IEEE Transactions on Information Theory最新文献

{"title":"Strong Consistency of Spectral Clustering for the Sparse Degree-Corrected Hypergraph Stochastic Block Model","authors":"Chong Deng;Xin-Jian Xu;Shihui Ying","doi":"10.1109/TIT.2023.3302283","DOIUrl":"10.1109/TIT.2023.3302283","url":null,"abstract":"We prove strong consistency of spectral clustering under the degree-corrected hypergraph stochastic block model in the sparse regime where the maximum expected hyperdegree is as small as \u0000<inline-formula> <tex-math>$Omega (log n)$ </tex-math></inline-formula>\u0000 with \u0000<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\u0000 denoting the number of nodes. We show that the basic spectral clustering without preprocessing or postprocessing is strongly consistent in an even wider range of the model parameters, in contrast to previous studies that either trim high-degree nodes or perform local refinement. At the heart of our analysis is the entry-wise eigenvector perturbation bound derived by the “leave-one-out”technique. To the best of our knowledge, this is the first entry-wise error bound for degree-corrected hypergraph models, resulting in the strong consistency for clustering non-uniform hypergraphs with heterogeneous hyperdegrees.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 3","pages":"1962-1977"},"PeriodicalIF":2.5,"publicationDate":"2023-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62928781","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}

{"title":"Multiple-Access Channel Coding With Non-Signaling Correlations","authors":"Omar Fawzi;Paul Fermé","doi":"10.1109/TIT.2023.3301719","DOIUrl":"10.1109/TIT.2023.3301719","url":null,"abstract":"We address the problem of coding for classical multiple-access channels (MACs) with the assistance of non-signaling correlations between parties. It is well-known that non-signaling assistance does not change the capacity of classical point-to-point channels. However, it was recently observed that one can construct MACs from two-player nonlocal games while relating the winning probability of the game to the capacity of the MAC. By considering games for which entanglement (a special kind of non-signaling correlation) increases the winning probability (e.g., the Magic Square game), this shows that for some specific kinds of channels, entanglement between the senders can increase the capacity. In this work, we make several contributions towards understanding the capacity region for MACs with the assistance of non-signaling correlations between the parties. We develop a linear program computing the optimal success probability for coding over \u0000<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\u0000 copies of a MAC \u0000<inline-formula> <tex-math>$W$ </tex-math></inline-formula>\u0000 with size growing polynomially in \u0000<inline-formula> <tex-math>$n$ </tex-math></inline-formula>\u0000. Solving this linear program allows us to achieve inner bounds for MACs. Applying this method to the binary adder channel, we show that using non-signaling assistance, the sum-rate \u0000<inline-formula> <tex-math>$frac {log _{2}(72)}{4} simeq 1.5425$ </tex-math></inline-formula>\u0000 can be reached even with zero error, which beats the maximum sum-rate capacity of 1.5 in the unassisted case. For noisy channels, where the zero-error non-signaling assisted capacity region is trivial, we can use concatenated codes to obtain achievable points in the capacity region. Applied to a noisy version of the binary adder channel, we show that non-signaling assistance still improves the sum-rate capacity. Complementing these achievability results, we give an outer bound on the non-signaling assisted capacity region that has the same expression as the unassisted region except that the channel inputs are not required to be independent. Finally, we show that the capacity region with non-signaling assistance shared only between each sender and the receiver independently is the same as without assistance.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 3","pages":"1693-1719"},"PeriodicalIF":2.5,"publicationDate":"2023-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47176218","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}

{"title":"A Lower Bound on the List-Decodability of Insdel Codes","authors":"Shu Liu;Ivan Tjuawinata;Chaoping Xing","doi":"10.1109/TIT.2023.3302862","DOIUrl":"https://doi.org/10.1109/TIT.2023.3302862","url":null,"abstract":"For codes equipped with metrics such as Hamming metric, symbol pair metric or cover metric, the Johnson bound guarantees list-decodability of such codes. That is, the Johnson bound provides a lower bound on the list-decoding radius of a code in terms of its relative minimum distance \u0000<inline-formula> <tex-math>$delta $ </tex-math></inline-formula>\u0000, list size \u0000<inline-formula> <tex-math>$L$ </tex-math></inline-formula>\u0000 and the alphabet size \u0000<inline-formula> <tex-math>$q$ </tex-math></inline-formula>\u0000. For study of list-decodability of codes with insertion and deletion errors (we call such codes insdel codes), it is natural to ask the open problem whether there is also a Johnson-type bound. The problem was first investigated by Wachter-Zeh and the result was amended by Hayashi and Yasunaga where a lower bound on the list-decodability for insdel codes was derived. The main purpose of this paper is to move a step further towards solving the above open problem. In this work, we provide a new lower bound for the list-decodability of an insdel code. As a consequence, we show that unlike the Johnson bound for codes under other metrics that is tight, the bound on list-decodability of insdel codes given by Hayashi and Yasunaga is not tight. Our main idea is to show that if an insdel code with a given Levenshtein distance \u0000<inline-formula> <tex-math>$d$ </tex-math></inline-formula>\u0000 is not list-decodable with list size \u0000<inline-formula> <tex-math>$L$ </tex-math></inline-formula>\u0000, then the list decoding radius is lower bounded by a bound involving \u0000<inline-formula> <tex-math>$L$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$d$ </tex-math></inline-formula>\u0000. In other words, if the list decoding radius is less than this lower bound, the code must be list-decodable with list size \u0000<inline-formula> <tex-math>$L$ </tex-math></inline-formula>\u0000. At the end of the paper we use such bound to provide an insdel-list-decodability bound for various well-known codes, which has not been extensively studied before.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 11","pages":"6989-7002"},"PeriodicalIF":2.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841918","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}

