IEEE Transactions on Information Theory最新文献

{"title":"Tessellated Distributed Computing","authors":"Ali Khalesi;Petros Elia","doi":"10.1109/TIT.2025.3556384","DOIUrl":"https://doi.org/10.1109/TIT.2025.3556384","url":null,"abstract":"The work considers the <italic>N</i>-server distributed computing scenario with <italic>K</i> users requesting functions that are linearly-decomposable over an arbitrary basis of <italic>L</i> real (potentially non-linear) subfunctions. In our problem, the aim is for each user to receive their function outputs, allowing for reduced reconstruction error (distortion) <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>, reduced computing cost (<inline-formula> <tex-math>$gamma $ </tex-math></inline-formula>; the fraction of subfunctions each server must compute), and reduced communication cost (<inline-formula> <tex-math>$delta $ </tex-math></inline-formula>; the fraction of users each server must connect to). For any given set of <italic>K</i> requested functions — which is here represented by a coefficient matrix <inline-formula> <tex-math>$mathbf {F} in mathbb {R}^{K times L}$ </tex-math></inline-formula> — our problem is made equivalent to the open problem of sparse matrix factorization that seeks — for a given parameter <italic>T</i>, representing the number of shots for each server — to minimize the reconstruction distortion <inline-formula> <tex-math>$frac {1}{KL}|mathbf {F} - mathbf {D}mathbf {E}|^{2}_{F}$ </tex-math></inline-formula> over all <inline-formula> <tex-math>$delta $ </tex-math></inline-formula>-sparse and <inline-formula> <tex-math>$gamma $ </tex-math></inline-formula>-sparse matrices <inline-formula> <tex-math>$mathbf {D}in mathbb {R}^{K times NT}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$mathbf {E} in mathbb {R}^{NT times L}$ </tex-math></inline-formula>. With these matrices respectively defining which servers compute each subfunction, and which users connect to each server, we here design our <inline-formula> <tex-math>$mathbf {D},mathbf {E}$ </tex-math></inline-formula> by designing tessellated-based and SVD-based fixed support matrix factorization methods that first split F into properly sized and carefully positioned submatrices, which we then approximate and then decompose into properly designed submatrices of D and E. For the zero-error case and under basic dimensionality assumptions, the work reveals achievable computation-vs-communication corner points <inline-formula> <tex-math>$(gamma ,delta)$ </tex-math></inline-formula> which, for various cases, are proven optimal over a large class of <inline-formula> <tex-math>$mathbf {D},mathbf {E}$ </tex-math></inline-formula> by means of a novel tessellations-based converse. Subsequently, for large <italic>N</i>, and under basic statistical assumptions on F, the average achievable error <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> is concisely expressed using the incomplete first moment of the standard Marchenko-Pastur distribution, where this performance is shown to be optimal over a large class of D and E. In the end, the work also reveals that the overall achieved gains over baseline methods are unbounded.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4754-4784"},"PeriodicalIF":2.2,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117279","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":"Soft Decision Decoding of Recursive Plotkin Constructions Based on Hidden Code Words","authors":"Martin Bossert","doi":"10.1109/TIT.2025.3556776","DOIUrl":"https://doi.org/10.1109/TIT.2025.3556776","url":null,"abstract":"The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Exploiting a property of the code words constructed by the recursive Plotkin construction, we present novel soft-decision decoders. These are based on the decoding of hidden code words which are inherent contained in the constructed code words and can be uncovered by adding particular parts of the overall code word. The main idea is to use more than one decoding variant where each variant starts with the decoding of a different hidden code word. Given the decision of this first hidden code word allows error cancellation for the remaining decoding. The final decoding decision selects the best of the decisions of the used variants. The more variants are used the closer the performance gets to the maximum-likelihood (ML) decoding performance. This is verified by an ML-bound for the cases where the ML performance is not known. The decoding algorithms use only additions, comparisons, and sign operations. Further, due to the recursive structure, only relatively short codes have to be decoded, thus, the decoding complexity is very low. We also present a new decoder for first-order RM codes with low complexity. In addition, we introduce two novel classes of half-rate codes based on recursive Plotkin constructions with RM codes. We show that the novel soft decision decoders can also be applied to recursive Plotkin constructions with BCH codes and to particular classes of generalized concatenated codes (GCC).