{"title":"$L$-systems and the Lovász number","authors":"William Linz","doi":"arxiv-2402.05818","DOIUrl":"https://doi.org/arxiv-2402.05818","url":null,"abstract":"Given integers $n > k > 0$, and a set of integers $L subset [0, k-1]$, an\u0000$L$-system is a family of sets $mathcal{F} subset binom{[n]}{k}$ such that\u0000$|F cap F'| in L$ for distinct $F, F'in mathcal{F}$. $L$-systems correspond\u0000to independent sets in a certain generalized Johnson graph $G(n, k, L)$, so\u0000that the maximum size of an $L$-system is equivalent to finding the\u0000independence number of the graph $G(n, k, L)$. The Lov'asz number\u0000$vartheta(G)$ is a semidefinite programming approximation of the independence\u0000number of a graph $G$. In this paper, we determine the order of magnitude of $vartheta(G(n, k, L))$\u0000of any generalized Johnson graph with $k$ and $L$ fixed and $nrightarrow\u0000infty$. As an application of this theorem, we give an explicit construction of\u0000a graph $G$ on $n$ vertices with large gap between the Lov'asz number and the\u0000Shannon capacity $c(G)$. Specifically, we prove that for any $epsilon > 0$,\u0000for infinitely many $n$ there is a generalized Johnson graph $G$ on $n$\u0000vertices which has ratio $vartheta(G)/c(G) = Omega(n^{1-epsilon})$, which\u0000greatly improves on the best known explicit construction.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Resources of the Quantum World","authors":"Gilad Gour","doi":"arxiv-2402.05474","DOIUrl":"https://doi.org/arxiv-2402.05474","url":null,"abstract":"This book delves into the burgeoning field of quantum resource theories, a\u0000novel and vibrant area of research within quantum information science that\u0000seeks to unify diverse quantum phenomena under a single framework. By\u0000recognizing various attributes of physical systems as \"resources,\" this\u0000approach offers a fresh perspective on quantum phenomena, transforming our\u0000understanding and application of concepts such as quantum entanglement,\u0000coherence, and more. With a focus on the pedagogical, the book aims to equip\u0000readers with the advanced mathematical tools and physical principles needed to\u0000navigate and contribute to this rapidly evolving field. It covers a wide range\u0000of topics, from the foundational aspects of quantum mechanics and quantum\u0000information to detailed explorations of specific resource theories, including\u0000entanglement, asymmetry, and thermodynamics. Through rigorous mathematical\u0000exposition and a unique axiomatic approach, the book provides deep insights\u0000into the operational and conceptual frameworks that underpin quantum resource\u0000theories, making it an invaluable resource for graduate students, early-career\u0000researchers, and anyone interested in the cutting-edge developments in quantum\u0000information science.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Improved upper bounds for wide-sense frameproof codes","authors":"Yuhao Zhao, Xiande Zhang","doi":"arxiv-2402.05596","DOIUrl":"https://doi.org/arxiv-2402.05596","url":null,"abstract":"Frameproof codes have been extensively studied for many years due to their\u0000application in copyright protection and their connection to extremal set\u0000theory. In this paper, we investigate upper bounds on the cardinality of\u0000wide-sense $t$-frameproof codes. For $t=2$, we apply results from Sperner\u0000theory to give a better upper bound, which significantly improves a recent\u0000bound by Zhou and Zhou. For $tgeq 3$, we provide a general upper bound by\u0000establishing a relation between wide-sense frameproof codes and cover-free\u0000families. Finally, when the code length $n$ is at most\u0000$frac{15+sqrt{33}}{24}(t-1)^2$, we show that a wide-sense $t$-frameproof code\u0000has at most $n$ codewords, and the unique optimal code consists of all\u0000weight-one codewords. As byproducts, our results improve several best known\u0000results on binary $t$-frameproof codes.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimized Denial-of-Service Threats on the Scalability of LT Coded Blockchains","authors":"Harikrishnan K., J. Harshan, Anwitaman Datta","doi":"arxiv-2402.05620","DOIUrl":"https://doi.org/arxiv-2402.05620","url":null,"abstract":"Coded blockchains have acquired prominence in the recent past as a promising\u0000approach to slash the storage costs as well as to facilitate scalability.\u0000Within this class, Luby Transform (LT) coded blockchains are an appealing\u0000choice for scalability in heterogeneous networks owing to the availability of a\u0000wide range of low-complexity LT decoders. While these architectures have been\u0000studied from the aspects of storage savings and scalability, not much is known\u0000in terms of their security vulnerabilities. Pointing at this research gap, in\u0000this work, we present novel denial-of-service (DoS) threats on LT coded\u0000blockchains that target nodes with specific decoding capabilities, thereby\u0000preventing them from joining the network. Our proposed threats are\u0000non-oblivious in nature, wherein adversaries gain access to the archived\u0000blocks, and choose to execute their threat on a subset of them based on\u0000underlying coding scheme. We show that our optimized threats can achieve the\u0000same level of damage as that of blind attacks, however, with limited amount of\u0000resources. This is the first work of its kind that opens up new questions on\u0000designing coded blockchains to jointly provide storage savings, scalability and\u0000resilience to optimized threats.