IEEE Transactions on Information Theory最新文献_第7页

On de Bruijn Array Codes—Part I: Nonlinear Codes

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-16 DOI: 10.1109/TIT.2024.3518434

Tuvi Etzion

引用次数: 0

The Multiple-Access Channel With Entangled Transmitters

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-12 DOI: 10.1109/TIT.2024.3516507

Uzi Pereg;Christian Deppe;Holger Boche

{"title":"The Multiple-Access Channel With Entangled Transmitters","authors":"Uzi Pereg;Christian Deppe;Holger Boche","doi":"10.1109/TIT.2024.3516507","DOIUrl":"https://doi.org/10.1109/TIT.2024.3516507","url":null,"abstract":"Communication over a classical multiple-access channel (MAC) with entanglement resources is considered, whereby two transmitters share entanglement resources a priori before communication begins. Leditzky et al. (2020) presented an example of a classical MAC, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide. Furthermore, we address the combined setting of entanglement resources and conferencing, where the transmitters can also communicate with each other over rate-limited links. Using superdense coding, entanglement can double the conferencing rate.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1096-1120"},"PeriodicalIF":2.2,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10795236","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

N-Sum Box: An Abstraction for Linear Computation Over Many-to-One Quantum Networks

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-11 DOI: 10.1109/TIT.2024.3514921

Matteo Allaix;Yuxiang Lu;Yuhang Yao;Tefjol Pllaha;Camilla Hollanti;Syed A. Jafar

{"title":"N-Sum Box: An Abstraction for Linear Computation Over Many-to-One Quantum Networks","authors":"Matteo Allaix;Yuxiang Lu;Yuhang Yao;Tefjol Pllaha;Camilla Hollanti;Syed A. Jafar","doi":"10.1109/TIT.2024.3514921","DOIUrl":"https://doi.org/10.1109/TIT.2024.3514921","url":null,"abstract":"Linear computations over quantum many-to-one communication networks offer opportunities for communication cost improvements through schemes that exploit quantum entanglement among transmitters to achieve superdense coding gains, combined with classical techniques such as interference alignment. The problem becomes much more broadly accessible if suitable abstractions can be found for the underlying quantum functionality via classical black box models. This work formalizes such an abstraction in the form of an “N-sum box”, a black box generalization of a two-sum protocol of Song et al. with recent applications to N-server private information retrieval. The N-sum box has a communication cost of N qudits and classical output of a vector of <inline-formula> <tex-math>$N~q$ </tex-math></inline-formula>-ary digits linearly dependent (via an <inline-formula> <tex-math>$N times 2N$ </tex-math></inline-formula> transfer matrix) on <inline-formula> <tex-math>$2N$ </tex-math></inline-formula> classical inputs distributed among N transmitters. We characterize which transfer matrices are feasible by our construction, both with and without the possibility of additional locally invertible classical operations at the transmitters and receivers. Furthermore, we provide a sample application to Cross-Subspace Alignment (CSA) schemes to obtain efficient instances of Quantum Private Information Retrieval (QPIR) and Quantum Secure Distributed Batch Matrix Multiplication (QSDBMM). We first describe N-sum boxes based on maximal stabilizers and we then consider non-maximal-stabilizer-based constructions to obtain an instance of Quantum Symmetric Private Information Retrieval.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1121-1139"},"PeriodicalIF":2.2,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10789218","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Minimax Estimation of Linear Functions of Eigenvectors in the Face of Small Eigen-Gaps

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-11 DOI: 10.1109/TIT.2024.3514795

Gen Li;Changxiao Cai;H. Vincent Poor;Yuxin Chen

{"title":"Minimax Estimation of Linear Functions of Eigenvectors in the Face of Small Eigen-Gaps","authors":"Gen Li;Changxiao Cai;H. Vincent Poor;Yuxin Chen","doi":"10.1109/TIT.2024.3514795","DOIUrl":"https://doi.org/10.1109/TIT.2024.3514795","url":null,"abstract":"Eigenvector perturbation analysis plays a vital role in various data science applications. A large body of prior works, however, focused on establishing <inline-formula> <tex-math>$ell _{2}$ </tex-math></inline-formula> eigenvector perturbation bounds, which are often highly inadequate in addressing tasks that rely on fine-grained behavior of an eigenvector. This paper makes progress on this by studying the perturbation of linear functions of an unknown eigenvector. Focusing on two fundamental problems — matrix denoising and principal component analysis — in the presence of Gaussian noise, we develop a suite of statistical theory that characterizes the perturbation of arbitrary linear functions of an unknown eigenvector. In order to mitigate a non-negligible bias issue inherent to the natural “plug-in” estimator, we develop de-biased estimators that <xref>(1)</xref> achieve minimax lower bounds for a family of scenarios (modulo some logarithmic factor), and <xref>(2)</xref> can be computed in a data-driven manner without sample splitting. Noteworthily, the proposed estimators are nearly minimax optimal even when the associated eigen-gap is <italic>substantially smaller</i> than what is required in prior statistical theory.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1200-1247"},"PeriodicalIF":2.2,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rate-Adaptive Protograph-Based MacKay-Neal Codes