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4228-4249"},"PeriodicalIF":2.2,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117277","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":"Edge-Subset Lattice and Its Application to Linear Network Error Correction Coding","authors":"Xuan Guang;Ruopu Cui;Raymond W. Yeung","doi":"10.1109/TIT.2025.3556551","DOIUrl":"https://doi.org/10.1109/TIT.2025.3556551","url":null,"abstract":"In this paper, we first explore the underlying mathematical structure of edge subsets on a finite directed acyclic graph in using a lattice-theoretic approach. We prove that a collection of edge subsets, depending on different conditions it satisfies, together with the corresponding “cut-separating” partial order, can form a meet-semilattice, a join-semilattice or a lattice. The bottom and top thus derived generalize the concept of the primary minimum cut introduced by Guang and Yeung (2018) and hence we provide a new way from the lattice-theoretic point of view to understand the primary minimum cut and its existence and uniqueness. The introduced concepts and obtained results regarded as a bridge connect graph theory and lattice theory, which appear to be of fundamental interest in graph theory, lattice theory, and even beyond. In addition, we consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In LNEC coding, the minimum required field size for the existence of LNEC codes, in particular LNEC maximum distance separable (MDS) codes which are regarded as a most important type of optimal codes, is an open problem not only of theoretical interest but also of practical importance. By applying the approach of the above edge-subset (semi-)lattice, we obtain an improved upper bound on the minimum required field size for the existence of LNEC (MDS) codes. We quantify the improvement over the existing results by both theoretical analysis and numerical simulations and thus show that the improvement is in general significant. The improved upper bound, which is graph-theoretic, depends only on the network topology and requirement of the error correction capability but not on a specific code construction. We also develop an efficient algorithm that can compute the bound in a linear time of the number of edges.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5700-5719"},"PeriodicalIF":2.2,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331663","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 MRA Schemes Based on the CRT for Polynomial Rings","authors":"Jing Yang;Xianfang Wang;Can Xiang;Fang-Wei Fu;Shu-Tao Xia","doi":"10.1109/TIT.2025.3556433","DOIUrl":"https://doi.org/10.1109/TIT.2025.3556433","url":null,"abstract":"At present, existing multi-receiver authentication (MRA) schemes can only handle situations where the capacities of all receivers in the schemes are the same. However, in reality, different receivers may need to have different storage capacities. In this paper, inspired by the secret sharing scheme based on the Chinese Remainder Theorem (CRT) for polynomial rings where each participant holds the share with different sizes, we propose three new constructions of unconditionally secure MRA schemes for multiple messages using the CRT for polynomial rings, including a <inline-formula> <tex-math>$(k,n)$ </tex-math></inline-formula>-threshold MRA scheme, a <inline-formula> <tex-math>$(k,n,omega)$ </tex-math></inline-formula>-weighted threshold MRA scheme, and a <inline-formula> <tex-math>$(mathcal {Q},mathcal {F})$ </tex-math></inline-formula>-general MRA scheme. As far as we know, our proposed MRA schemes are the first MRA schemes with different storage capacities for different receivers and the first ones based on the CRT for polynomial rings. Moreover, the proposed schemes can be seen as extensions of the MRA scheme in Safavi-Naini and Wang. In particular, as for our <inline-formula> <tex-math>$(mathcal {Q},mathcal {F})$ </tex-math></inline-formula>-general MRA scheme, it has generally more communication complexity and much less computation complexity than the existing <inline-formula> <tex-math>$(mathcal {Q},mathcal {F})$ </tex-math></inline-formula>-general MRA scheme.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4671-4685"},"PeriodicalIF":2.2,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117330","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":"Thermal-Aware Communication","authors":"Yeow Meng Chee;Tuvi Etzion;Kees A. Schouhamer Immink;Tuan Thanh Nguyen;Van Khu Vu;Jos H. Weber;Eitan Yaakobi","doi":"10.1109/TIT.2025.3555665","DOIUrl":"https://doi.org/10.1109/TIT.2025.3555665","url":null,"abstract":"Temperature control is of utmost importance in transmission systems. In this paper, a binary channel model is considered in which the transmission of a one causes a temperature increase while communicating a zero causes a temperature drop. By putting constraints on the input sequences, it is guaranteed that the channel temperature will not exceed a certain pre-determined maximum. In the asymptotic regime, the capacity of such a channel is studied. For the non-asymptotic regime, fixed-length codes are presented, with the property that codewords can be freely cascaded without violating the temperature constraint. Optimization of the code size is investigated and codewords are enumerated using generating functions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4145-4155"},"PeriodicalIF":2.