IEEE Transactions on Information Theory最新文献

{"title":"Coset Constructions of Constant Dimension Codes by Cosets of Optimal Ferrers Diagrams Rank Metric Codes","authors":"Dengming Xu;Yihui Song","doi":"10.1109/TIT.2025.3596103","DOIUrl":"https://doi.org/10.1109/TIT.2025.3596103","url":null,"abstract":"Constant dimension codes (CDCs) have received a lot of attention due to their application in random network coding. One main problem with CDCs is to improve the lower bound of <inline-formula> <tex-math>$A_{q}(n,d,k)$ </tex-math></inline-formula> for given parameters <inline-formula> <tex-math>$n,d$ </tex-math></inline-formula> and <italic>k</i>, where <inline-formula> <tex-math>$A_{q}(n,d,k)$ </tex-math></inline-formula> denotes the maximum size of all <inline-formula> <tex-math>$(n,M,d,k)_{q}$ </tex-math></inline-formula> CDCs. The paper aims to construct CDCs by combining the coset and linkage construction. Precisely, we first combine the coset and linkage construction in different ways and then turn our attention to the coset construction. To enlarge the size of CDCs constructed from the coset construction, we are devoted to constructing lists of CDCs with fixed distance having size as large as possible by the cosets of optimal Ferrers diagram rank metric codes and the parallelisms in <inline-formula> <tex-math>${mathcal {G}}_{q}(n, k)$ </tex-math></inline-formula>. As applications, numerous CDCs with larger size than the previously best known codes are obtained, including <inline-formula> <tex-math>$A_{q}(18, 6,9), A_{q}(14, 6, 7), ~A_{q}(12, 4, 6), A_{q}(10, 4, 5),A_{q}(14, 4, 7),$ </tex-math></inline-formula> <inline-formula> <tex-math>$A_{q}(16, 4, 8)$ </tex-math></inline-formula> and <inline-formula> <tex-math>$A_{q}(n, 4,4)$ </tex-math></inline-formula> for <inline-formula> <tex-math>$13leq nleq 16$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7959-7975"},"PeriodicalIF":2.9,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110196","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":"Maximum Likelihood Estimation of Optimal Receiver Operating Characteristic Curves From Likelihood Ratio Observations","authors":"Bruce Hajek;Xiaohan Kang","doi":"10.1109/TIT.2025.3595488","DOIUrl":"https://doi.org/10.1109/TIT.2025.3595488","url":null,"abstract":"The optimal receiver operating characteristic (ROC) curve, giving the maximum probability of detection as a function of the probability of false alarm, is a key information-theoretic indicator of the difficulty of a binary hypothesis testing problem (BHT). It is well known that the optimal ROC curve for a given BHT, corresponding to the likelihood ratio test, is determined by the probability distribution of the observed data under each of the two hypotheses. In some cases, these two distributions may be unknown or computationally intractable, but independent samples of the likelihood ratio can be observed. This raises the problem of estimating the optimal ROC for a BHT from such samples. The maximum likelihood estimator of the optimal ROC curve is derived, and it is shown to converge almost surely to the true optimal ROC curve in the Lévy metric, as the number of observations tends to infinity. Finite sample size bounds are obtained for three other estimators: the classical empirical estimator, based on estimating the two types of error probabilities from two separate sets of samples, and two variations of the maximum likelihood estimator called the split estimator and fused estimator, respectively. The maximum likelihood estimator is observed in simulation experiments to be considerably more accurate than the empirical estimator, especially when the number of samples obtained under one of the two hypotheses is small. The area under the maximum likelihood estimator is derived; it is a consistent estimator of the area under the true optimal ROC curve.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7568-7584"},"PeriodicalIF":2.9,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11111686","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110262","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":"Common Randomness Generation From Finite Compound Sources Aided by One-Way Communication","authors":"Rami Ezzine;Moritz Wiese;Christian Deppe;Holger Boche","doi":"10.1109/TIT.2025.3595704","DOIUrl":"https://doi.org/10.1109/TIT.2025.3595704","url":null,"abstract":"We investigate the problem of generating common randomness (CR) from a finite compound source aided by unidirectional communication over a rate-limited perfect channel. The two communicating parties observe independent and identically distributed (i.i.d.) samples of a finite compound source and aim to agree on a common random variable with high probability for every possible state. Both parties know the set of source states as well as their statistics. However, they don’t know the actual state. We establish a single-letter formula for the compound CR capacity in the presence of communication over the channel and study key properties of the compound CR capacity: super-additivity, concavity, and continuity. We also consider the case where there is no communication between the terminals, and only the source outputs observed by the terminal at the receiving end of the perfect channel are state-dependent. In this setting, we establish single-letter bounds on the compound CR capacity. The single-letter lower bound is derived under the assumption that the source distributions are pairwise distinct for all states. Finally, within the same setting, we propose a CR generation scheme for a two-state binary source example. Notably, this scheme does not depend on the previously mentioned assumption.