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-11 DOI: 10.1109/TIT.2024.3515460

Ayman Zahr;Emna Ben Yacoub;Balázs Matuz;Gianluigi Liva

{"title":"Rate-Adaptive Protograph-Based MacKay-Neal Codes","authors":"Ayman Zahr;Emna Ben Yacoub;Balázs Matuz;Gianluigi Liva","doi":"10.1109/TIT.2024.3515460","DOIUrl":"https://doi.org/10.1109/TIT.2024.3515460","url":null,"abstract":"Rate-adaptive MacKay-Neal (MN) codes based on protographs are analyzed. The code construction employs an outer distribution matcher (DM) to adapt the rate of the scheme. The DM is coupled with an inner protograph-based low-density parity-check (LDPC) code. The performance achievable by the resulting code structure, that is nonlinear, is studied by means of an equivalent communication model that reduces the problem to the analysis of the inner (linear) LDPC code with transmission that takes place in parallel over the communication channel, and over a suitably defined binary symmetric channel. A density evolution analysis of protograph MN code ensembles is outlined, and it is complemented by an error floor analysis that relies on the derivation of the average input-output weight distribution of the inner LDPC code ensemble. Conditions on the shape of the normalized logarithmic asymptotic input-output weight distribution are defined, which allow discarding code ensembles with bad error floor properties during the code design phase. Examples of code designs are provided, showing how the use of a single LDPC code ensemble allows operating within 1 dB from the Shannon limit over a wide range of code rates, where the code rate is selected by tuning the DM parameters. By enabling rate flexibility with a constant blocklength, and with a fixed LDPC code as inner code, the construction provides an appealing solution for very high-throughput wireless (optical) links that employ binary-input modulations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"914-929"},"PeriodicalIF":2.2,"publicationDate":"2024-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143107000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Distributed Matrix Multiplication With Straggler Tolerance Using Algebraic Function Fields

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-09 DOI: 10.1109/TIT.2024.3513693

Adrián Fidalgo-Díaz;Umberto Martínez-Peñas

引用次数: 0

Robust Indexing for the Sliced Channel: Almost Optimal Codes for Substitutions and Deletions

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-09 DOI: 10.1109/TIT.2024.3513040

Jin Sima;Netanel Raviv;Jehoshua Bruck

引用次数: 0

Batch Array Codes

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-09 DOI: 10.1109/TIT.2024.3512933

Xiangliang Kong;Chen Wang;Yiwei Zhang

引用次数: 0

Better and Simpler Lower Bounds for Differentially Private Statistical Estimation

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-09 DOI: 10.1109/TIT.2024.3511624

Shyam Narayanan

{"title":"Better and Simpler Lower Bounds for Differentially Private Statistical Estimation","authors":"Shyam Narayanan","doi":"10.1109/TIT.2024.3511624","DOIUrl":"https://doi.org/10.1109/TIT.2024.3511624","url":null,"abstract":"We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any <inline-formula> <tex-math>$alpha le O(1)$ </tex-math></inline-formula>, estimating the covariance of a Gaussian up to spectral error <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula> requires <inline-formula> <tex-math>$tilde {Omega }left ({{frac {d^{3/2}}{alpha varepsilon } + frac {d}{alpha ^{2}}}}right)$ </tex-math></inline-formula> samples, which is tight up to logarithmic factors. This result improves over previous work which established this for <inline-formula> <tex-math>$alpha le Oleft ({{frac {1}{sqrt {d}}}}right)$ </tex-math></inline-formula>, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded kth moments requires <inline-formula> <tex-math>$tilde {Omega }left ({{frac {d}{alpha ^{k/(k-1)} varepsilon } + frac {d}{alpha ^{2}}}}right)$ </tex-math></inline-formula> samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of <inline-formula> <tex-math>$k = 2$ </tex-math></inline-formula>. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1376-1388"},"PeriodicalIF":2.2,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mean Estimation Under Heterogeneous Privacy Demands

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-12-05 DOI: 10.1109/TIT.2024.3511498

Syomantak Chaudhuri;Konstantin Miagkov;Thomas A. Courtade

引用次数: 0