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fixed width treelike neural networks capacity analysis -- generic activations","authors":"Mihailo Stojnic","doi":"arxiv-2402.05696","DOIUrl":"https://doi.org/arxiv-2402.05696","url":null,"abstract":"We consider the capacity of emph{treelike committee machines} (TCM) neural\u0000networks. Relying on Random Duality Theory (RDT), cite{Stojnictcmspnncaprdt23}\u0000recently introduced a generic framework for their capacity analysis. An upgrade\u0000based on the so-called emph{partially lifted} RDT (pl RDT) was then presented\u0000in cite{Stojnictcmspnncapliftedrdt23}. Both lines of work focused on the\u0000networks with the most typical, emph{sign}, activations. Here, on the other\u0000hand, we focus on networks with other, more general, types of activations and\u0000show that the frameworks of\u0000cite{Stojnictcmspnncaprdt23,Stojnictcmspnncapliftedrdt23} are sufficiently\u0000powerful to enable handling of such scenarios as well. In addition to the\u0000standard emph{linear} activations, we uncover that particularly convenient\u0000results can be obtained for two very commonly used activations, namely, the\u0000emph{quadratic} and emph{rectified linear unit (ReLU)} ones. In more concrete\u0000terms, for each of these activations, we obtain both the RDT and pl RDT based\u0000memory capacities upper bound characterization for emph{any} given (even)\u0000number of the hidden layer neurons, $d$. In the process, we also uncover the\u0000following two, rather remarkable, facts: 1) contrary to the common wisdom, both\u0000sets of results show that the bounding capacity decreases for large $d$ (the\u0000width of the hidden layer) while converging to a constant value; and 2) the\u0000maximum bounding capacity is achieved for the networks with precisely\u0000textbf{emph{two}} hidden layer neurons! Moreover, the large $d$ converging\u0000values are observed to be in excellent agrement with the statistical physics\u0000replica theory based predictions.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Localized and Distributed Beyond Diagonal Reconfigurable Intelligent Surfaces with Lossy Interconnections: Modeling and Optimization","authors":"Matteo Nerini, Golsa Ghiaasi, Bruno Clerckx","doi":"arxiv-2402.05881","DOIUrl":"https://doi.org/arxiv-2402.05881","url":null,"abstract":"Reconfigurable intelligent surface (RIS) is a key technology to control the\u0000communication environment in future wireless networks. Recently, beyond\u0000diagonal RIS (BD-RIS) emerged as a generalization of RIS achieving larger\u0000coverage through additional tunable impedance components interconnecting the\u0000RIS elements. However, conventional RIS and BD-RIS can effectively serve only\u0000users in their proximity, resulting in limited coverage. To overcome this\u0000limitation, in this paper, we investigate distributed RIS, whose elements are\u0000distributed over a wide region, in opposition to localized RIS commonly\u0000considered in the literature. The scaling laws of distributed BD-RIS reveal\u0000that it offers significant gains over distributed conventional RIS and\u0000localized BD-RIS, enabled by its interconnections allowing signal propagation\u0000within the BD-RIS. To assess the practical performance of distributed BD-RIS,\u0000we model and optimize BD-RIS with lossy interconnections through transmission\u0000line theory. Our model accounts for phase changes and losses over the BD-RIS\u0000interconnections arising when the interconnection lengths are not much smaller\u0000than the wavelength. Numerical results show that the performance of localized\u0000BD-RIS is only slightly impacted by losses, given the short interconnection\u0000lengths. Besides, distributed BD-RIS can achieve orders of magnitude of gains\u0000over conventional RIS, even in the presence of low losses.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Can Channels be Fully Inferred Between Two Antenna Panels?","authors":"Y. Qiu, D. W, Y. Zeng","doi":"arxiv-2402.05387","DOIUrl":"https://doi.org/arxiv-2402.05387","url":null,"abstract":"This letter considers a two-panel massive multiple-input multiple-output\u0000(MIMO) communication system, where the base station (BS) is equipped with two\u0000antenna panels that may use different frequency bands for communication. By\u0000exploiting the geometric relationships between antenna panels, efficient\u0000channel inference methods across antenna panels are proposed to reduce the\u0000overhead of real-time channel estimation. Four scenarios are considered, namely\u0000far-field free-space, near-field free-space, multi-path sharing far-field\u0000scatterers, and multi-path sharing near-field scatterers. For both far-field\u0000and near-field free-space scenarios, we show that the channel of one panel can\u0000be fully inferred from that of the other panel, as long as the multi-path\u0000components (MPCs) composing the channel can be resolved. On the other hand, for\u0000the multi-path scenarios sharing far-field or near-field scatterers, only the\u0000angles or range of angles of the MPCs can be inferred, respectively. Simulation\u0000results based on commercial 3D ray-tracing software are presented to validate\u0000our developed channel inference techniques.