{"title":"The Many Faces of Adversarial Risk: An Expanded Study","authors":"Muni Sreenivas Pydi;Varun Jog","doi":"10.1109/TIT.2023.3303221","DOIUrl":"10.1109/TIT.2023.3303221","url":null,"abstract":"Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk—not all mathematically rigorous and differing subtly in the details—have appeared in the literature. In this paper, we revisit these definitions, fix measure theoretic issues, and critically examine their similarities and differences. Our technical tools derive from optimal transport, robust statistics, functional analysis, and game theory. Our contributions include the following: generalizing Strassen’s theorem to the unbalanced optimal transport setting with applications to adversarial classification with unequal priors; showing an equivalence between adversarial robustness and robust hypothesis testing with \u0000<inline-formula> <tex-math>$infty $ </tex-math></inline-formula>\u0000-Wasserstein uncertainty sets; proving the existence of a pure Nash equilibrium in the two-player game between the adversary and the algorithm; and characterizing adversarial risk by the minimum Bayes error between a pair of distributions belonging to the \u0000<inline-formula> <tex-math>$infty $ </tex-math></inline-formula>\u0000-Wasserstein uncertainty sets. Our results generalize and deepen recently discovered connections between optimal transport and adversarial robustness and reveal new connections to Choquet capacities and game theory.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 1","pages":"550-570"},"PeriodicalIF":2.5,"publicationDate":"2023-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62929146","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}

{"title":"On Lattice Tilings of ℤn by Limited Magnitude Error Balls B(n, 2, 1, 1)","authors":"Tao Zhang;Yanlu Lian;Gennian Ge","doi":"10.1109/TIT.2023.3301669","DOIUrl":"https://doi.org/10.1109/TIT.2023.3301669","url":null,"abstract":"Limited magnitude error model has applications in flash memory. In this model, a perfect code is equivalent to a tiling of \u0000<inline-formula> <tex-math>$mathbb {Z}^{n}$ </tex-math></inline-formula>\u0000 by limited magnitude error balls. In this paper, we give a complete classification of lattice tilings of \u0000<inline-formula> <tex-math>$mathbb {Z}^{n}$ </tex-math></inline-formula>\u0000 by limited magnitude error balls \u0000<inline-formula> <tex-math>$mathcal {B}(n,2,1,1)$ </tex-math></inline-formula>\u0000.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 11","pages":"7110-7121"},"PeriodicalIF":2.5,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67840945","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}

{"title":"Provably Private Distributed Averaging Consensus: An Information-Theoretic Approach","authors":"Mohammad Fereydounian;Aryan Mokhtari;Ramtin Pedarsani;Hamed Hassani","doi":"10.1109/TIT.2023.3300711","DOIUrl":"https://doi.org/10.1109/TIT.2023.3300711","url":null,"abstract":"In this work, we focus on solving a decentralized consensus problem in a private manner. Specifically, we consider a setting in which a group of nodes, connected through a network, aim at computing the mean of their local values without revealing those values to each other. The distributed consensus problem is a classic problem that has been extensively studied and its convergence characteristics are well-known. However, state-of-the-art consensus methods build on the idea of exchanging local information with neighboring nodes which leaks information about the users’ local values. We propose an algorithmic framework that is capable of achieving the convergence limit and rate of classic consensus algorithms while keeping the users’ local values private. The key idea of our proposed method is to carefully design noisy messages that are passed from each node to its neighbors such that the consensus algorithm still converges precisely to the average of local values, while a minimum amount of information about local values is leaked. We formalize this by precisely characterizing the mutual information between the private message of a node and all the messages that another adversary collects over time. We prove that our method is capable of preserving users’ privacy for any network without a so-called generalized leaf, and formalize the trade-off between privacy and convergence time. Unlike many private algorithms, any desired accuracy is achievable by our method, and the required level of privacy only affects the convergence time.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 11","pages":"7317-7335"},"PeriodicalIF":2.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67840851","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}

