist only linear encoding and decoding strategies at the Stackelberg equilibrium, and derive the equilibrium strategies and costs. Regarding the Nash equilibrium, we explicitly characterize affine equilibria for the single-stage setup and show that the optimal encoder (resp. decoder) is affine for an affine decoder (resp. encoder) for the multi-stage setup. On the decoder side, between the information coming from the encoder and noisy observation of the source, our results describe what should be the combining ratio of these two channels. Regarding the encoder, we derive the conditions under which it is meaningful to transmit a message.

We develop a new formulation of nonanticipative rate distortion function (NRDF) to characterize and compute multidimensional partially observable Gauss-Markov processes with MSE distortion. The key result to obtain this new formulation is a “genie-aided” design of our decoder that encapsulates both its previous decoding symbols and the past observation symbols. The new formulation is applied to a system modeled by jointly Gaussian processes to obtain the following new results. (i) An optimal characterization of a new finite dimensional optimization problem and its corresponding optimal realization. Surprisingly, the information structure of the optimal realization reveals that the decoder is in fact independent of all the previous observations symbols. (ii) For time-invariant processes, we convexify our characterization under the assumption that all matrices commute by pairs and derive strong structural properties for the involved matrices for which our assumption is valid. (iii) We solve the convex program using KKT conditions to obtain a solution via a general reverse-waterfilling algorithm which demonstrates that the distortion allocation at each dimension can be computed by a third-degree polynomial equation.

We study the problem of rate-distortion equivocation with side-information only available at the decoder when an independent private random key is shared between the sender and the receiver. The sender compresses the sequence, and the receiver reconstructs it such that the average distortion between the source and the output is limited. The equivocation is measured at an eavesdropper that intercepts the source encoded message, utilizing side-information correlated with the source and the side-information at the decoder. We have derived the entire achievable rate-distortion-equivocation region for this problem.

We generalize the problem of controlling the interference created to an external observer while communicating over a discrete memoryless channel (DMC) which was studied in [1]. In particular, we consider the scenario where the transmission is established over a compound DMC channel with unknown state at both the encoder and the decoder. Depending on the exact state s of the channel, we ask for a different level of average precision Δson the establishment of the interference coordination with the external observer. For this setup, we fully characterize the capacity region.

In this paper, we study the connection between entropic optimal transport and entropy power inequality (EPI). First, we prove an HWI-type inequality making use of the infinitesimal displacement convexity of optimal transport map. Second, we derive two Talagrand-type inequalities using the saturation of EPI that corresponds to a numerical term in our expression. We evaluate for a wide variety of distributions this term whereas for Gaussian and i.i.d. Cauchy distributions this term is found in explicit form. We show that our results extend previous results of Gaussian Talagrand inequality for Sinkhorn distance to the strongly log-concave case.

We introduce the concept of achievable cumulative rate distribution functions (CRDF) to characterize sequentially encoding processes that ensure a lossless or lossy reconstruction subject to an average distortion using a non-causal decoder. Utilizing tools from majorization theory, we derive necessary and sufficient conditions on the CRDF for a given IID source. It turns out that the optimal achievable distortion level can be adequately characterized by the concave-hull of the CRDF.

We study the problem of empirical coordination subject to a fidelity criterion for a general set-up. We prove a result which indicates a strong connection between our frame-work and the framework of empirical coordination developed in [1]. It turns out that when we design codes that achieve empirical coordination according to a given distribution and subject to the fidelity criterion, it is sufficient to consider codes that produce actions of the same joint type for a class of types which is close enough to our desired distribution is some sense.

We consider a fixed-rate zero-delay source coding problem where a stationary vector-valued Gauss-Markov source is compressed subject to an average mean-squared error (MSE) distortion constraint. We address the problem by considering the Gaussian nonanticipative rate distortion function (NRDF) which is a lower bound to the zero-delay Gaussian RDF. Then, we use its corresponding optimal “test-channel” to characterize the stationary Gaussian NRDF and evaluate the corresponding information rates. We show that the Gaussian NRDF can be achieved by p-parallel fixed-rate scalar uniform quantizers of finite support with dithering signal up to a multiplicative distortion factor and a constant rate penalty. We demonstrate our framework with a numerical example.

We deal with zero-delay source coding of a vector Gaussian autoregressive (AR) source subject to an average mean squared error (MSE) fidelity criterion. Toward this end, we consider the nonanticipative rate distortion function (NRDF) which is a lower bound to the causal and zero-delay rate distortion function (RDF). We use the realization scheme with feedback proposed in [1] to model the corresponding optimal “test-channel” of the NRDF, when considering vector Gaussian AR(1) sources subject to an average MSE distortion. We give conditions on the vector Gaussian AR(1) source to ensure asymptotic stationarity of the realization scheme (bounded performance). Then, we encode the vector innovations due to Kalman filtering via lattice quantization with subtractive dither and memoryless entropy coding. This coding scheme provides a tight upper bound to the zero-delay Gaussian RDF. We extend this result to vector Gaussian AR sources of any finite order. Further, we show that for infinite dimensional vector Gaussian AR sources of any finite order, the NRDF coincides with the zero-delay RDF. Our theoretical framework is corroborated with a simulation example.

