arXiv - MATH - Information Theory最新文献_第6页

A Generalization of Axiomatic Approach to Information Leakage 信息泄漏公理法的一般化

arXiv - MATH - Information Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04108

Mohammad Amin Zarrabian, Parastoo Sadeghi

{"title":"A Generalization of Axiomatic Approach to Information Leakage","authors":"Mohammad Amin Zarrabian, Parastoo Sadeghi","doi":"arxiv-2409.04108","DOIUrl":"https://doi.org/arxiv-2409.04108","url":null,"abstract":"In this paper, we extend the framework of quantitative information flow (QIF)\u0000to include adversaries that use Kolmogorov-Nagumo $f$-mean to infer secrets of\u0000a private system. Specifically, in our setting, an adversary uses\u0000Kolmogorov-Nagumo $f$-mean to compute its best actions before and after\u0000observing the system's randomized outputs. This leads to generalized notions of\u0000prior and posterior vulnerability and generalized axiomatic relations that we\u0000will derive to elucidate how these $f$-mean based vulnerabilities interact with\u0000each other. We demonstrate usefulness of this framework by showing how some\u0000notions of leakage that had been derived outside of the QIF framework and so\u0000far seemed incompatible with it are indeed explainable via such extension of\u0000QIF. These leakage measures include $alpha$-leakage, which is the same as\u0000Arimoto mutual information of order $alpha$, maximal $alpha$-leakage which is\u0000the $alpha$-leakage capacity, and $(alpha,beta)$ leakage, which is a\u0000generalization of the above and captures local differential privacy as a\u0000special case. We also propose a new pointwise notion of gain function, which we\u0000coin pointwise information gain. We show that this pointwise information gain\u0000can explain R'eyni divergence and Sibson mutual information of order $alpha\u0000in [0,infty]$ as the Kolmogorov-Nagumo average of the gain with a proper\u0000choice of function $f$.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217217","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}

引用次数: 0

Locally recoverable algebro-geometric codes with multiple recovery sets from projective bundles 从投影束出发的具有多个恢复集的局部可恢复阿尔基几何码

arXiv - MATH - Information Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04201

Konrad Aguilar, Angelynn Álvarez, René Ardila, Pablo S. Ocal, Cristian Rodriguez Avila, Anthony Várilly-Alvarado

引用次数: 0

Low-latency Secure Integrated Sensing and Communication with Transmitter Actions 低延迟安全集成传感和通信与发射机行动

arXiv - MATH - Information Theory Pub Date : 2024-09-06 DOI: arxiv-2409.04619

Truman Welling, Onur Günlü, Aylin Yener

引用次数: 0

Communication-Assisted Sensing Systems: Fundamental Limits and ISAC Waveform Design 通信辅助传感系统：基本限制和 ISAC 波形设计

arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03561

Fuwang Dong, Fan Liu, Yifeng Xiong, Yuanhao Cui, Wei Wang, Shi Jin

{"title":"Communication-Assisted Sensing Systems: Fundamental Limits and ISAC Waveform Design","authors":"Fuwang Dong, Fan Liu, Yifeng Xiong, Yuanhao Cui, Wei Wang, Shi Jin","doi":"arxiv-2409.03561","DOIUrl":"https://doi.org/arxiv-2409.03561","url":null,"abstract":"The communication-assisted sensing (CAS) systems are expected to endow the\u0000users with beyond-line-of-sight sensing capabilities without the aid of\u0000additional sensors. In this paper, we study the dual-functional signaling\u0000strategy, focusing on three primary aspects, namely, the information-theoretic\u0000framework, the optimal distribution of channel input, and the optimal waveform\u0000design for Gaussian signals. First, we establish the information-theoretic\u0000framework and develop a modified source-channel separation theorem (MSST)\u0000tailored for CAS systems. The proposed MSST elucidates the relationship between\u0000achievable distortion, coding rate, and communication channel capacity in cases\u0000where the distortion metric is separable for sensing and communication (S&C)\u0000processes. Second, we present an optimal channel input design for\u0000dual-functional signaling, which aims to minimize total distortion under the\u0000constraints of the MSST and resource budget. We then conceive a two-step\u0000Blahut-Arimoto (BA)-based optimal search algorithm to numerically solve the\u0000functional optimization problem. Third, in light of the current signaling\u0000strategy, we further propose an optimal waveform design for Gaussian signaling\u0000in multi-input multi-output (MIMO) CAS systems. The associated covariance\u0000matrix optimization problem is addressed using a successive convex\u0000approximation (SCA)-based waveform design algorithm. Finally, we provide\u0000numerical simulation results to demonstrate the effectiveness of the proposed\u0000algorithms and to show the unique performance tradeoff between S&C processes.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"161 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217224","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}