{"title":"New Constructions of q-Ary MDS Array Codes With Multiple Parities and Their Effective Decoding","authors":"Jingjie Lv;Weijun Fang;Xiangyu Chen;Jing Yang;Shu-Tao Xia","doi":"10.1109/TIT.2023.3300919","DOIUrl":"10.1109/TIT.2023.3300919","url":null,"abstract":"From the perspective of parity-check matrices, we present new constructions of \u0000<inline-formula> <tex-math>$q$ </tex-math></inline-formula>\u0000-ary maximum distance separable (MDS) array codes with multiple parities. Applying these constructions, some new types of MDS array codes with array numbers \u0000<inline-formula> <tex-math>$m-tau $ </tex-math></inline-formula>\u0000 can be derived, where \u0000<inline-formula> <tex-math>${mathrm{ gcd}}(m,q)=1$ </tex-math></inline-formula>\u0000. Moreover, an explicit construction of binary MDS array codes is also presented. Compared to the existing MDS array codes, one important characteristic of these codes is that their available code lengths are much longer, which is suitable for large-scale storage systems. In some particular cases, the maximum code lengths of these codes and their extension can be up to \u0000<inline-formula> <tex-math>$2^{m-tau }$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$2^{m-tau }+1$ </tex-math></inline-formula>\u0000 (or \u0000<inline-formula> <tex-math>$2^{m-tau }+2$ </tex-math></inline-formula>\u0000), respectively. Moreover, to demonstrate the applicability of our constructed MDS array codes, we present an effective generic decoding method for the erased errors. In particular, when there are no more than three erasures occurring, a scheduled algorithm for the syndrome computation of our explicit construction is further proposed, whose computational complexity is asymptotically optimal. Furthermore, this algorithm can be directly applied to the encoding procedure of their extended form. The simulation shows that our new MDS array codes have better encoding and decoding performances than the corresponding extended RS codes coupled with different algorithms.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 11","pages":"7082-7098"},"PeriodicalIF":2.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62928667","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}

{"title":"New MDS Self-Dual Codes Over Finite Field Fr2","authors":"Ruhao Wan, Yang Li, Shixin Zhu","doi":"10.1109/TIT.2023.3261904","DOIUrl":"https://doi.org/10.1109/TIT.2023.3261904","url":null,"abstract":"MDS self-dual codes have nice algebraic structures and are uniquely determined by lengths. Recently, the construction of MDS self-dual codes of new lengths has become an important and hot issue in coding theory. In this paper, we construct six new classes of MDS self-dual codes by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes. Together with our constructions, the proportion of all known MDS self-dual codes relative to possible MDS self-dual codes generally exceed 57%. As far as we know, this is the largest known ratio. Moreover, some new families of MDS self-orthogonal codes are also constructed.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 1","pages":"5009-5016"},"PeriodicalIF":2.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"62928135","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}

{"title":"Comments on “Analytical Algorithm for Capacities of Classical and Classical-Quantum Channels”","authors":"Masahito Hayashi","doi":"10.1109/TIT.2023.3299885","DOIUrl":"https://doi.org/10.1109/TIT.2023.3299885","url":null,"abstract":"After completing the review process of the above article, the author found the reference Muroga (1953), which has already derived an analytical calculation method for the channel capacity under a certain condition. This comment explains the relation between Muroga’s article and this article.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 11","pages":"7478-7478"},"PeriodicalIF":2.5,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841029","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}

{"title":"The Efficacy of Pessimism in Asynchronous Q-Learning","authors":"Yuling Yan;Gen Li;Yuxin Chen;Jianqing Fan","doi":"10.1109/TIT.2023.3299840","DOIUrl":"https://doi.org/10.1109/TIT.2023.3299840","url":null,"abstract":"This paper is concerned with the asynchronous form of Q-learning, which applies a stochastic approximation scheme to Markovian data samples. Motivated by the recent advances in offline reinforcement learning, we develop an algorithmic framework that incorporates the principle of pessimism into asynchronous Q-learning, which penalizes infrequently-visited state-action pairs based on suitable lower confidence bounds (LCBs). This framework leads to, among other things, improved sample efficiency and enhanced adaptivity in the presence of near-expert data. Our approach permits the observed data in some important scenarios to cover only partial state-action space, which is in stark contrast to prior theory that requires uniform coverage of all state-action pairs. When coupled with the idea of variance reduction, asynchronous Q-learning with LCB penalization achieves near-optimal sample complexity, provided that the target accuracy level is small enough. In comparison, prior works were suboptimal in terms of the dependency on the effective horizon even when i.i.d. sampling is permitted. Our results deliver the first theoretical support for the use of pessimism principle in the presence of Markovian non-i.i.d. data.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"69 11","pages":"7185-7219"},"PeriodicalIF":2.5,"publicationDate":"2023-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/18/10288603/10196488.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67841063","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}