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

Consta-Dihedral Codes and Their Asymptotic Properties Consta-Dihedral Codes及其渐近性质

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-08 DOI: 10.1109/TIT.2025.3587112

Yun Fan;Yue Leng

引用次数: 0

When Can an Expander Code Correct Ω(n) Errors in O(n) Time? 扩展器代码何时能在O(n)个时间内纠正Ω(n)个错误？

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-07 DOI: 10.1109/TIT.2025.3586842

Yuanting Shen;Chong Shangguan;Minghui Ouyang;Kuan Cheng

{"title":"When Can an Expander Code Correct Ω(n) Errors in O(n) Time?","authors":"Yuanting Shen;Chong Shangguan;Minghui Ouyang;Kuan Cheng","doi":"10.1109/TIT.2025.3586842","DOIUrl":"https://doi.org/10.1109/TIT.2025.3586842","url":null,"abstract":"Tanner codes are error-correcting codes built from a bipartite graph <italic>G and a short inner code <inline-formula> <tex-math>$C_{0}$ </tex-math></inline-formula>. Expander codes are a special type of Tanner code, where the graph is highly interconnected, ensuring stronger error correction capabilities. This paper is motivated by the following natural and fundamental problem in decoding expander codes: What are the sufficient and necessary conditions that <inline-formula> <tex-math>$delta in [{0,1}]$ </tex-math></inline-formula> and <inline-formula> <tex-math>$d_{0}in mathbb {N}$ </tex-math></inline-formula> must satisfy, so that <italic>every bipartite expander <italic>G with vertex expansion ratio <inline-formula> <tex-math>$delta $ </tex-math></inline-formula> and <italic>every linear inner code <inline-formula> <tex-math>$C_{0}$ </tex-math></inline-formula> with minimum distance <inline-formula> <tex-math>$d_{0}$ </tex-math></inline-formula> together define an expander code that corrects <inline-formula> <tex-math>$Omega (n)$ </tex-math></inline-formula> errors in <inline-formula> <tex-math>$O(n)$ </tex-math></inline-formula> time? For <inline-formula> <tex-math>$C_{0}$ </tex-math></inline-formula> being the parity-check code, the landmark work of Sipser and Spielman (IEEE-TIT’96) showed that <inline-formula> <tex-math>$delta gt 3/4$ </tex-math></inline-formula> is sufficient; later, Viderman (ACM-TOCT’13) improved this to <inline-formula> <tex-math>$delta gt 2/3-Omega (1)$ </tex-math></inline-formula> and he also showed that <inline-formula> <tex-math>$delta gt 1/2$ </tex-math></inline-formula> is necessary. For general linear code <inline-formula> <tex-math>$C_{0}$ </tex-math></inline-formula>, the previously best-known result of Dowling and Gao (IEEE-TIT’18) showed that <inline-formula> <tex-math>$d_{0}=Omega (cdelta ^{-2})$ </tex-math></inline-formula> is sufficient, where <italic>c is the left-degree of <italic>G. We present a near-optimal solution to the above problem for general <inline-formula> <tex-math>$C_{0}$ </tex-math></inline-formula> by showing that <inline-formula> <tex-math>$delta d_{0}gt 3$ </tex-math></inline-formula> is sufficient and <inline-formula> <tex-math>$delta d_{0}gt 1$ </tex-math></inline-formula> is necessary, thereby significantly improving Dowling-Gao’s result. To prove the sufficient condition, we present two novel algorithms for decoding arbitrary expander codes with <inline-formula> <tex-math>$delta d_{0}gt 3$ </tex-math></inline-formula>, where the first algorithm is deterministic, and the second one is randomized and has a larger decoding radius. To prove the necessary condition, we generalize the aforementioned necessary result of Viderman, and construct for every pair of <inline-formula> <tex-math>$delta,d_{0}$ </tex-math></inline-formula> with <inline-formula> <tex-math>$delta d_{0}=1$ </tex-math></inline-formula>, an expander code with constant distance, that only corrects a","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7626-7643"},"PeriodicalIF":2.9,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110332","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