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117256","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":"Finite-Sample Bounds for Adaptive Inverse Reinforcement Learning Using Passive Langevin Dynamics","authors":"Luke Snow;Vikram Krishnamurthy","doi":"10.1109/TIT.2025.3555479","DOIUrl":"https://doi.org/10.1109/TIT.2025.3555479","url":null,"abstract":"This paper provides a finite-sample analysis of a passive stochastic gradient Langevin dynamics (PSGLD) algorithm. This algorithm is designed to achieve adaptive inverse reinforcement learning (IRL). Adaptive IRL aims to estimate the cost function of a forward learner performing a stochastic gradient algorithm (e.g., policy gradient reinforcement learning) by observing their estimates in real-time. The PSGLD algorithm is considered passive because it incorporates noisy gradients provided by an external stochastic gradient algorithm (forward learner), of which it has no control. The PSGLD algorithm acts as a randomized sampler to achieve adaptive IRL by reconstructing the forward learner’s cost function nonparametrically from the stationary measure of a Langevin diffusion. This paper analyzes the non-asymptotic (finite-sample) performance; we provide explicit bounds on the 2-Wasserstein distance between PSGLD algorithm sample measure and the stationary measure encoding the cost function, and provide guarantees for a kernel density estimation scheme which reconstructs the cost function from empirical samples. Our analysis uses tools from the study of Markov diffusion operators. The derived bounds have both practical and theoretical significance. They provide finite-time guarantees for an adaptive IRL mechanism, and substantially generalize the analytical framework of a line of research in passive stochastic gradient algorithms.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4637-4670"},"PeriodicalIF":2.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117446","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":"Unsourced Random Access in MIMO Quasi-Static Rayleigh Fading Channels: Finite Blocklength and Scaling Law Analyses","authors":"Junyuan Gao;Yongpeng Wu;Giuseppe Caire;Wei Yang;H. Vincent Poor;Wenjun Zhang","doi":"10.1109/TIT.2025.3555398","DOIUrl":"https://doi.org/10.1109/TIT.2025.3555398","url":null,"abstract":"This paper considers the unsourced random access (URA) problem with a random and unknown number of active users in multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channels. We derive non-asymptotic achievability bounds on the probability of incorrectly estimating the number of active users, and provide scaling laws on the gap between the estimated and true numbers of active users. We prove that the error probability reaches a plateau as the power <italic>P</i> and blocklength <italic>n</i> increase, whereas it decays exponentially with the number <italic>L</i> of receive antennas and eventually vanishes. Then, we explore the fundamental limits of URA by deriving non-asymptotic achievability bounds and converse bounds (including two single-user converse bounds and one multi-user ensemble converse bound) on the minimum energy-per-bit required by each active user to transmit <italic>J</i> bits with blocklength <italic>n</i> under misdetection and false-alarm constraints. Numerical results show that the extra required energy-per-bit due to the uncertainty in the number <inline-formula> <tex-math>${mathrm {K}}_{a}$ </tex-math></inline-formula> of active users decreases as <italic>L</i> and <inline-formula> <tex-math>$mathbb {E}[{mathrm {K}}_{a}]$ </tex-math></inline-formula> increase and the error requirement becomes milder. In the non-asymptotic regime, using codewords distributed on a sphere outperforms Gaussian random coding. Existing schemes are shown to exhibit a large gap to our bounds when the number of active users is large, calling for more advanced schemes that perform energy-efficiently in this case. In the asymptotic regime with <inline-formula> <tex-math>$nto infty $ </tex-math></inline-formula>, we establish scaling laws on the minimum required <italic>P</i> and <italic>L</i> to reliably support <inline-formula> <tex-math>${mathrm {K}}_{a}$ </tex-math></inline-formula> active users as functions of <italic>n</i>, which highlight the potential of MIMO in enabling low-cost communication and indicate that it is possible for the minimum required <italic>P</i> and <italic>L</i> to remain on the same order when the number of active users increases but stays below a threshold.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4342-4373"},"PeriodicalIF":2.