IEEE Transactions on Information Theory最新文献

{"title":"The b-Symbol Hamming Weight Spectra of Quaternary Kerdock Codes and Related Codes","authors":"Hongwei Zhu;Xiaoxiao Li;Minjia Shi;Shu-Tao Xia;Tor Helleseth","doi":"10.1109/TIT.2025.3590510","DOIUrl":"https://doi.org/10.1109/TIT.2025.3590510","url":null,"abstract":"The symbol-pair coding theory was put forward by Cassuto and Blaum [IEEE TIT, 2011] to be applicable in high-density storage situations. Yaakobi et al. [IEEE TIT, 2016] extended the concept of symbol-pair metric to <italic>b</i>-symbol metric when <inline-formula> <tex-math>$bgeq 2$ </tex-math></inline-formula>. The extensive research on the <italic>b</i>-symbol Hamming weight spectra of cyclic codes has been centered on the case where the alphabet is a finite field. The case of cyclic codes over <inline-formula> <tex-math>${mathbb {Z}}_{4}$ </tex-math></inline-formula>, an extremely important class of codes, has been overlooked for a long time in the exploration of the <italic>b</i>-symbol Hamming weight spectra. In this paper, we study the <italic>b</i>-symbol Hamming weight spectra of the shortened Kerdock codes <inline-formula> <tex-math>${mathcal {K}}_{m}^{-}$ </tex-math></inline-formula> and the Kerdock codes <inline-formula> <tex-math>${mathcal {K}}_{m}$ </tex-math></inline-formula> over <inline-formula> <tex-math>${mathbb {Z}}_{4}$ </tex-math></inline-formula>. The formulas for calculating the symbol-pair Hamming weight of the codewords in <inline-formula> <tex-math>${mathcal {K}}_{m}^{-}$ </tex-math></inline-formula> and <inline-formula> <tex-math>${mathcal {K}}_{m}$ </tex-math></inline-formula> are given, and their values hinge on the trace-like function values of specific elements in the Teichmüller set. In particular, we present a class of <inline-formula> <tex-math>${mathbb {Z}}_{4}$ </tex-math></inline-formula>-cyclic codes with three non-zero <italic>b</i>-symbol Hamming weights. As by-products, the <italic>b</i>-symbol Hamming weight hierarchies of the Preparata codes and the Goethals codes are provided.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6727-6742"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892345","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":"Vers: Coded Computing System With Distributed Encoding","authors":"Nastaran Abadi Khooshemehr;Mohammad Ali Maddah-Ali","doi":"10.1109/TIT.2025.3591523","DOIUrl":"https://doi.org/10.1109/TIT.2025.3591523","url":null,"abstract":"Coded computing has proved to be useful in distributed computing, and has addressed challenges such as straggler workers. We have observed that almost all coded computing systems studied so far consider a setup of one leader and some workers. However, recently emerging technologies such as blockchain, internet of things, and federated learning introduce new requirements for coded computing systems. In these systems, data is generated (and probably stored) in a distributed manner, so central encoding/decoding by a leader is not feasible and scalable. This paper presents a multi-leader distributed coded computing system that consists of <inline-formula> <tex-math>$kin mathbb {N}$ </tex-math></inline-formula> data owners and <inline-formula> <tex-math>$Nin mathbb {N}$ </tex-math></inline-formula> workers, where data owners employ workers to do some computations on their data, as specified by a target function <italic>f</i> of degree <inline-formula> <tex-math>$din mathbb {N}$ </tex-math></inline-formula>. As there is no central encoder, workers perform encoding themselves, prior to computation phase. The challenge in this system is the presence of adversarial data owners that do not know the data of honest data owners but cause discrepancies by sending different versions of data to different workers, which is detrimental to local encodings in workers. There are at most <inline-formula> <tex-math>$beta in mathbb {N}$ </tex-math></inline-formula> adversarial data owners, and each distributes at most <inline-formula> <tex-math>$vin mathbb {N}$ </tex-math></inline-formula> different versions of data. Since the adversaries and their possibly colluded behavior are not known to workers and honest data owners, workers compute tags of their received data, in addition to their main computational task, and send them to data owners in order to help them in decoding. We introduce a tag function that allows data owners to partition workers into sets that previously had received the same data from all data owners. Then, we characterize the fundamental limit of this multi-leader distributed coded computing system, denoted by <inline-formula> <tex-math>$t^{*}$ </tex-math></inline-formula>, which is the minimum number of workers whose work can be used to correctly calculate the desired function of data of honest data owners. We show that <inline-formula> <tex-math>$t^{*}=v^{beta }d(K-1)+1$ </tex-math></inline-formula>, and present converse and achievable