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact quantum sensing limits for bosonic dephasing channels","authors":"Zixin Huang, Ludovico Lami, Mark M. Wilde","doi":"arxiv-2402.05793","DOIUrl":"https://doi.org/arxiv-2402.05793","url":null,"abstract":"Dephasing is a prominent noise mechanism that afflicts quantum information\u0000carriers, and it is one of the main challenges towards realizing useful quantum\u0000computation, communication, and sensing. Here we consider discrimination and\u0000estimation of bosonic dephasing channels, when using the most general adaptive\u0000strategies allowed by quantum mechanics. We reduce these difficult quantum\u0000problems to simple classical ones based on the probability densities defining\u0000the bosonic dephasing channels. By doing so, we rigorously establish the\u0000optimal performance of various distinguishability and estimation tasks and\u0000construct explicit strategies to achieve this performance. To the best of our\u0000knowledge, this is the first example of a non-Gaussian bosonic channel for\u0000which there are exact solutions for these tasks.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Eduardo Noboro Tominaga, Onel Luis Alcaraz López, Tommy Svensson, Richard Demo Souza, Hirley Alves
{"title":"On the Spectral Efficiency of Indoor Wireless Networks with a Rotary Uniform Linear Array","authors":"Eduardo Noboro Tominaga, Onel Luis Alcaraz López, Tommy Svensson, Richard Demo Souza, Hirley Alves","doi":"arxiv-2402.05583","DOIUrl":"https://doi.org/arxiv-2402.05583","url":null,"abstract":"Contemporary wireless communication systems rely on Multi-User Multiple-Input\u0000Multiple-Output (MU-MIMO) techniques. In such systems, each Access Point (AP)\u0000is equipped with multiple antenna elements and serves multiple devices\u0000simultaneously. Notably, traditional systems utilize fixed antennas, i.e.,\u0000antennas without any movement capabilities, while the idea of movable antennas\u0000has recently gained traction among the research community. By moving in a\u0000confined region, movable antennas are able to exploit the wireless channel\u0000variation in the continuous domain. This additional degree of freedom may\u0000enhance the quality of the wireless links, and consequently the communication\u0000performance. However, movable antennas for MU-MIMO proposed in the literature\u0000are complex, bulky, expensive and present a high power consumption. In this\u0000paper, we propose an alternative to such systems that has lower complexity and\u0000lower cost. More specifically, we propose the incorporation of rotation\u0000capabilities to APs equipped with Uniform Linear Arrays (ULAs) of antennas. We\u0000consider the uplink of an indoor scenario where the AP serves multiple devices\u0000simultaneously. The optimal rotation of the ULA is computed based on estimates\u0000of the positions of the active devices and aiming at maximizing the per-user\u0000mean achievable Spectral Efficiency (SE). Adopting a spatially correlated\u0000Rician channel model, our numerical results show that the rotation capabilities\u0000of the AP can bring substantial improvements in the SE in scenarios where the\u0000line-of-sight component of the channel vectors is strong. Moreover, our\u0000proposed system is robust against imperfect positioning estimates.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"208 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mustapha Bounoua, Giulio Franzese, Pietro Michiardi
{"title":"S$Ω$I: Score-based O-INFORMATION Estimation","authors":"Mustapha Bounoua, Giulio Franzese, Pietro Michiardi","doi":"arxiv-2402.05667","DOIUrl":"https://doi.org/arxiv-2402.05667","url":null,"abstract":"The analysis of scientific data and complex multivariate systems requires\u0000information quantities that capture relationships among multiple random\u0000variables. Recently, new information-theoretic measures have been developed to\u0000overcome the shortcomings of classical ones, such as mutual information, that\u0000are restricted to considering pairwise interactions. Among them, the concept of\u0000information synergy and redundancy is crucial for understanding the high-order\u0000dependencies between variables. One of the most prominent and versatile\u0000measures based on this concept is O-information, which provides a clear and\u0000scalable way to quantify the synergy-redundancy balance in multivariate\u0000systems. However, its practical application is limited to simplified cases. In\u0000this work, we introduce S$Omega$I, which allows for the first time to compute\u0000O-information without restrictive assumptions about the system. Our experiments\u0000validate our approach on synthetic data, and demonstrate the effectiveness of\u0000S$Omega$I in the context of a real-world use case.","PeriodicalId":501433,"journal":{"name":"arXiv - CS - Information Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139761409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}