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117450","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":"Quantum Circuit Tensors and Enumerators With Applications to Quantum Fault Tolerance","authors":"Alon Kukliansky;Brad Lackey","doi":"10.1109/TIT.2025.3555189","DOIUrl":"https://doi.org/10.1109/TIT.2025.3555189","url":null,"abstract":"We extend the recently introduced notion of tensor enumerator to the circuit enumerator. We provide a mathematical framework that offers a novel method for analyzing circuits and error models without resorting to Monte Carlo techniques. We introduce an analogue of the Poisson summation formula for stabilizer codes, facilitating a method for the exact computation of the number of error paths within the syndrome extraction circuit of the code that does not require direct enumeration. We demonstrate the efficacy of our approach by explicitly providing the exact number of error paths in a distance five surface code under various error models, a task infeasible via direct enumeration. We also show our circuit enumerator is related to the process matrix of a channel through a type of MacWilliams identity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4406-4427"},"PeriodicalIF":2.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117105","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":"Single-Shot Entanglement Manipulation of States and Channels Revisited","authors":"Thomas Theurer;Kun Fang;Gilad Gour","doi":"10.1109/TIT.2025.3570770","DOIUrl":"https://doi.org/10.1109/TIT.2025.3570770","url":null,"abstract":"We study entanglement distillation and dilution of states and channels in the single-shot regime. With the help of a recently introduced conversion distance, we provide compact closed-form expressions for the dilution and distillation of pure states and show how this can be used to efficiently calculate these quantities on multiple copies of pure states. These closed-form expressions also allow us to obtain second-order asymptotics. We then prove that the <inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>-single-shot entanglement cost of mixed states is given exactly in terms of an expression containing a suitably smoothed version of the conditional max-entropy. For pure states, this expression reduces to the smoothed max-entropy of the reduced state, for which we provide a closed-form expression. Analogously, we provide a closed-form expression for the smoothed min-entropy and connect it to the <inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>-single-shot distillable entanglement. Based on these results, we bound the single-shot entanglement cost of channels. We then turn to the one-way entanglement distillation of states and channels and provide bounds in terms of a quantity we denote coherent information of entanglement.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 7","pages":"5330-5360"},"PeriodicalIF":2.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144331548","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":"Efficient Algorithms for Attributed Graph Alignment With Vanishing Edge Correlation","authors":"Ziao Wang;Weina Wang;Lele Wang","doi":"10.1109/TIT.2025.3555187","DOIUrl":"https://doi.org/10.1109/TIT.2025.3555187","url":null,"abstract":"Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of <italic>n</i> vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erdős–Rényi graph pair model, where the two graphs are Erdős–Rényi graphs with edge probability <inline-formula> <tex-math>$q_{mathrm {u}}$ </tex-math></inline-formula>, correlated under certain vertex correspondence. To achieve exact recovery of the correspondence, all existing algorithms at least require the edge correlation coefficient <inline-formula> <tex-math>$rho _{mathrm {u}}$ </tex-math></inline-formula> between the two graphs to be <italic>non-vanishing</i> as <inline-formula> <tex-math>$nrightarrow infty $ </tex-math></inline-formula>. Moreover, it is conjectured that no polynomial-time algorithm can achieve exact recovery under vanishing edge correlation <inline-formula> <tex-math>${rho _{mathrm {u}}}lt 1/mathrm {polylog}(n)$ </tex-math></inline-formula>. In this paper, we show that with a vanishing amount of additional <italic>attribute information</i>, exact recovery is polynomial-time feasible under <italic>vanishing</i> edge correlation <inline-formula> <tex-math>${rho _{mathrm {u}}}ge n^{-Theta (1)}$ </tex-math></inline-formula>. We identify a <italic>local</i> tree structure, which incorporates one layer of user information and one layer of attribute information, and apply the subgraph counting technique to such structures. A polynomial-time algorithm is proposed that recovers the vertex correspondence for most of the vertices, and then refines the output to achieve exact recovery. The consideration of attribute information is motivated by real-world applications like LinkedIn and Twitter, where user attributes like birthplace and education background can aid alignment.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 6","pages":"4556-4580"},"PeriodicalIF":2.2,"publicationDate":"2025-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117155","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}