IEEE Transactions on Information Theory最新文献

{"title":"Faster List Decoding of AG Codes","authors":"Peter Beelen;Vincent Neiger","doi":"10.1109/TIT.2025.3550750","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550750","url":null,"abstract":"In this article, we present a fast algorithm performing an instance of the Guruswami-Sudan list decoder for algebraic geometry codes. We show that any such code can be decoded in <inline-formula> <tex-math>$tilde {mathcal {O}} (s^{2}ell ^{omega -1}mu ^{omega -1}(n+g) + ell ^{omega } mu ^{omega })$ </tex-math></inline-formula> operations in the underlying finite field, where <italic>n</i> is the code length, <italic>g</i> is the genus of the function field used to construct the code, <italic>s</i> is the multiplicity parameter, <inline-formula> <tex-math>$ell $ </tex-math></inline-formula> is the designed list size and <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> is the smallest positive element in the Weierstrass semigroup of some chosen place.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3397-3408"},"PeriodicalIF":2.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875156","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 Differential and Boomerang Properties of a Class of Binomials","authors":"Sihem Mesnager;Huawei Wu","doi":"10.1109/TIT.2025.3550851","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550851","url":null,"abstract":"Let <italic>q</i> be an odd prime power with <inline-formula> <tex-math>$qequiv 3 ({mathrm {mod}},4)$ </tex-math></inline-formula>. In this paper, we study the differential and boomerang properties of the function <inline-formula> <tex-math>$F_{2,u}(x)=x^{2}big (1+ueta (x)big)$ </tex-math></inline-formula> over <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$uin mathbb {F}_{q}^{*}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$eta $ </tex-math></inline-formula> is the quadratic character of <inline-formula> <tex-math>$mathbb {F}_{q}$ </tex-math></inline-formula>. We determine the differential uniformity of <inline-formula> <tex-math>$F_{2,u}$ </tex-math></inline-formula> for any <inline-formula> <tex-math>$uin mathbb {F}_{q}^{*}$ </tex-math></inline-formula>, as well as the differential spectra and boomerang uniformity of the locally-APN functions <inline-formula> <tex-math>$F_{2,pm 1}$ </tex-math></inline-formula>, thereby disproving a conjecture proposed in Budaghyan and Pal (2024), which states that there exist infinitely many values of <italic>q</i> and <italic>u</i> such that <inline-formula> <tex-math>$F_{2,u}$ </tex-math></inline-formula> is an APN function.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4854-4871"},"PeriodicalIF":2.2,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117278","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":"Optimal Linear Codes With Few Weights From Simplicial Complexes","authors":"Bing Chen;Yunge Xu;Zhao Hu;Nian Li;Xiangyong Zeng","doi":"10.1109/TIT.2025.3550182","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550182","url":null,"abstract":"Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let q be a prime power. In this paper, by using the simplicial complexes of <inline-formula> <tex-math>${mathbb {F}}_{q}^{m}$ </tex-math></inline-formula> with one single maximal element, we construct four families of linear codes over the ring <inline-formula> <tex-math>${mathbb {F}}_{q}+u{mathbb {F}}_{q}$ </tex-math></inline-formula> (<inline-formula> <tex-math>$u^{2}=0$ </tex-math></inline-formula>), which generalizes the results of Wu et al. (2020). The parameters and Lee weight distributions of these four families of codes are completely determined. Most notably, via the Gray map, we obtain several classes of optimal linear codes over <inline-formula> <tex-math>${mathbb {F}}_{q}$ </tex-math></inline-formula>, including (near) Griesmer codes and distance-optimal codes. Moreover, it is shown that most of the Gray images are minimal or self-orthogonal codes which are useful in applications.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3531-3543"},"PeriodicalIF":2.2,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875080","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 Zero-Error Capacity of Graphs With One Edge","authors":"Qi Cao;Qi Chen;Baoming Bai","doi":"10.1109/TIT.2025.3547929","DOIUrl":"https://doi.org/10.1109/TIT.2025.3547929","url":null,"abstract":"In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity. Moreover, this code can achieve zero-error capacity when the symbols in a vertex with degree one are the same. We further apply our method to the one-edge graphs representing the binary channels with two memories. There are 28 possible graphs, which can be organized into 11 categories based on their symmetries. The code constructed by our method is proved to achieve the zero-error capacity for all these graphs except for the two graphs in Case 11.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3350-3359"},"PeriodicalIF":2.2,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875187","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":"Space Complexity of Euclidean Clustering","authors":"Xiaoyi Zhu;Yuxiang Tian;Lingxiao Huang;Zengfeng Huang","doi":"10.1109/TIT.2025.3550192","DOIUrl":"https://doi.org/10.1109/TIT.2025.3550192","url":null,"abstract":"The <inline-formula> <tex-math>$(k, z)$ </tex-math></inline-formula><sc>-Clustering</small> problem in Euclidean space <inline-formula> <tex-math>$mathbb {R}^{d}$ </tex-math></inline-formula> has been extensively studied. Given the scale of data involved, compression methods for the Euclidean <inline-formula> <tex-math>$(k, z)$ </tex-math></inline-formula><sc>-Clustering</small> problem, such as data compression and dimension reduction, have received significant