On Signal Constellations Over Eisenstein Integers 爱森斯坦整数上的信号星座

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-07 DOI: 10.1109/TIT.2025.3586264

Abdul Hadi;Uha Isnaini;Indah Emilia Wijayanti;Martianus Frederic Ezerman

引用次数: 0

r-Minimal Codes With Respect to Rank Metric 关于秩度量的r-最小码

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-04 DOI: 10.1109/TIT.2025.3585604

Yang Xu;Haibin Kan;Guangyue Han

{"title":"r-Minimal Codes With Respect to Rank Metric","authors":"Yang Xu;Haibin Kan;Guangyue Han","doi":"10.1109/TIT.2025.3585604","DOIUrl":"https://doi.org/10.1109/TIT.2025.3585604","url":null,"abstract":"In this paper, we propose and study <italic>r-minimal codes, a natural extension of minimal codes which have been extensively studied with respect to Hamming metric, rank metric and sum-rank metric. We first propose <italic>r-minimal codes in a general setting where the ambient space is a finite dimensional left module over a division ring and is supported on a lattice. We characterize minimal subcodes and <italic>r-minimal codes, derive a general singleton bound, and give existence results for <italic>r-minimal codes by using combinatorial arguments. We then consider <italic>r-minimal rank metric codes over a field extension <inline-formula> <tex-math>$mathbb {E}/mathbb {F}$ </tex-math></inline-formula> of degree <italic>m, where <inline-formula> <tex-math>$mathbb {E}$ </tex-math></inline-formula> can be infinite unless otherwise specified. We characterize these codes in terms of cutting <italic>r-blocking sets, generalized rank weights of the codes and those of the dual codes, and classify codes whose <italic>r-dimensional subcodes have constant rank support weight. Next, with the help of the evasiveness property of cutting <italic>r-blocking sets and some upper bounds for the dimensions of evasive subspaces, we derive several lower and upper bounds for the minimal length of <italic>r-minimal codes. Furthermore, when <inline-formula> <tex-math>$mathbb {E}$ </tex-math></inline-formula> is finite, we establish a general upper bound which generalizes and improves the counterpart for minimal codes in the literature. As a corollary, we show that if <inline-formula> <tex-math>$m=3$ </tex-math></inline-formula>, then for any <inline-formula> <tex-math>$kgeqslant 2$ </tex-math></inline-formula>, the minimal length of <italic>k-dimensional minimal codes is equal to <inline-formula> <tex-math>$2k$ </tex-math></inline-formula>. To the best of our knowledge, when <inline-formula> <tex-math>$mgeqslant 3$ </tex-math></inline-formula>, there is no known explicit formula for the minimal length of <italic>k-dimensional minimal codes for arbitrary <italic>k in the literature.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6692-6711"},"PeriodicalIF":2.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892402","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

Permutation and Multi-Permutation Codes Correcting Multiple Deletions 纠正多重删除的排列和多排列代码

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-04 DOI: 10.1109/TIT.2025.3585691

