IEEE Transactions on Information Theory最新文献

{"title":"Quantitative Bounds for Sorting-Based Permutation-Invariant Embeddings","authors":"Nadav Dym;Matthias Wellershoff;Efstratios Tsoukanis;Daniel Levy;Radu Balan","doi":"10.1109/TIT.2026.3679460","DOIUrl":"https://doi.org/10.1109/TIT.2026.3679460","url":null,"abstract":"We study permutation-invariant embeddings of <inline-formula> <tex-math>$d$ </tex-math></inline-formula>-dimensional point sets, which are defined by sorting <inline-formula> <tex-math>$D$ </tex-math></inline-formula> independent one-dimensional projections of the input. Such embeddings arise in graph deep learning where outputs should be invariant to permutations of graph nodes. Previous work showed that for large enough <inline-formula> <tex-math>$D$ </tex-math></inline-formula> and projections in general position, this mapping is injective, and moreover satisfies a bi-Lipschitz condition. However, two gaps remain: firstly, the optimal size <inline-formula> <tex-math>$D$ </tex-math></inline-formula> required for injectivity is not yet known, and secondly, no estimates of the bi-Lipschitz constants of the mapping are known. In this paper, we make substantial progress in addressing both of these gaps. Regarding the first gap, we improve upon the best known upper bounds for the embedding dimension <inline-formula> <tex-math>$D$ </tex-math></inline-formula> necessary for injectivity, and also provide a lower bound on the minimal injectivity dimension. Regarding the second gap, we construct matrices of projection vectors, so that the bi-Lipschitz distortion of the mapping depends quadratically on the number of points <inline-formula> <tex-math>$n$ </tex-math></inline-formula>, and is completely independent of the dimension <inline-formula> <tex-math>$d$ </tex-math></inline-formula>. We also show that for any choice of projection vectors, the distortion of the mapping will never be better than a bound proportional to the square root of <inline-formula> <tex-math>$n$ </tex-math></inline-formula>. Finally, we show that similar guarantees can be provided even when linear projections are applied to the mapping to reduce its dimension.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4297-4311"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509633","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":"Abelian Group Codes for Classical-Quantum Channels: One-Shot and Asymptotic Rate Bounds","authors":"James Pang;S. Sandeep Pradhan;Hessam Mahdavifar","doi":"10.1109/TIT.2026.3687161","DOIUrl":"https://doi.org/10.1109/TIT.2026.3687161","url":null,"abstract":"We study the problem of transmission of information over classical-quantum (CQ) channels in the one-shot regime where the underlying codes are constrained to be shifted <italic>group codes</i>. Given a group <inline-formula> <tex-math>$G$ </tex-math></inline-formula>, a group code of length <inline-formula> <tex-math>$n$ </tex-math></inline-formula> is a subgroup of <inline-formula> <tex-math>$G^{n}$ </tex-math></inline-formula>. In the achievability part, we introduce a new collection of input probability distributions that incorporates the encoding homomorphism and the underlying channel law. Using a random coding argument, we characterize the performance of group codes in terms of hypothesis testing relative-entropic quantities. In the converse part, we establish bounds by leveraging a hypothesis testing-based approach. Furthermore, we apply the one-shot result to the asymptotic stationary memoryless setting, and establish a single-letter lower bound on the <italic>group capacity</i> of a CQ channel. Moreover, we derive a matching upper bound on the asymptotic group capacity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4056-4072"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510087","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 Quantum Measurements: Computational Max- and Measured Rényi Divergences and Applications","authors":"Álvaro Yángüez;Thomas A. Hahn;Jan Kochanowski","doi":"10.1109/TIT.2026.3680247","DOIUrl":"https://doi.org/10.1109/TIT.2026.3680247","url":null,"abstract":"Quantum information processing is limited, in practice, to efficiently implementable operations. This motivates the study of quantum divergences that preserve their operational meaning while faithfully capturing these computational constraints. Using geometric, computational, and information theoretic tools, we define two new types of computational divergences, which we term <italic>computational max-divergence</i> and <italic>computational measured Rényi divergences</i>. Both are constrained by a family of efficient binary measurements, and thus useful for state discrimination tasks in the computational setting. We prove that, in the infinite-order limit, the computational measured Rényi divergence coincides with the computational max-divergence, mirroring the corresponding relation in the unconstrained information-theoretic setting. For the many-copy regime, we introduce regularized versions and establish a one-sided computational Stein bound on achievable hypothesis-testing exponents under efficient measurements, giving the regularized computational measured relative entropy an operational meaning. We further define resource measures induced by our computational divergences and prove an asymptotic continuity bound for the computational measured relative entropy of resource. Focusing on entanglement, we relate our results to previously proposed computational entanglement measures and provide explicit separations from the information-theoretic setting. Together, these results provide a principled, cohesive approach towards state discrimination tasks and resource quantification under computational constraints.