IEEE Transactions on Information Theory最新文献

{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2024.3515437","DOIUrl":"https://doi.org/10.1109/TIT.2024.3515437","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 1","pages":"C3-C3"},"PeriodicalIF":2.2,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10816278","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142890233","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}

{"title":"Schrödinger-Föllmer Sampler","authors":"Jian Huang;Yuling Jiao;Lican Kang;Xu Liao;Jin Liu;Yanyan Liu","doi":"10.1109/TIT.2024.3522494","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522494","url":null,"abstract":"Sampling from probability distributions is a critical problem in statistics and machine learning, particularly in Bayesian inference, where direct integration over the posterior distribution is often infeasible, making sampling from the posterior essential for inference. This paper introduces the Schrödinger-Föllmer sampler (SFS), a novel approach for sampling from potentially unnormalized distributions. The SFS leverages the Schrödinger-Föllmer diffusion process on the unit interval, incorporating a time-dependent drift term that evolves the distribution from a degenerate form at time zero to the target distribution at time one. Unlike existing Markov chain Monte Carlo methods that rely on ergodicity, SFS operates independently of ergodicity. Computationally, SFS is straightforward to implement using the Euler-Maruyama discretization. In our theoretical analysis, we derive non-asymptotic error bounds for the SFS sampling distribution in the Wasserstein distance, subject to reasonable conditions. Numerical experiments demonstrate that SFS generates higher-quality samples than several established methods.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1283-1299"},"PeriodicalIF":2.2,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361254","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":"Robust Gray Codes Approaching the Optimal Rate","authors":"Roni Con;Dorsa Fathollahi;Ryan Gabrys;Mary Wootters;Eitan Yaakobi","doi":"10.1109/TIT.2024.3522986","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522986","url":null,"abstract":"Robust Gray codes were introduced by (Lolck and Pagh, SODA 2024). Informally, a robust Gray code is a (binary) Gray code <inline-formula> <tex-math>$mathcal {G}$ </tex-math></inline-formula> so that, given a noisy version of the encoding <inline-formula> <tex-math>$mathcal {G}(j)$ </tex-math></inline-formula> of an integer j, one can recover <inline-formula> <tex-math>$hat {j}$ </tex-math></inline-formula> that is close to j (with high probability over the noise). Such codes have found applications in differential privacy. In this work, we present near-optimal constructions of robust Gray codes. In more detail, we construct a Gray code <inline-formula> <tex-math>$mathcal {G}$ </tex-math></inline-formula> of rate <inline-formula> <tex-math>$1 - H_{2}(p) - varepsilon $ </tex-math></inline-formula> that is efficiently encodable, and that is robust in the following sense. Supposed that <inline-formula> <tex-math>$mathcal {G}(j)$ </tex-math></inline-formula> is passed through the binary symmetric channel <inline-formula> <tex-math>${text {BSC}}_{p}$ </tex-math></inline-formula> with cross-over probability p, to obtain x. We present an efficient decoding algorithm that, given x, returns an estimate <inline-formula> <tex-math>$hat {j}$ </tex-math></inline-formula> so that <inline-formula> <tex-math>$| j - hat {j}|$ </tex-math></inline-formula> is small with high probability.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1647-1665"},"PeriodicalIF":2.2,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465643","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":"Convolution Type of Metaplectic Cohen’s Distribution Time-Frequency Analysis Theory, Method and Technology","authors":"Manjun Cui;Zhichao Zhang;Jie Han;Yunjie Chen;Chunzheng Cao","doi":"10.1109/TIT.2024.3522079","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522079","url":null,"abstract":"The conventional Cohen’s distribution can’t meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we embark on blending time-frequency operators and coordinate operator fractionizations to formulate the definition of the joint fractionizations metaplectic Wigner distribution (JFMWD), based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen’s distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the JFMWD domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including the classical Gaussian filter, the Cohen’s distribution filtering methods with fixed kernel functions, the classical Wiener filter, the adaptive generalized linear canonical convolution-based filtering method, the adaptive Cohen’s distribution filtering method, the adaptive JFMWD-based Cohen’s distribution filtering method, and the adaptive generalized metaplectic convolution-based Cohen’s distribution filtering method in noise suppression.