Shuche Wang;The Nguyen;Yeow Meng Chee;Van Khu Vu

{"title":"Permutation and Multi-Permutation Codes Correcting Multiple Deletions","authors":"Shuche Wang;The Nguyen;Yeow Meng Chee;Van Khu Vu","doi":"10.1109/TIT.2025.3585691","DOIUrl":"https://doi.org/10.1109/TIT.2025.3585691","url":null,"abstract":"Permutation codes in the Ulam metric, which can correct multiple deletions, have been investigated extensively recently. In this work, we are interested in the maximum size of permutation codes in the Ulam metric and aim to design permutation codes that can correct multiple deletions with efficient decoding algorithms. We first present an improvement on the Gilbert-Varshamov bound of the maximum size of these permutation codes by analyzing the independence number of the auxiliary graph. The idea is widely used in various cases and our contribution in this section is to enumerate the number of triangles in the auxiliary graph and show that it is small enough. Next, we design permutation codes correcting multiple deletions with a decoding algorithm. In particular, the constructed permutation codes can correct <italic>t deletions with at most <inline-formula> <tex-math>$(3t-1) log (n+1)+o(log n)$ </tex-math></inline-formula> bits of redundancy where <italic>n is the length of the code. Our construction is based on a new mapping that yields a new connection between permutation codes in the Hamming metric and permutation codes in various metrics. Furthermore, we construct permutation codes that correct multiple bursts of deletions using this new mapping. Finally, we extend the new mapping for multi-permutations and construct the best-known multi-permutation codes in the Ulam metric.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6759-6770"},"PeriodicalIF":2.9,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892346","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

Multi-Threshold AoII-Optimum Sampling Policies for Continuous-Time Markov Chain Information Sources 连续时间马尔可夫链信息源的多阈值aoii最优抽样策略

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-03 DOI: 10.1109/TIT.2025.3573640

Ismail Cosandal;Nail Akar;Sennur Ulukus

{"title":"Multi-Threshold AoII-Optimum Sampling Policies for Continuous-Time Markov Chain Information Sources","authors":"Ismail Cosandal;Nail Akar;Sennur Ulukus","doi":"10.1109/TIT.2025.3573640","DOIUrl":"https://doi.org/10.1109/TIT.2025.3573640","url":null,"abstract":"We study push-based sampling and transmission policies for a status update system consisting of a general finite-state continuous-time Markov chain (CTMC) information source with known dynamics, with the goal of minimizing the average age of incorrect information (AoII) defined via a linear time penalty function. The problem setting we investigate involves an exponentially distributed delay channel for transmissions and a constraint on the average sampling rate. We first show that the optimum sampling and transmission policy is a <italic>multi-threshold policy, where the thresholds depend on both the estimation value and the state of the original process, and sampling and transmission need to be initiated when the instantaneous AoII exceeds the corresponding threshold, called the estimation- and state-aware transmission (ESAT) policy. Subsequently, we formulate the problem of finding the thresholds as a constrained semi-Markov decision process (CSMDP) and the Lagrangian approach. Additionally, we propose two lower complexity sub-optimum policies, namely the estimation-aware transmission (EAT) policy, and the single-threshold (ST) policy, for which it is possible to obtain these thresholds for CTMCs with relatively larger number of states. The underlying CSMDP formulation relies on the <italic>multi-regime phase-type (MR-PH) distribution which is a generalization of the well-known phase-type distribution, which allows us to obtain the first two moments of time until absorption in a CTMC whose transition rates change with respect to time, in a piece-wise manner. The effectiveness of the proposed ESAT, EAT, and ST sampling and transmission policies are shown through numerical examples, along with comparisons with a baseline scheme that transmits packets according to a Poisson process in out-of-sync periods.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6968-6988"},"PeriodicalIF":2.9,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891088","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

A Provable Initialization and Robust Clustering Method for General Mixture Models 一种可证明的通用混合模型初始化和鲁棒聚类方法

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-03 DOI: 10.1109/TIT.2025.3585804