attention in the literature. However, the space complexity of the clustering problem, specifically, the number of bits required to compress the cost function within a multiplicative error <inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>, remains unclear in existing literature. This paper initiates the study of space complexity for Euclidean <inline-formula> <tex-math>$(k, z)$ </tex-math></inline-formula><sc>-Clustering</small> and offers both upper and lower bounds. Our space bounds are nearly tight when <italic>k</i> is constant, indicating that storing a coreset, a well-known data compression approach, serves as the optimal compression scheme. Furthermore, our lower bound result for <inline-formula> <tex-math>$(k, z)$ </tex-math></inline-formula><sc>-Clustering</small> establishes a tight space bound of <inline-formula> <tex-math>$Theta (n d)$ </tex-math></inline-formula> for terminal embedding, where <italic>n</i> represents the dataset size. Our technical approach leverages new geometric insights for principal angles and discrepancy methods, which may hold independent interest.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4515-4536"},"PeriodicalIF":2.2,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117153","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":"Binary Error-Correcting Codes With Minimal Noiseless Feedback","authors":"Meghal Gupta;Venkatesan Guruswami;Rachel Yun Zhang","doi":"10.1109/TIT.2025.3545097","DOIUrl":"https://doi.org/10.1109/TIT.2025.3545097","url":null,"abstract":"In the setting of error-correcting codes with feedback, Alice wishes to communicate a k-bit message x to Bob by sending a sequence of bits over a channel while noiselessly receiving feedback from Bob. It has been long known (Berlekamp, 1964) that in this model, Bob can still correctly determine x even if <inline-formula> <tex-math>$approx frac {1}{3}$ </tex-math></inline-formula> of Alice’s bits are flipped adversarially. This improves upon the classical setting without feedback, where recovery is not possible for error fractions exceeding <inline-formula> <tex-math>$frac {1}{4}$ </tex-math></inline-formula>. In the corresponding setting of erasures rather than bit flips, feedback improves the error resilience from <inline-formula> <tex-math>$frac {1}{2}-epsilon $ </tex-math></inline-formula> to <inline-formula> <tex-math>$1-epsilon $ </tex-math></inline-formula> for any <inline-formula> <tex-math>$epsilon gt 0$ </tex-math></inline-formula>. The original feedback setting assumes that after transmitting each bit, Alice knows (via feedback) what bit Bob received. In this work, our focus in on the limited feedback model, where Bob is only allowed to send a few bits at a small number of pre-designated points in the protocol. For any desired <inline-formula> <tex-math>$epsilon gt 0$ </tex-math></inline-formula>, we construct a coding scheme that tolerates a <inline-formula> <tex-math>$ 1/3-epsilon $ </tex-math></inline-formula> fraction of bit flips (respectively a <inline-formula> <tex-math>$1-epsilon $ </tex-math></inline-formula> fraction of erasures) relying only on <inline-formula> <tex-math>$O_{epsilon } (log k)$ </tex-math></inline-formula> bits of feedback from Bob sent in a fixed <inline-formula> <tex-math>$O_{epsilon } (1)$ </tex-math></inline-formula> number of rounds. We complement this with a matching lower bound showing that <inline-formula> <tex-math>$Omega (log k)$ </tex-math></inline-formula> bits of feedback are necessary to recover from an error fraction exceeding <inline-formula> <tex-math>$1/4$ </tex-math></inline-formula> (respectively <inline-formula> <tex-math>$1/2$ </tex-math></inline-formula> for erasures), and for schemes resilient to a <inline-formula> <tex-math>$1/3-epsilon $ </tex-math></inline-formula> fraction of bit flips (respectively a <inline-formula> <tex-math>$1-epsilon $ </tex-math></inline-formula> fraction of erasures), the number of rounds must grow as <inline-formula> <tex-math>$epsilon to 0$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3424-3446"},"PeriodicalIF":2.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875081","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":"Erasures in Channel Polarization","authors":"Mine Alsan","doi":"10.1109/TIT.2025.3549695","DOIUrl":"https://doi.org/10.1109/TIT.2025.3549695","url":null,"abstract":"The channel polarization process was introduced by Arikan as an elegant mathematical model for the study of the channel coding problem over binary-input discrete memoryless channels (B-DMCs). By studying the convergence properties of specific information measures associated to the channel polarization process, in particular the symmetric capacity and the Bhattacharyya parameter, Arikan devised the now well established polar coding error correction framework. This paper provides additional results on the convergence properties of the channel polarization process for the class of B-DMCs. In particular, we study the convergence properties of the erasure probabilities of the synthetic channels.