IEEE Transactions on Information Theory最新文献

{"title":"Robust Offline Reinforcement Learning for Non-Markovian Decision Processes","authors":"Ruiquan Huang;Yingbin Liang;Jing Yang","doi":"10.1109/TIT.2025.3587509","DOIUrl":"https://doi.org/10.1109/TIT.2025.3587509","url":null,"abstract":"Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in robust RL focus on Markov decision processes (MDPs), robust non-Markovian RL is limited to planning problem where the transitions in the uncertainty set are known. In this paper, we study the learning problem of robust offline non-Markovian RL. Specifically, when the nominal model admits a low-rank structure, we propose a new algorithm, featuring a novel dataset distillation and a lower confidence bound (LCB) design for robust values under different types of the uncertainty set. We also derive new dual forms for these robust values in non-Markovian RL, making our algorithm more amenable to practical implementation. By further introducing a novel type-I concentrability coefficient tailored for offline low-rank non-Markovian decision processes, we prove that our algorithm can find an <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>-optimal robust policy using <inline-formula> <tex-math>$O(1/epsilon ^{2})$ </tex-math></inline-formula> offline samples. Moreover, we extend our algorithm to the case when the nominal model does not have specific structure. With a new type-II concentrability coefficient, the extended algorithm also enjoys polynomial sample efficiency under all different types of the uncertainty set.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7208-7228"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891181","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":"Computationally Efficient Reductions Between Some Statistical Models","authors":"Mengqi Lou;Guy Bresler;Ashwin Pananjady","doi":"10.1109/TIT.2025.3587354","DOIUrl":"https://doi.org/10.1109/TIT.2025.3587354","url":null,"abstract":"We study the problem of approximately transforming a sample from a source statistical model to a sample from a target statistical model without knowing the parameters of the source model, and construct several computationally efficient such reductions between canonical statistical experiments. In particular, we provide computationally efficient procedures that approximately reduce uniform, Erlang, and Laplace location models to general target families. We illustrate our methodology by establishing nonasymptotic reductions between some canonical high-dimensional problems, spanning mixtures of experts, phase retrieval, and signal denoising. Notably, the reductions are structure-preserving and can accommodate missing data. We also point to a possible application in transforming one differentially private mechanism to another.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7097-7133"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891166","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":"Continuity Bounds for Quantum Entropies Arising From a Fundamental Entropic Inequality","authors":"Koenraad Audenaert;Bjarne Bergh;Nilanjana Datta;Michael G. Jabbour;Ángela Capel;Paul Gondolf","doi":"10.1109/TIT.2025.3586478","DOIUrl":"https://doi.org/10.1109/TIT.2025.3586478","url":null,"abstract":"We establish a tight upper bound for the difference in von Neumann entropies between two quantum states, <inline-formula> <tex-math>$rho _{1}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$rho _{2}$ </tex-math></inline-formula>. This bound is expressed in terms of the von Neumann entropies of the mutually orthogonal states derived from the Jordan-Hahn decomposition of the difference operator <inline-formula> <tex-math>$(rho _{1} - rho _{2})$ </tex-math></inline-formula>. This yields a novel entropic inequality that implies the well-known Audenaert-Fannes (AF) inequality. In fact, it also leads to a refinement of the AF inequality. We employ this inequality to obtain a uniform continuity bound for the quantum conditional entropy of two states whose marginals on the conditioning system coincide. We additionally use it to derive a continuity bound for the quantum relative entropy in both variables. Interestingly, the fundamental entropic inequality is also valid in infinite dimensions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7029-7038"},"PeriodicalIF":2.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891163","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":"Consta-Dihedral Codes and Their Asymptotic Properties","authors":"Yun Fan;Yue Leng","doi":"10.1109/TIT.2025.3587112","DOIUrl":"https://doi.org/10.1109/TIT.2025.3587112","url":null,"abstract":"It is proved in a reference (Fan, Lin, IEEE TIT, vol.67, pp.5016-5025) that the self-dual (LCD respectively) dihedral codes over a finite field <italic>F</i> with <inline-formula> <tex-math>$|F|=q$ </tex-math></inline-formula> are asymptotically good if <italic>q</i> is even (odd respectively). In this paper, we investigate the algebraic structures and the asymptotic properties of consta-dihedral codes over <italic>F</i>, and show that: if <italic>q</i> is even or <inline-formula> <tex-math>$4,|,(q-1)$ </tex-math></inline-formula>, then the self-dual consta-dihedral codes are asymptotically good; otherwise, the LCD consta-dihedral codes are asymptotically good. And, with the help of a technique developed in this paper, some errors in the reference mentioned above are corrected.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6785-6800"},"PeriodicalIF":2.9,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892352","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 Signal Constellations Over Eisenstein Integers","authors":"Abdul Hadi;Uha Isnaini;Indah Emilia Wijayanti;Martianus Frederic Ezerman","doi":"10.1109/TIT.2025.3586264","DOIUrl":"https://doi.org/10.1109/TIT.2025.3586264","url":null,"abstract":"We propose constructions of signal constellations over quotient rings of Eisenstein integers equipped with the Euclidean, square Euclidean, and hexagonal distances as a generalization of those over Eisenstein integer fields. By set partitioning, we effectively divide the quotient ring of Eisenstein integers into equal-sized subsets for distinct encoding. Unlike in Eisenstein integer fields where partitioning is not feasible due to structural limitations, we can partition the quotient rings into additive subgroups in such a way that the minimum squared Euclidean and hexagonal distances of each subgroup are strictly larger than in the original set. This technique facilitates multilevel coding and enhances signal constellation efficiency.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6801-6819"},"PeriodicalIF":2.9,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892347","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":"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</i>-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</i>-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</i>-minimal codes, derive a general singleton bound, and give existence results for <italic>r</i>-minimal codes by using combinatorial arguments. We then consider <italic>r</i>-minimal rank metric codes over a field extension <inline-formula> <tex-math>$mathbb {E}/mathbb {F}$ </tex-math></inline-formula> of degree <italic>m</i>, 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</i>-blocking sets, generalized rank weights of the codes and those of the dual codes, and classify codes whose <italic>r</i>-dimensional subcodes have constant rank support weight. Next, with the help of the evasiveness property of cutting <italic>r</i>-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</i>-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</i>-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</i>-dimensional minimal codes for arbitrary <italic>k</i> 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}

{"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</i> 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</i> 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}

{"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</i> 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</i> (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}

{"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}

{"title":"Next-Token Prediction Capacity: General Upper Bounds and a Lower Bound for Transformers","authors":"Liam Madden;Curtis Fox;Christos Thrampoulidis","doi":"10.1109/TIT.2025.3584013","DOIUrl":"https://doi.org/10.1109/TIT.2025.3584013","url":null,"abstract":"Given a sequence of tokens, such as words, the task of next-token prediction is to predict the next-token conditional probability distribution. Decoder-only transformers have become effective models for this task, but their properties are still not fully understood. In particular, the largest number of distinct context sequences that a decoder-only transformer can interpolate next-token distributions for has not been established. To fill this gap, we prove upper and lower bounds on this number, which are equal up to a multiplicative constant. We prove these bounds in the general setting where next-token distributions can be arbitrary as well as the empirical setting where they are calculated from a finite number of document sequences. Our lower bounds are for one-layer multi-head decoder-only transformers and our proofs highlight an important injectivity property satisfied by self-attention. Furthermore, we provide numerical evidence that the minimal number of parameters for memorization is sufficient for being able to train the model to the entropy lower bound.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7134-7148"},"PeriodicalIF":2.9,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891182","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}