proofs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7609-7625"},"PeriodicalIF":2.9,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110304","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 Intersection of Two Generalized Reed-Solomon Codes","authors":"Jingge Liu;Bocong Chen","doi":"10.1109/TIT.2025.3591269","DOIUrl":"https://doi.org/10.1109/TIT.2025.3591269","url":null,"abstract":"In this paper, we show that, algebraically, the intersection of two GRS codes is a direct sum of some like-generalized Reed-Solomon codes, and that the dimension of such code can be given via the dimensions of the GRS codes and the degrees of some relevant polynomials. We also provide a necessary and sufficient condition for this intersection to be a GRS code. Our results naturally extend the main results on the hulls of GRS codes from existing literature. Particularly, we deterministically construct two GRS codes with given code length, dimensions, and intersection dimension. As an application of our main results, we derive the algebraic structure of the hull of a GRS code and exhibit a necessary and sufficient condition for the hull to be a GRS code. In addition, we discuss when a GRS code is self-orthogonal or dual-containing and when the hull of an RS code is again an RS code. Finally, as an application, we resolve the problem of explicit construction of MDS entanglement-assisted quantum error-correcting codes (EAQECCs) from classical codes for <inline-formula> <tex-math>$n leq q$ </tex-math></inline-formula>. Several examples are included to illustrate our results.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7595-7608"},"PeriodicalIF":2.9,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110265","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":"CP-OFDM Achieves the Lowest Average Ranging Sidelobe Under QAM/PSK Constellations","authors":"Fan Liu;Ying Zhang;Yifeng Xiong;Shuangyang Li;Weijie Yuan;Feifei Gao;Shi Jin;Giuseppe Caire","doi":"10.1109/TIT.2025.3591267","DOIUrl":"https://doi.org/10.1109/TIT.2025.3591267","url":null,"abstract":"This paper aims to answer a fundamental question in the area of Integrated Sensing and Communications (ISAC): <italic>What is the optimal communication-centric ISAC waveform for ranging?</i> Towards that end, we first established a generic framework to analyze the sensing performance of communication-centric ISAC waveforms built upon orthonormal signaling bases and random data symbols. Then, we evaluated their ranging performance by adopting both the periodic and aperiodic auto-correlation functions (P-ACF and A-ACF), and defined the expectation of the integrated sidelobe level (EISL) as a sensing performance metric. On top of that, we proved that among all communication waveforms with cyclic prefix (CP), the orthogonal frequency division multiplexing (OFDM) modulation is the only globally optimal waveform that achieves the lowest ranging sidelobe for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations, in terms of both the EISL and the sidelobe level at each individual lag of the P-ACF. As a step forward, we proved that among all communication waveforms without CP, OFDM is a locally optimal waveform for QAM/PSK in the sense that it achieves a local minimum of the EISL of the A-ACF. Finally, we demonstrated by numerical results that under QAM/PSK constellations, there is no other orthogonal communication-centric waveform that achieves a lower ranging sidelobe level than that of the OFDM, in terms of both P-ACF and A-ACF cases.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6950-6967"},"PeriodicalIF":2.9,"publicationDate":"2025-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11087656","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891085","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":"Gram–Schmidt Methods for Unsupervised Feature Extraction and Selection","authors":"Bahram Yaghooti;Netanel Raviv;Bruno Sinopoli","doi":"10.1109/TIT.2025.3589174","DOIUrl":"https://doi.org/10.1109/TIT.2025.3589174","url":null,"abstract":"Feature extraction and selection in the presence of nonlinear dependencies among the data is a fundamental challenge in unsupervised learning. We propose using a Gram-Schmidt (GS) type orthogonalization process over function spaces to detect and map out such dependencies. Specifically, by applying the GS process over some family of functions, we construct a series of covariance matrices that can either be used to identify new large-variance directions, or to remove those dependencies from known directions. In the former case, we provide information-theoretic guarantees in terms of entropy reduction. In the latter, we provide precise conditions by which the chosen function family eliminates existing redundancy in the data. Each approach provides both a feature extraction and a feature selection algorithm. Our feature extraction methods are linear, and can be seen as natural generalization of