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4125-4136"},"PeriodicalIF":2.2,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117451","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 Strong Data Processing Inequality Under the Heat Flow","authors":"Bo'az Klartag;Or Ordentlich","doi":"10.1109/TIT.2025.3548961","DOIUrl":"https://doi.org/10.1109/TIT.2025.3548961","url":null,"abstract":"Let <inline-formula> <tex-math>$nu $ </tex-math></inline-formula> and <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> be probability distributions on <inline-formula> <tex-math>$mathbb {R}^{n}$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$nu _{s},mu _{s}$ </tex-math></inline-formula> be their evolution under the heat flow, that is, the probability distributions resulting from convolving their density with the density of an isotropic Gaussian random vector with variance <italic>s</i> in each entry. This paper studies the rate of decay of <inline-formula> <tex-math>$smapsto D(nu _{s}|mu _{s})$ </tex-math></inline-formula> for various divergences, including the <inline-formula> <tex-math>$chi ^{2}$ </tex-math></inline-formula> and Kullback-Leibler (KL) divergences. We prove upper and lower bounds on the strong data-processing inequality (SDPI) coefficients corresponding to the source <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> and the Gaussian channel. We also prove generalizations of de Bruijn’s identity, and Costa’s result on the concavity in <italic>s</i> of the differential entropy of <inline-formula> <tex-math>$nu _{s}$ </tex-math></inline-formula>. As a byproduct of our analysis, we obtain new lower bounds on the mutual information between <italic>X</i> and <inline-formula> <tex-math>$Y=X+sqrt {s} Z$ </tex-math></inline-formula>, where <italic>Z</i> is a standard Gaussian vector in <inline-formula> <tex-math>$mathbb {R}^{n}$ </tex-math></inline-formula>, independent of <italic>X</i>, and on the minimum mean-square error (MMSE) in estimating <italic>X</i> from <italic>Y</i>, in terms of the Poincaré constant of <italic>X</i>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3317-3333"},"PeriodicalIF":2.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875185","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":"Exponentially Consistent Outlier Hypothesis Testing for Continuous Sequences","authors":"Lina Zhu;Lin Zhou","doi":"10.1109/TIT.2025.3548918","DOIUrl":"https://doi.org/10.1109/TIT.2025.3548918","url":null,"abstract":"In outlier hypothesis testing, one aims to detect outlying sequences among a given set of sequences, where most sequences are generated i.i.d. from a nominal distribution while outlying sequences (outliers) are generated i.i.d. from a different anomalous distribution. Most existing studies focus on discrete-valued sequences, where each data sample takes values in a finite set. To account for practical scenarios where data sequences usually take real values and the number of outlying sequence is unknown, we study outlier hypothesis testing for continuous sequences when there might exist multiple outliers, and both the nominal and anomalous distributions are <italic>unknown</i>. Specifically, we propose distribution free tests and prove that the probabilities of misclassification error, false reject and false alarm decay exponentially fast for three different test designs: fixed-length test, sequential test, and two-phase test. In a fixed-length test, one fixes the sample size of each observed sequence; in a sequential test, one takes a sample sequentially from each sequence per unit time until a reliable decision can be made; in a two-phase test, one adapts the sample size from two different fixed values. Remarkably, the two-phase test achieves a good balance between test design complexity and theoretical performance.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3287-3304"},"PeriodicalIF":2.2,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875072","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":"Memory Complexity of Estimating Entropy and Mutual Information","authors":"Tomer Berg;Or Ordentlich;Ofer Shayevitz","doi":"10.1109/TIT.2025.3547871","DOIUrl":"https://doi.org/10.1109/TIT.2025.3547871","url":null,"abstract":"We observe an infinite sequence of independent identically distributed random variables <inline-formula> <tex-math>$X_{1},X_{2},ldots $ </tex-math></inline-formula> drawn from an unknown distribution <italic>p</i> over <inline-formula> <tex-math>$[n]$ </tex-math></inline-formula>, and our goal is to estimate the entropy <inline-formula> <tex-math>$H(p)=-mathop {mathrm {mathbb {E}}}nolimits [log p(X)]$ </tex-math></inline-formula> within an <inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>-additive error. To that end, at each time point we are allowed to update a finite-state machine with <italic>S</i> states, using a possibly randomized but time-invariant rule, where each state of the machine is assigned an entropy estimate. Our goal is to characterize the minimax memory complexity <inline-formula> <tex-math>$S^{*}$ </tex-math></inline-formula> of this problem, which is the minimal number of states for which the estimation task is feasible with probability at least <inline-formula> <tex-math>$1-delta $ </tex-math></inline-formula> asymptotically, uniformly in <italic>p</i>. Specifically, we show that there exist universal constants <inline-formula> <tex-math>$C_{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$C_{2}$ </tex-math></inline-formula> such that <inline-formula> <tex-math>$ S^{*} leq C_{1}cdot frac {n (log n)^{4}}{varepsilon ^{2}delta }$ </tex-math></inline-formula> for <inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula> not too small, and <inline-formula> <tex-math>$S^{*} geq C_{2} cdot max left {{{n, frac {log n}{varepsilon }}}right }$ </tex-math></inline-formula> for <inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula> not too large. The upper bound is proved using approximate counting to estimate the logarithm of <italic>p</i>, and a finite memory bias estimation machine to estimate the expectation operation. The lower bound is proved via a reduction of entropy estimation to uniformity testing. We also apply these results to derive bounds on the memory complexity of mutual information estimation.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 5","pages":"3334-3349"},"PeriodicalIF":2.2,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875188","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}