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4085-4114"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11471875","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510117","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":"Sliding Finite Window Codes: Near-Optimality and Q-Learning for Zero-Delay Coding","authors":"Liam Cregg;Fady Alajaji;Serdar Yüksel","doi":"10.1109/TIT.2026.3681183","DOIUrl":"https://doi.org/10.1109/TIT.2026.3681183","url":null,"abstract":"We study the problem of zero-delay coding for the transmission of a Markov source over a noisy channel with feedback and present a reinforcement learning solution which is guaranteed to approach optimality. To this end, we formulate the problem as a Markov decision process (MDP) where the state is a probability-measure valued predictor/belief and the actions are quantizer maps. This MDP formulation has been used to show the optimality of certain classes of encoder policies in prior work, but their computation is prohibitively complex due to the uncountable nature of the constructed state space. Based on recent results for partially observed MDPs, we present an approximation of the belief MDP using a sliding finite window of channel outputs and quantizers. Under an appropriate notion of predictor stability, we show that the lowest distortion achievable by such a sliding finite window policy approaches the true lowest distortion as the window length increases. We give sufficient conditions for predictor stability to hold. Finally, we propose a Q-learning algorithm which provably converges to the optimal policy and provide a detailed comparison of the sliding finite window scheme with another approximation scheme which quantizes the belief MDP in a nearest neighbor fashion, as well as other coding schemes from the literature.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3910-3926"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511793","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 Constructions of Non-GRS MDS Codes, Recovery and Determination Algorithms for GRS Codes","authors":"Guodong Wang;Hongwei Liu;Jinquan Luo","doi":"10.1109/TIT.2026.3683741","DOIUrl":"https://doi.org/10.1109/TIT.2026.3683741","url":null,"abstract":"In this paper, we propose a new method for constructing a class of non-GRS MDS codes. The lengths of these codes can reach up to <inline-formula> <tex-math>$frac {q+3}{2}$ </tex-math></inline-formula> (for finite fields of odd characteristic) and <inline-formula> <tex-math>$frac {q+4}{2}$ </tex-math></inline-formula> (for even characteristic), respectively. Owing to their special structure, we can use the Cauchy matrix method to obtain the necessary and sufficient conditions for these codes to be MDS codes and non-GRS MDS codes. Additionally, the inequivalence between these codes and twisted GRS codes is analyzed. Furthermore, we analyze the relationships among several existing classes of codes used for constructing non-GRS MDS codes, propose explicit constructions, and discuss the lengths of non-GRS MDS codes based on these constructions. Finally, we design two efficient algorithms to address two main problems in GRS code research, i.e., determining whether an unknown code <inline-formula> <tex-math>$C$ </tex-math></inline-formula> is a GRS code from its generator matrix <inline-formula> <tex-math>$G$ </tex-math></inline-formula>, and recovering the key vectors <inline-formula> <tex-math>$boldsymbol {alpha }$ </tex-math></inline-formula> and <inline-formula> <tex-math>$boldsymbol {v}$ </tex-math></inline-formula> such that <inline-formula> <tex-math>$C = text {GRS}_{n,k}(boldsymbol {alpha }, boldsymbol {v})$ </tex-math></inline-formula> if <inline-formula> <tex-math>$C$ </tex-math></inline-formula> is indeed a GRS code. A computational complexity comparison of the proposed algorithms (<inline-formula> <tex-math>$O(nk+n)$ </tex-math></inline-formula>) with that of the Sidelnikov-Shestakov attack (exceeding <inline-formula> <tex-math>$O(qk^{2}n+qk^{3})$ </tex-math></inline-formula>) shows that our methods offer superior computational efficiency.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3848-3861"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509740","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 Asymptotic Number of Equivalence Classes of Linear Codes With Given Dimension","authors":"Andrea Di Giusto;Alberto Ravagnani","doi":"10.1109/TIT.2026.3683726","DOIUrl":"https://doi.org/10.1109/TIT.2026.3683726","url":null,"abstract":"We investigate the asymptotic number of equivalence classes of linear codes with prescribed length and dimension. While the total number of inequivalent codes of a given length has been studied previously, the case where the dimension varies as a function of the length has not yet been considered. We derive explicit asymptotic formulas for the number of equivalence classes under three standard notions of equivalence, for a fixed alphabet size and increasing length. Our approach also yields an exact asymptotic expression for the sum of all <inline-formula> <tex-math>$q$ </tex-math></inline-formula>-binomial coefficients, which is of independent interest and answers an open question in this context. Finally, we establish a natural connection between these asymptotic quantities and certain discrete Gaussian distributions arising from Brownian motion, providing a probabilistic interpretation of our results.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"3840-3847"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148509741","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":"IEEE Transactions on Information Theory Publication Information","authors":"","doi":"10.1109/TIT.2026.3690978","DOIUrl":"https://doi.org/10.1109/TIT.2026.3690978","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"C2-C2"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11534143","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148511792","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":"Doubly Minimized Petz and Sandwiched Rényi Mutual Information: Properties","authors":"Laura Burri","doi":"10.1109/TIT.2026.3677886","DOIUrl":"https://doi.org/10.1109/TIT.2026.3677886","url":null,"abstract":"The doubly minimized Petz Rényi mutual information of order <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula> is defined as the minimization of the Petz