This paper investigates the asymptotics of the maximal throughput of communication over AWGN channels by $n$ channel uses under a covert constraint in terms of an upper bound $\delta$ of Kullback-Leibler divergence (KL divergence). It is shown that the first and second order asymptotics of the maximal throughput are $\sqrt{n\delta \log e}$ and $(2)^{1/2}(n\delta)^{1/4}(\log e)^{3/4}\cdot Q^{-1}(\epsilon)$, respectively. The technique we use in the achievability is quasi-$\varepsilon$-neighborhood notion from information geometry. We prove that if the generating distribution of the codebook is close to Dirac measure in the weak sense, then the corresponding output distribution at the adversary satisfies covert constraint in terms of most common divergences. This helps link the local differential geometry of the distribution of noise with covert constraint. For the converse, the optimality of Gaussian distribution for minimizing KL divergence under second order moment constraint is extended from dimension $1$ to dimension $n$. It helps to establish the upper bound on the average power of the code to satisfy the covert constraint, which further leads to the direct converse bound in terms of covert metric.
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Machine learning (ML) models are overparameterized to support generality and avoid overfitting. Prior works have shown that these additional parameters can be used for both malicious (e.g., hiding a model covertly within a trained model) and beneficial purposes (e.g., watermarking a model). In this paper, we propose a novel information theoretic perspective of the problem; we consider the ML model as a storage channel with a capacity that increases with overparameterization. Specifically, we consider a sender that embeds arbitrary information in the model at training time, which can be extracted by a receiver with a black-box access to the deployed model. We derive an upper bound on the capacity of the channel based on the number of available parameters. We then explore black-box write and read primitives that allow the attacker to: (i) store data in an optimized way within the model by augmenting the training data at the transmitter side, and (ii) to read it by querying the model after it is deployed. We also analyze the detectability of the writing primitive and consider a new version of the problem which takes information storage covertness into account. Specifically, to obtain storage covertness, we introduce a new constraint such that the data augmentation used for the write primitives minimizes the distribution shift with the initial (baseline task) distribution. This constraint introduces a level of "interference" with the initial task, thereby limiting the channel's effective capacity. Therefore, we develop optimizations to improve the capacity in this case, including a novel ML-specific substitution based error correction protocol. We believe that the proposed modeling of the problem offers new tools to better understand and mitigate potential vulnerabilities of ML, especially in the context of increasingly large models.
Virtual reality (VR) telepresence applications and the so-called "metaverse" promise to be the next major medium of interaction with the internet. However, with numerous recent studies showing the ease at which VR users can be profiled, deanonymized, and data harvested, metaverse platforms carry all the privacy risks of the current internet and more while at present having none of the defensive privacy tools we are accustomed to using on the web. To remedy this, we present the first known method of implementing an "incognito mode" for VR. Our technique leverages local differential privacy to quantifiably obscure sensitive user data attributes, with a focus on intelligently adding noise when and where it is needed most to maximize privacy while minimizing usability impact. Moreover, our system is capable of flexibly adapting to the unique needs of each metaverse application to further optimize this trade-off. We implement our solution as a universal Unity (C#) plugin that we then evaluate using several popular VR applications. Upon faithfully replicating the most well-known VR privacy attack studies, we show a significant degradation of attacker capabilities when using our proposed solution.
We consider hypergraph network design problems where the goal is to construct a hypergraph satisfying certain properties. In graph network design problems, the number of edges in an arbitrary solution is at most the square of the number of vertices. In contrast, in hypergraph network design problems, the number of hyperedges in an arbitrary solution could be exponential in the number of vertices and hence, additional care is necessary to design polynomial-time algorithms. The central theme of this work is to show that certain hypergraph network design problems admit solutions with polynomial number of hyperedges and moreover, can be solved in strongly polynomial time. Our work improves on the previous fastest pseudo-polynomial run-time for these problems. In addition, we develop algorithms that return (near-)uniform hypergraphs as solutions. The hypergraph network design problems that we focus upon are splitting-off operation in hypergraphs, connectivity augmentation using hyperedges, and covering skew-supermodular functions using hyperedges. Our definition of the splitting-off operation in hypergraphs and our proof showing the existence of the operation using a strongly polynomial-time algorithm to compute it are likely to be of independent graph-theoretical interest.