principal component analysis (PCA). We provide experimental results for synthetic and real-world benchmark datasets which show superior performance over state-of-the-art (linear) feature extraction and selection algorithms. Surprisingly, our linear feature extraction algorithms are comparable and often outperform several important nonlinear feature extraction methods such as autoencoders, kernel PCA, and UMAP. Furthermore, one of our feature selection algorithms strictly generalizes a recent Fourier-based feature selection mechanism (Heidari et al., IEEE Transactions on Information Theory, 2022), yet at significantly reduced complexity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7856-7885"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110283","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":"Two Classes of Reducible Cyclic Codes With Large Minimum Symbol-Pair Distances","authors":"Xiaoqiang Wang;Yue Su;Dabin Zheng;Wei Lu","doi":"10.1109/TIT.2025.3589258","DOIUrl":"https://doi.org/10.1109/TIT.2025.3589258","url":null,"abstract":"Motivated by high-density storage needs, symbol-pair codes were introduced by Cassuto and Blaum to address channels with overlapping symbol outputs. In this paper, we present a systematic study of two families of reducible cyclic codes under the symbol-pair metric. By employing analytical techniques rooted in cyclotomic numbers and Gaussian period theory over finite fields, we characterize the admissible symbol-pair weights of these codes. Significantly, we demonstrate that their minimum symbol-pair distances attain twice the minimum Hamming distances under specific algebraic constraints. Furthermore, we identify and rigorously determine the symbol-pair weight distributions for several three-weight code families. Notably, we construct a class of MDS symbol-pair codes that achieve optimal distance parameters by the puncturing technique. As supplementary contributions, the paper resolves several computational problems concerning generalized cyclotomic numbers, thereby enriching the mathematical foundation for code parameter analysis.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6626-6640"},"PeriodicalIF":2.9,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892381","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":"An Efficient Parameterized Algorithm for Computing Quantum Channel Fidelity via Symmetries Exploitation","authors":"Yeow Meng Chee;Hoang Ta;Van Khu Vu","doi":"10.1109/TIT.2025.3589660","DOIUrl":"https://doi.org/10.1109/TIT.2025.3589660","url":null,"abstract":"Determining the optimal fidelity for the transmission of quantum information over noisy quantum channels is one of the central problems in quantum information theory. Recently, [Berta-Borderi-Fawzi-Scholz, Mathematical Programming, 2021] introduced an asymptotically converging semidefinite programming hierarchy of outer bounds for this quantity. However, the size of the semidefinite programs (SDPs) grows exponentially with respect to the level of the hierarchy, thus making their computation unscalable. In this work, by exploiting the symmetries in the SDP, we show that, for a fixed output dimension of the quantum channel, we can compute the SDP in time polynomial with respect to the level of the hierarchy and input dimension. As a direct consequence of our result, the optimal fidelity can be approximated with an accuracy of <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> in <inline-formula> <tex-math>$mathrm {poly}(1/epsilon, text {input dimension})$ </tex-math></inline-formula> time, compared to the <inline-formula> <tex-math>$exp (1/epsilon, text {input dimension})$ </tex-math></inline-formula> running time required for direct computation.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7003-7015"},"PeriodicalIF":2.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891087","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":"Bounds on Covert Capacity With Sub-Exponential Random Slot Selection","authors":"Shi-Yuan Wang;Keerthi Suria Kumar Arumugam;Matthieu R. Bloch","doi":"10.1109/TIT.2025.3589575","DOIUrl":"https://doi.org/10.1109/TIT.2025.3589575","url":null,"abstract":"We consider the problem of covert communication with random slot selection over binary-input Discrete Memoryless Channels (DMCs) and Additive White Gaussian Noise (AWGN) channels, in which a transmitter attempts to reliably communicate with a legitimate receiver while simultaneously maintaining covertness with respect to (w.r.t.) an eavesdropper. Covertness refers to the inability of the eavesdropper to distinguish the transmission of a message from the absence of communication, modeled by the transmission of a fixed channel input. Random slot selection refers to the transmitter’s ability to send a codeword in a time slot with known boundaries selected uniformly at random among a predetermined number of slots. Our main contribution is to develop bounds for the