divergence of order <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula> of a fixed bipartite quantum state relative to any product state. The doubly minimized sandwiched Rényi mutual information is defined analogously using the sandwiched divergence in place of the Petz divergence. In this work, we establish several properties of these two types of Rényi mutual information. In particular, for the Petz case, we prove additivity for <inline-formula> <tex-math>$alpha in [{1/2,2}]$ </tex-math></inline-formula>. For the sandwiched case, we establish a novel duality relation for <inline-formula> <tex-math>$alpha in [2/3,infty]$ </tex-math></inline-formula> via Sion’s minimax theorem, and we subsequently use this duality relation to prove additivity for the same range of <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula>. Previously, additivity for the sandwiched case was known only for <inline-formula> <tex-math>$alpha in [1,infty]$ </tex-math></inline-formula>, but it had been conjectured to hold for <inline-formula> <tex-math>$alpha in [1/2,infty]$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4115-4139"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11456775","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148508897","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":"Capacities of Entanglement Distribution From a Central Source","authors":"Xinan Chen;Stefano Chessa;Ian George;Felix Leditzky;Eric Chitambar","doi":"10.1109/TIT.2026.3684413","DOIUrl":"https://doi.org/10.1109/TIT.2026.3684413","url":null,"abstract":"Distribution of entanglement is an essential task in quantum information processing and the realization of quantum networks. In our work, we theoretically investigate the scenario where a central source prepares an <inline-formula> <tex-math>$N$ </tex-math></inline-formula>-partite entangled state and transmits each entangled subsystem to one of <inline-formula> <tex-math>$N$ </tex-math></inline-formula> receivers through noisy quantum channels. The receivers are then able to perform local operations assisted by unlimited classical communication to distill target entangled states from the noisy channel output. In this operational context, we define the EPR distribution capacity and the GHZ distribution capacity of a quantum channel as the largest rates at which Einstein-Podolsky-Rosen (EPR) states and Greenberger-Horne-Zeilinger (GHZ) states can be faithfully distributed through the channel, respectively. We establish lower and upper bounds on the EPR distribution capacity by connecting it with the task of assisted entanglement distillation. We also construct an explicit protocol consisting of a combination of a quantum communication code and a classical-post-processing-assisted entanglement generation code, which yields a simple achievable lower bound for generic channels. As applications of these results, we give an exact expression for the EPR distribution capacity over two erasure channels and bounds on the EPR distribution capacity over two generalized amplitude damping channels. We also bound the GHZ distribution capacity, which results in an exact characterization of the GHZ distribution capacity when the most noisy channel is a dephasing channel.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 6","pages":"4001-4011"},"PeriodicalIF":2.6,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11482228","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148510086","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":"Random Multiplexing","authors":"Lei Liu;Yuhao Chi;Shunqi Huang;Zhaoyang Zhang","doi":"10.1109/TIT.2026.3653055","DOIUrl":"https://doi.org/10.1109/TIT.2026.3653055","url":null,"abstract":"As wireless communication applications evolve from traditional multipath environments to high-mobility scenarios like unmanned aerial vehicles, multiplexing techniques have advanced accordingly. Traditional single-carrier frequency-domain equalization (SC-FDE) and orthogonal frequency-division multiplexing (OFDM) have given way to emerging orthogonal time-frequency space (OTFS) and affine frequency-division multiplexing (AFDM). These approaches exploit specific channel structures—e.g., Toeplitz-structured multipath channel matrix for OFDM and SC-FDE or doubly selective channels for OTFS and AFDM—to diagonalize or sparsify the effective channel, thereby enabling low-complexity detection. However, their reliance on these structures significantly limits their robustness in dynamic, real-world environments. To address these challenges, this paper studies a random multiplexing technique that is decoupled from the physical channels, thereby enabling its application to arbitrary norm-bounded and spectrally convergent channel matrices. Random multiplexing achieves statistical fading-channel ergodicity for transmitted signals by constructing an equivalent input-isotropic channel matrix in the random transform domain. It guarantees the asymptotic replica MAP bit-error rate (BER) optimality of AMP-type detectors for linear systems with arbitrary norm-bounded, spectrally convergent channel matrices and signaling configurations, under the unique fixed point assumption. A low-complexity cross-domain memory AMP (CD-MAMP) detector is considered for random multiplexing systems, leveraging the sparsity of the time-domain channel and the input isotropy of the equivalent channel. Optimal power allocations are derived to minimize the replica MAP BER and maximize the replica constrained capacity of random multiplexing systems, respectively. The optimal coding principle and replica constrained-capacity optimality of CD-MAMP detector are investigated for random multiplexing systems. Additionally, the versatility of random multiplexing in diverse wireless applications is explored. Numerical results are presented to validate the theoretical findings.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 4","pages":"2277-2306"},"PeriodicalIF":2.6,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148506912","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}