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"2292-2314"},"PeriodicalIF":2.2,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143455278","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 Classes of Optimal Cyclic Codes With Hierarchical Locality","authors":"Xing Liu;Qi Zeng","doi":"10.1109/TIT.2024.3522782","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522782","url":null,"abstract":"In order to correct different numbers of erasures in distributed storage systems, the design of locally repairable codes with hierarchical locality (H-LRCs) is crucial. In this paper, we construct three classes of optimal cyclic H-LRCs. The minimum Hamming distance of the first class of optimal cyclic H-LRCs is <inline-formula> <tex-math>$d=delta _{1}=delta +mu n'+nu +1$ </tex-math></inline-formula> while that of the second class of optimal cyclic H-LRCs is <inline-formula> <tex-math>$d=delta _{1}+1=delta +mu n'+nu +2$ </tex-math></inline-formula> for some flexible integers <inline-formula> <tex-math>$delta,mu,nu $ </tex-math></inline-formula>. The first two classes of optimal cyclic H-LRCs also have unbounded length. Although the length of the third class of optimal cyclic H-LRCs is not unbounded, it can reach large values. These classes of optimal cyclic H-LRCs by our constructions have new and flexible parameters compared with those in the literature.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"862-870"},"PeriodicalIF":2.2,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106995","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":"Minimax Optimal Q Learning With Nearest Neighbors","authors":"Puning Zhao;Lifeng Lai","doi":"10.1109/TIT.2024.3522347","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522347","url":null,"abstract":"Markov decision process (MDP) is an important model of sequential decision making problems. Existing theoretical analysis focus primarily on finite state spaces. For continuous state spaces, a recent interesting work (Shah and Xie, 2018) proposes a nearest neighbor Q learning approach. Under the streaming setting, in shich samples are received in a sequential manner, the sample complexity of this method is <inline-formula> <tex-math>$tilde {O}left ({{frac {|mathcal {A}|}{epsilon ^{d+3}(1-gamma)^{d+7}}}}right)$ </tex-math></inline-formula> for <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>-accurate Q function estimation of infinite horizon discounted MDP with discount factor <inline-formula> <tex-math>$gamma $ </tex-math></inline-formula>, in which <inline-formula> <tex-math>$|mathcal {A}|$ </tex-math></inline-formula> is the size of the action space. However, the sample complexity is not optimal, and the method is suitable only for bounded state spaces. In this paper, we propose two new nearest neighbor Q learning methods, one for the offline setting and the other for the streaming setting. We show that the sample complexities of these two methods are <inline-formula> <tex-math>$tilde {O}left ({{frac {|mathcal {A}|}{epsilon ^{d+2}(1-gamma)^{d+2}}}}right)$ </tex-math></inline-formula> and <inline-formula> <tex-math>$tilde {O}left ({{frac {|mathcal {A}|}{epsilon ^{d+2}(1-gamma)^{d+3}}}}right)$ </tex-math></inline-formula> for offline and streaming settings respectively, which significantly improve over existing results and have minimax optimal dependence over <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>. We achieve such improvement by utilizing samples more efficiently. In particular, the method by Shah and Xie, 2018, clears up all samples after each iteration, thus these samples are somewhat wasted. On the other hand, our offline method does not remove any samples, and our streaming method only removes samples with time earlier than <inline-formula> <tex-math>$beta t$ </tex-math></inline-formula> at time t, thus our methods significantly reduce the loss of information. Apart from the sample complexity, our methods also have additional advantages of better computational complexity, as well as suitability to unbounded state spaces. Finally, we extend our work to the case where both state and action spaces are continuous.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1300-1322"},"PeriodicalIF":2.2,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361305","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":"Graph Structure of Chebyshev Permutation Polynomials Over Ring ℤpk","authors":"Chengqing Li;Xiaoxiong Lu;Kai Tan;Guanrong Chen","doi":"10.1109/TIT.2024.3522095","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522095","url":null,"abstract":"Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the structure of the associated functional graph of Chebyshev permutation polynomials over a ring <inline-formula> <tex-math>$mathbb {Z}_{p^{k}}$ </tex-math></inline-formula>, with p being a prime number greater than three, where every number in the ring is considered as a vertex and the existing