Hiding the wireless communication by transmitter Alice to intended receiver Bob from a capable and attentive adversary Willie has been widely studied under the moniker "covert communications". However, when such covert communication is done in the presence of allowable system communications, there has been little study of both hiding the signal and preserving the performance of those allowable communications. Here, by treating Alice, Bob, and Willie as a generator, decoder, and discriminator neural network, we perform joint training in an adversarial setting to yield a covert communication scheme that can be added to any normal autoencoder. The method does not depend on the characteristics of the cover signal or the type of channel and it is developed for both single-user and multi-user systems. Numerical results indicate that we are able to establish a reliable undetectable channel between Alice and Bob, regardless of the cover signal or type of fading, and that the signal causes almost no disturbance to the ongoing normal operation of the system.
This paper investigates the utilization of simultaneously transmitting and reflecting RIS (STAR-RIS) in supporting joint physical layer security (PLS) and covert communications (CCs) in a multi-antenna millimeter wave (mmWave) system, where the base station (BS) communicates with both covert and security users while defeating eavesdropping by wardens with the help of a STAR-RIS. Specifically, analytical derivations are performed to obtain the closed-form expression of warden's minimum detection error probability (DEP). Furthermore, the asymptotic result of the minimum DEP and the lower bound of the secure rates are derived, considering the practical assumption that BS only knows the statistical channel state information (CSI) between STAR-RIS and the wardens. Subsequently, an optimization problem is formulated with the aim of maximizing the average sum of the covert rate and the minimum secure rate while ensuring the covert requirement and quality of service (QoS) for legal users by jointly optimizing the active and passive beamformers. Due to the strong coupling among variables, an iterative algorithm based on the alternating strategy and the semi-definite relaxation (SDR) method is proposed to solve the non-convex optimization problem. Simulation results indicate that the performance of the proposed STAR-RIS-assisted scheme greatly surpasses that of the conventional RIS scheme, which validates the superiority of STAR-RIS in simultaneously implementing PLS and CCs.
Multiple-input multiple-output (MIMO) has become a key technology for contemporary wireless communication systems. For typical MIMO systems, antenna arrays are separated by half of the signal wavelength, which are termed collocated arrays. In this paper, we ask the following question: For future wireless communication systems, is it possible to achieve better performance than collocated arrays by using sparse arrays, whose element spacing is larger than half wavelength? The answer to this question is not immediately clear since while sparse arrays may achieve narrower beam for the main lobe, they also generate undesired grating lobes. In this paper, we show that the answer to the above question is affirmative. To this end, we first provide an insightful explanation by investigating the key properties of beam patterns of sparse and collocated arrays, together with the typical distribution of spatial angle difference \Delta, which all critically impact the inter-user interference (IUI). In particular, we show that sparse arrays are less likely to experience severe IUI than collocated arrays, since the probability of \Delta typically reduces with the increasing of |\Delta|. This naturally helps to reject those higher-order grating lobes of sparse arrays, especially when users are densely located. Then we provide a rigorous derivation of the achievable data rate for sparse and collocated arrays, and derive the condition under which sparse arrays strictly outperform collocated counterparts. Finally, numerical results are provided to validate our theoretical studies.
Given a composite null $\mathcal P$ and composite alternative $\mathcal Q$, when and how can we construct a p-value whose distribution is exactly uniform under the null, and stochastically smaller than uniform under the alternative? Similarly, when and how can we construct an e-value whose expectation exactly equals one under the null, but its expected logarithm under the alternative is positive? We answer these basic questions, and other related ones, when $\mathcal P$ and $\mathcal Q$ are convex polytopes (in the space of probability measures). We prove that such constructions are possible if and only if $\mathcal Q$ does not intersect the span of $\mathcal P$. If the p-value is allowed to be stochastically larger than uniform under $P\in\mathcal P$, and the e-value can have expectation at most one under $P\in\mathcal P$, then it is achievable whenever $\mathcal P$ and $\mathcal Q$ are disjoint. More generally, even when $\mathcal P$ and $\mathcal Q$ are not polytopes, we characterize the existence of a bounded nontrivial e-variable whose expectation exactly equals one under any $P \in \mathcal P$. The proofs utilize recently developed techniques in simultaneous optimal transport. A key role is played by coarsening the filtration: sometimes, no such p-value or e-value exists in the richest data filtration, but it does exist in some reduced filtration, and our work provides the first general characterization of this phenomenon. We also provide an iterative construction that explicitly constructs such processes, and under certain conditions it finds the one that grows fastest under a specific alternative $Q$. We discuss implications for the construction of composite nonnegative (super)martingales, and end with some conjectures and open problems.