引用次数: 0

On the Optimal Performance of Distributed Cell-Free Massive MIMO with LoS Propagation 论具有 LoS 传播的分布式无小区大规模多输入多输出（MIMO）的最佳性能

arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03551

Noor Ul Ain, Lorenzo Miretti, Sławomir Stańczak

引用次数: 0

A Logarithmic Decomposition and a Signed Measure Space for Entropy 熵的对数分解和有符号度量空间

arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03732

Keenan J. A. Down, Pedro A. M. Mediano

{"title":"A Logarithmic Decomposition and a Signed Measure Space for Entropy","authors":"Keenan J. A. Down, Pedro A. M. Mediano","doi":"arxiv-2409.03732","DOIUrl":"https://doi.org/arxiv-2409.03732","url":null,"abstract":"The Shannon entropy of a random variable X has much behaviour analogous to a\u0000signed measure. Previous work has explored this connection by defining a signed\u0000measure on abstract sets, which are taken to represent the information that\u0000different random variables contain. This construction is sufficient to derive\u0000many measure-theoretical counterparts to information quantities such as the\u0000mutual information $I(X; Y) = mu(tilde{X} cap tilde{Y})$, the joint entropy\u0000$H(X,Y) = mu(tilde{X} cup tilde{Y})$, and the conditional entropy $H(X|Y) =\u0000mu(tilde{X} setminus tilde{Y})$. Here we provide concrete characterisations\u0000of these abstract sets and a corresponding signed measure, and in doing so we\u0000demonstrate that there exists a much finer decomposition with intuitive\u0000properties which we call the logarithmic decomposition (LD). We show that this\u0000signed measure space has the useful property that its logarithmic atoms are\u0000easily characterised with negative or positive entropy, while also being\u0000consistent with Yeung's I-measure. We present the usability of our approach by\u0000re-examining the G'acs-K\"orner common information and the Wyner common\u0000information from this new geometric perspective and characterising it in terms\u0000of our logarithmic atoms - a property we call logarithmic decomposability. We\u0000present possible extensions of this construction to continuous probability\u0000distributions before discussing implications for quality-led information\u0000theory. Lastly, we apply our new decomposition to examine the Dyadic and\u0000Triadic systems of James and Crutchfield and show that, in contrast to the\u0000I-measure alone, our decomposition is able to qualitatively distinguish between\u0000them.","PeriodicalId":501082,"journal":{"name":"arXiv - MATH - Information Theory","volume":"69 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142217222","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}

引用次数: 0

Constituent automorphism decoding of Reed-Muller codes 里德-穆勒码的构元自动形态解码

arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03700

Yicheng Qu, Amir Tasbihi, Frank R. Kschischang

引用次数: 0

A note on the differential spectrum of the Ness-Helleseth function 关于奈斯-赫勒塞斯函数微分谱的说明

arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03189

Ketong Ren, Maosheng Xiong, Haode Yan

引用次数: 0

An Efficient Algorithm for Group Testing with Runlength Constraints 具有运行长度限制的分组测试高效算法

arXiv - MATH - Information Theory Pub Date : 2024-09-05 DOI: arxiv-2409.03491

Marco Dalai, Stefano Della Fiore, Adele A. Rescigno, Ugo Vaccaro