mapping relation between two vertices is regarded as a directed edge. Based on some new properties of Chebyshev polynomials and their derivatives, we disclose how the basic structure of the functional graph evolves with respect to parameter k. First, we present a complete and explicit form of the length of a path starting from any given vertex. Then, we show that the functional graph’s strong patterns indicate that the number of cycles of any given length always remains constant as k increases. Moreover, we rigorously prove the rules on the elegant structure of the functional graph and verify them experimentally. Our results could be useful for studying the emergence mechanism of the complexity of a nonlinear map in digital computers and security analysis of its cryptographic applications.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1419-1433"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361250","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 Generating Idempotent Is a Minimum-Weight Codeword for Some Binary BCH Codes","authors":"Yaron Shany;Amit Berman","doi":"10.1109/TIT.2024.3522185","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522185","url":null,"abstract":"In a paper from 2015, Ding et al. (IEEE Trans. IT, May 2015) conjectured that for odd m, the minimum distance of the binary BCH code of length <inline-formula> <tex-math>$2^{m}-1$ </tex-math></inline-formula> and designed distance <inline-formula> <tex-math>$2^{m-2}+1$ </tex-math></inline-formula> is equal to the Bose distance calculated in the same paper. In this paper, we prove the conjecture. In fact, we prove a stronger result suggested by Ding et al.: the weight of the generating idempotent is equal to the Bose distance for both odd and even m. Our main tools are some new properties of the so-called fibbinary integers, in particular, the splitting field of related polynomials, and the relation of these polynomials to the idempotent of the BCH code.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1700-1704"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465725","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 Two-Stage Solution to Quantum Process Tomography: Error Analysis and Optimal Design","authors":"Shuixin Xiao;Yuanlong Wang;Jun Zhang;Daoyi Dong;Gary J. Mooney;Ian R. Petersen;Hidehiro Yonezawa","doi":"10.1109/TIT.2024.3522005","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522005","url":null,"abstract":"Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography. Utilizing a tensor structure, our algorithm exhibits a computational complexity of <inline-formula> <tex-math>$O(MLd^{2})$ </tex-math></inline-formula> where d is the dimension of the quantum system and <inline-formula> <tex-math>$M, L~(Mgeq d^{2}, Lgeq d^{2})$ </tex-math></inline-formula> represent the numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1803-1823"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465588","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":"Maximal-Capacity Discrete Memoryless Channel Identification","authors":"Maximilian Egger;Rawad Bitar;Antonia Wachter-Zeh;Deniz Gündüz;Nir Weinberger","doi":"10.1109/TIT.2024.3522132","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522132","url":null,"abstract":"The problem of identifying the channel with the highest capacity among several discrete memoryless channels (DMCs) is considered. The problem is cast as a pure-exploration multi-armed bandit problem, which follows the practical use of training sequences to sense the communication channel statistics. A gap-elimination algorithm termed <monospace>BestChanID</monospace> is proposed, which is oblivious to the capacity-achieving input distributions, and is guaranteed to output the DMC with the largest capacity, with a desired confidence. Furthermore, two additional algorithms <monospace>NaiveChanSel</monospace> and <monospace>MedianChanEl</monospace>, which output with certain confidence a DMC with capacity close to the maximal, are also presented. Each of these algorithms is shown to be beneficial in a different regime and can be used as a subroutine of <monospace>BestChanID</monospace>. To analyze the algorithms’ guarantees, a capacity estimator is proposed and tight confidence bounds on the estimator error are derived. Based on this estimator, the sample complexity of all the proposed algorithms is analyzed as a function of the desired confidence parameter, the number of channels, and the channels’ input and output alphabet sizes. The cost of best channel identification is shown to scale quadratically with the alphabet size, and a fundamental lower bound is derived on the number of channel senses required to identify the best channel with a certain confidence.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1248-1265"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10813602","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361252","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}