We derive sequential necessary and sufficient conditions for any channel input conditional distribution P0,n=Δ{PXt|Xt-1,Yt-1: t = 0, ..., n} to maximize the finite-time horizon directed information defined by CXn→YnFB =ΔsupP0,nI(Xn→ Yn), where I(Xn→ Yn) = Σt=0nI(Xt; Yt|Yt-1), for channel distributions {PYt|Yt-1,Xt: t = 0, ..., n} and {PYt|Yt-Mt-1,Xt: t = 0, ..., n}, where Yt =Δ{Y-1, Y0, ..., Yt} and Xt =Δ{X0, ..., Xt} are the channel input and output random processes, and M is a finite non-negative integer. We apply the necessary and sufficient conditions to application examples of time-varying channels with memory to derive recursive closed form expressions of the optimal distributions, which maximize the finite-time horizon directed information. Furthermore, we derive the feedback capacity from the asymptotic properties of the optimal distributions by investigating the limit CX∞→Y∞FB =Δlimn→∞(1/(n + 1))CXn→YnFBwithout any á priori assumptions, such as stationarity, ergodicity, or irreducibility of the channel distribution. The framework based on sequential necessary and sufficient conditions can be easily applied to a variety of channels with memory, beyond the ones considered in this paper.

We derive Sequential Necessary and Sufficient Conditions (SNSC) for any channel input distribution P0,n=̑{P((Xt)|Xt-1,Yt-1):t=0,1,...,n} to maximize directed information for channel distributions of the form {P(Yt|Yt-Mt-1,xt): t=0,1,...,n} where Xn=̑{X0...,Xn} , and Yn=̑{Y0,...,Yn} are the channel input and output random variables, and M is nonnegative and finite. The results are obtained using the information structures of the optimal channel input distributions and the corresponding Finite Transmission Feedback Information (FTFI) capacity, convexity properties of directed information, and dynamic programming recursions. The conditions are applied to a finite alphabet channel with M = 1 to derive recursive closed form expressions for the optimal (nonstationary) distributions, which achieve the FTFI capacity. Further, ergodic feedback capacity is obtained in closed form, using the asymptotic properties of the optimal distributions. A numerical example is presented to illustrate the convergence properties of the per unit time limiting version of the FTFI capacity.

Directed information or its variants are utilized extensively in the characterization of the capacity of channels with memory and feedback, nonanticipative lossy data compression, and their generalizations to networks. In this paper, we derive several functional and topological properties of directed information, defined on general abstract alphabets (complete separable metric spaces), using the topology of weak convergence of probability measures. These include the convexity of the set of consistent distributions, which uniquely define causally conditioned distributions, convexity, and concavity of directed information with respect to the sets of consistent distributions, weak compactness of such sets of distributions, their joint distributions, and their marginals. Furthermore, we show lower semicontinuity of directed information, and under certain conditions, we also establish continuity. Finally, we derive variational equalities for directed information, including sequential versions. These may be viewed as the analog of the variational equalities of mutual information (utilized in Blahut-Arimoto algorithms). In summary, we extend the basic functional and topological properties of mutual information to directed information. These properties are discussed throughout this paper, in the context of extremum problems of directed information.

The objective of this paper is to further investigate various applications of information Nonanticipative Rate Distortion Function (NRDF) by discussing two working examples, the Binary Symmetric Markov Source with parameter p (BSMS(p)) with Hamming distance distortion, and the multidimensional partially observed Gaussian-Markov source. For the BSMS(p), we give the solution to the NRDF, and we use it to compute the Rate Loss (RL) of causal codes with respect to noncausal codes. For the multidimensional Gaussian-Markov source, we give the solution to the NRDF, we show its operational meaning via joint source-channel matching over a vector of parallel Gaussian channels, and we compute the RL of causal and zero-delay codes with respect to noncausal codes.

In this paper we introduce two variational equalities of directed information, which are analogous to those of mutual information employed in the Blahut-Arimoto Algorithm (BAA). Subsequently, we introduce nonanticipative Rate Distortion Function (RDF) Ro, nna(D) defined via directed information introduced in, and we establish its equivalence to Gorbunov-Pinsker's nonanticipatory ε-entropy Ro, nε(D). By invoking certain results we first establish existence of the infimizing reproduction distribution for Ro, nna(D), and then we give its implicit form for the stationary case. Finally, we utilize one of the variational equalities and the closed form expression of the optimal reproduction distribution to provide an algorithm for the computation of Ro, nna(D).

This paper describes a framework in which directed information is defined on abstract spaces. The framework is employed to derive properties of directed information such as convexity, concavity, lower semicontinuity, by using the topology of weak convergence of probability measures on Polish spaces. Two extremum problems of directed information related to capacity of channels with memory and feedback, and non-anticipative and sequential rate distortion are analyzed showing existence of maximizing and minimizing distributions, respectively.