Soham Jana;Jianqing Fan;Sanjeev Kulkarni

{"title":"A Provable Initialization and Robust Clustering Method for General Mixture Models","authors":"Soham Jana;Jianqing Fan;Sanjeev Kulkarni","doi":"10.1109/TIT.2025.3585804","DOIUrl":"https://doi.org/10.1109/TIT.2025.3585804","url":null,"abstract":"Clustering is a fundamental tool in statistical machine learning in the presence of heterogeneous data. Most recent results focus primarily on optimal mislabeling guarantees when data are distributed around centroids with sub-Gaussian errors. Yet, the restrictive sub-Gaussian model is often invalid in practice, since various real-world applications exhibit heavy-tail distributions around the centroids or suffer from possible adversarial attacks that call for robust clustering with a robust data-driven initialization. In this paper, we present initialization and subsequent clustering methods that provably guarantee near-optimal mislabeling for general mixture models when the number of clusters and data dimensions are finite. We first introduce a hybrid clustering technique with a novel multivariate trimmed mean type centroid estimate to produce mislabeling guarantees under a weak initialization condition for general error distributions around the centroids. A matching lower bound is derived, up to factors depending on the number of clusters. In addition, our approach also produces similar mislabeling guarantees even in the presence of adversarial outliers. Our results reduce to the sub-Gaussian case in finite dimensions when errors follow sub-Gaussian distributions. To solve the problem thoroughly, we also present novel data-driven robust initialization techniques and show that, with probabilities approaching one, these initial centroid estimates are sufficiently good for the subsequent clustering algorithm to achieve the optimal mislabeling rates. Furthermore, we demonstrate that Lloyd’s algorithm is suboptimal for more than two clusters even when errors are Gaussian and for two clusters when error distributions have heavy tails. Both simulated data and real data examples further support our robust initialization procedure and clustering algorithm.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7176-7207"},"PeriodicalIF":2.9,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891179","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

On the Cost of Consecutive Estimation Error: Significance-Aware Non-Linear Aging 连续估计误差的代价：意义感知非线性老化

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-03 DOI: 10.1109/TIT.2025.3585733

Jiping Luo;Nikolaos Pappas

{"title":"On the Cost of Consecutive Estimation Error: Significance-Aware Non-Linear Aging","authors":"Jiping Luo;Nikolaos Pappas","doi":"10.1109/TIT.2025.3585733","DOIUrl":"https://doi.org/10.1109/TIT.2025.3585733","url":null,"abstract":"This paper considers the semantics-aware remote state estimation of an asymmetric Markov chain with <italic>prioritized states. Due to resource constraints, the sensor needs to trade off estimation quality against communication cost. The aim is to exploit the <italic>significance of information through the history of system realizations to determine the optimal timing of transmission, thereby reducing the amount of uninformative data transmitted in the network. To this end, we introduce a new metric, the <italic>significance-aware Age of Consecutive Error (AoCE), that captures three semantic attributes: the <italic>significance of estimation error, the <italic>cost of consecutive error (or <italic>lasting impact, for short), and the <italic>urgency of lasting impact. Different costs and non-linear age functions are assigned to different estimation errors to account for their relative importance to system performance. We identify the optimal transmission problem as a countably infinite state Markov decision process (MDP) with unbounded costs. We first give sufficient conditions on the age functions, source pattern, and channel reliability so that an optimal policy exists to have bounded average costs. We show that the optimal policy exhibits a <italic>switching structure. That is, the sensor triggers a transmission only when the system has been trapped in an error for a certain number of consecutive time slots. We also provide sufficient conditions under which the switching policy degenerates into a simple <italic>threshold policy, i.e., featuring identical thresholds for all estimation errors. Furthermore, we exploit the structural results and develop a <italic>structured policy iteration (SPI) algorithm that considerably reduces computation overhead. Numerical results show that the optimal policy outperforms the classic rule-, distortion- and age-based policies. An important takeaway is that <italic>the more semantic attributes we utilize, the fewer transmissions are needed.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7976-7989"},"PeriodicalIF":2.9,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110286","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

Next-Token Prediction Capacity: General Upper Bounds and a Lower Bound for Transformers 下一个令牌预测能力：变压器的一般上界和下界

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-02 DOI: 10.1109/TIT.2025.3584013

Liam Madden;Curtis Fox;Christos Thrampoulidis

引用次数: 0

Two-Insertion/Deletion/Substitution Correcting Codes 双插入/删除/替换纠错码

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-02 DOI: 10.1109/TIT.2025.3584987

Yuhang Pi;Zhifang Zhang

引用次数: 0