information-theoretic limit of communication in this model, called the covert capacity, when the number of time slots scales sub-exponentially with the codeword length. Our upper and lower bounds for the covert capacity are within a multiplicative factor of <inline-formula> <tex-math>$sqrt {2}$ </tex-math></inline-formula> independent of the channel. This result partially fills a characterization gap between the covert capacity without random slot selection and the covert capacity with random selection among an exponential number of slots in the codeword length. Our key technical contributions consist of 1) a tight upper bound for the relative entropy characterizing the effect of random slot selection on the covertness constraint in our achievability proof; 2) a careful converse analysis to characterize the maximum allowable weight or power of codewords to meet the covertness constraint. Our results suggest that, unlike the case without random slot selection, the choice of covertness metric does not change the covert capacity in the presence of random slot selection.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6586-6601"},"PeriodicalIF":2.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892392","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":"Quickest Change Detection for Multiple Data Streams Using the James–Stein Estimator","authors":"Topi Halme;Venugopal V. Veeravalli;Visa Koivunen","doi":"10.1109/TIT.2025.3588661","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588661","url":null,"abstract":"The problem of quickest change detection is studied in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams. The James-Stein estimator is used in constructing detection schemes that exhibit strong detection performance both asymptotically and non-asymptotically. Our results indicate that utilizing the James-Stein estimator in the recently developed window-limited CuSum test constitutes a uniform improvement over its typical maximum likelihood variant. That is, the proposed James-Stein version achieves a smaller detection delay simultaneously for all possible post-change parameter values and every false alarm rate constraint, as long as the number of parallel data streams is greater than three. Additionally, an alternative detection procedure that utilizes the James-Stein estimator is shown to have asymptotic detection delay properties that compare favorably to existing tests. The second-order asymptotic detection delay term is reduced in a predefined low-dimensional subspace of the parameter space, while second-order asymptotic minimaxity is preserved. The results are verified in simulations, where the proposed schemes are shown to achieve smaller detection delays compared to existing alternatives, especially when the number of data streams is large.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7802-7814"},"PeriodicalIF":2.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11079727","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110294","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":"On the Convergence of (Stochastic) Gradient Descent for Kolmogorov–Arnold Networks","authors":"Yihang Gao;Vincent Y. F. Tan","doi":"10.1109/TIT.2025.3588401","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588401","url":null,"abstract":"Kolmogorov–Arnold Networks (KANs), a recently proposed neural network architecture, have gained significant attention in the deep learning community, due to their potential as a viable alternative to multi-layer perceptrons (MLPs) and their broad applicability to various scientific tasks. Empirical investigations demonstrate that KANs optimized via stochastic gradient descent (SGD) are capable of achieving near-zero training loss in various machine learning (e.g., regression, classification, and time series forecasting, etc.) and scientific tasks (e.g., solving partial differential equations). In this paper, we provide a theoretical explanation for the empirical success by conducting a rigorous convergence analysis of gradient descent (GD) and SGD for two-layer KANs in solving both regression and physics-informed tasks. For regression problems, we establish using the neural tangent kernel perspective that GD achieves global linear convergence of the objective function when the hidden dimension of KANs is sufficiently large. We further extend these results to SGD, demonstrating a similar global convergence in expectation. Additionally, we analyze the global convergence of GD and SGD for physics-informed KANs, which unveils additional challenges due to the more complex loss structure. This is the first work establishing the global convergence guarantees for GD and SGD applied to optimize KANs and physics-informed KANs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7270-7291"},"PeriodicalIF":2.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891183","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}