The partial information decomposition (PID) framework is concerned with decomposing the information that a set of random variables has with respect to a target variable into three types of components: redundant, synergistic, and unique. Classical information theory alone does not provide a unique way to decompose information in this manner and additional assumptions have to be made. Recently, Kolchinsky proposed a new general axiomatic approach to obtain measures of redundant information, based on choosing an order relation between information sources (equivalently, order between communication channels). In this paper, we exploit this approach to introduce three new measures of redundant information (and the resulting decompositions) based on well-known preorders between channels, thus contributing to the enrichment of the PID landscape. We relate the new decompositions to existing ones, study some of their properties, and provide examples illustrating their novelty. As a side result, we prove that any preorder that satisfies Kolchinsky's axioms yields a decomposition that meets the axioms originally introduced by Williams and Beer when they first propose the PID.
Future wireless networks, in particular, 5G and beyond, are anticipated to deploy dense Low Earth Orbit (LEO) satellites to provide global coverage and broadband connectivity with reliable data services. However, new challenges for interference management have to be tackled due to the large scale of dense LEO satellite networks. Rate-Splitting Multiple Access (RSMA), widely studied in terrestrial communication systems and Geostationary Orbit (GEO) satellite networks, has emerged as a novel, general, and powerful framework for interference management and multiple access strategies for future wireless networks. In this paper, we propose a multilayer interference management scheme for spectrum sharing in heterogeneous GEO and LEO satellite networks, where RSMA is implemented distributedly at GEO and LEO satellites, namely Distributed-RSMA (D-RSMA), to mitigate the interference and boost the user fairness of the system. We study the problem of jointly optimizing the GEO/LEO precoders and message splits to maximize the minimum rate among User Terminals (UTs) subject to a transmit power constraint at all satellites. A Semi-Definite Programming (SDP)-based algorithm is proposed to solve the original non-convex optimization problem. Numerical results demonstrate the effectiveness and network load robustness of our proposed D-RSMA scheme for multilayer satellite networks. Because of the data sharing and the interference management capability, D-RSMA provides significant max-min fairness performance gains when compared to several benchmark schemes.
Next-generation wireless networks strive for higher communication rates, ultra-low latency, seamless connectivity, and high-resolution sensing capabilities. To meet these demands, terahertz (THz)-band signal processing is envisioned as a key technology offering wide bandwidth and sub-millimeter wavelength. Furthermore, THz integrated sensing and communications (ISAC) paradigm has emerged jointly access spectrum and reduced hardware costs through a unified platform. To address the challenges in THz propagation, THz-ISAC systems employ extremely large antenna arrays to improve the beamforming gain for communications with high data rates and sensing with high resolution. However, the cost and power consumption of implementing fully digital beamformers are prohibitive. While hybrid analog/digital beamforming can be a potential solution, the use of subcarrier-independent analog beamformers leads to the beam-squint phenomenon where different subcarriers observe distinct directions because of adopting the same analog beamformer across all subcarriers. In this paper, we develop a sparse array architecture for THz-ISAC with hybrid beamforming to provide a cost-effective solution. We analyze the antenna selection problem under beam-squint influence and introduce a manifold optimization approach for hybrid beamforming design. To reduce computational and memory costs, we propose novel algorithms leveraging grouped subarrays, quantized performance metrics, and sequential optimization. These approaches yield a significant reduction in the number of possible subarray configurations, which enables us to devise a neural network with classification model to accurately perform antenna selection.
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