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7715-7734"},"PeriodicalIF":2.9,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11112680","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110276","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":"Algorithmic Computability of the Capacity of Additive Colored Gaussian Noise Channels","authors":"Holger Boche;Andrea Grigorescu;Rafael F. Schaefer;H. Vincent Poor","doi":"10.1109/TIT.2025.3594999","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594999","url":null,"abstract":"Designing capacity-achieving coding schemes for the band-limited additive colored Gaussian noise (ACGN) channel has been and is still a challenge. In this paper, the capacity of the band-limited ACGN channel is studied from a fundamental algorithmic point of view by addressing the question of whether or not the capacity can be algorithmically computed. To this aim, the concept of Turing machines is used, which provides fundamental performance limits of digital computers. It is shown that there are band-limited ACGN channels having computable continuous spectral densities whose capacity are non-computable numbers. Moreover, it is demonstrated that for those channels, it is impossible to find computable sequences of asymptotically sharp upper bounds for their capacities. Furthermore, the implications of the non-computability of the ACGN channel capacity in information theory and coding are discussed, particularly regarding the impossibility of computing achievable rates in the finite blocklength regime and the challenges of finding universal algorithms that compute capacity-achieving power spectral densities for the ACGN channel.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7419-7434"},"PeriodicalIF":2.9,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110314","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":"Denoising and Multilinear Projected-Estimation of High-Dimensional Matrix-Variate Factor Time Series","authors":"Zhaoxing Gao;Ruey S. Tsay","doi":"10.1109/TIT.2025.3594536","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594536","url":null,"abstract":"This paper proposes a new multi-linear projection method for denoising and estimation of high-dimensional matrix-variate factor time series. It assumes that a <inline-formula> <tex-math>$p_{1}times p_{2}$ </tex-math></inline-formula> matrix-variate time series consists of a dynamically dependent, lower-dimensional matrix-variate factor process and a <inline-formula> <tex-math>$p_{1}times p_{2}$ </tex-math></inline-formula> matrix idiosyncratic series. In addition, the latter series assumes a matrix-variate factor structure such that its row and column covariances may have diverging/spiked eigenvalues to accommodate the case of low signal-to-noise ratio often encountered in applications. We use an iterative projection procedure to reduce the dimensions and noise effects in estimating front and back loading matrices and to obtain faster convergence rates than those of the traditional methods available in the literature. We further introduce a two-way projected Principal Component Analysis to mitigate the diverging noise effects, and implement a high-dimensional white-noise testing procedure to estimate the dimension of the matrix factor process. Asymptotic properties of the proposed method are established if the dimensions and sample size go to infinity. We also use simulations and real examples to assess the performance of the proposed method in finite samples and to compare its forecasting ability with some existing ones in the literature. The proposed method fares well in out-of-sample forecasting. In the appendix, we demonstrate the efficacy of the proposed approach even when the idiosyncratic terms exhibit serial correlations with or without a diverging white noise effect.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7886-7915"},"PeriodicalIF":2.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110303","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":"Classical Codes and Quantum Codes Involving the σ Inner Product","authors":"Meng Cao;Yang Li;Shixin Zhu","doi":"10.1109/TIT.2025.3594472","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594472","url":null,"abstract":"In 2019, Carlet et al. introduced the concept of <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> duals of linear codes involving the <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> inner product, which generalizes the Euclidean, Hermitian and <inline-formula> <tex-math>$ell $ </tex-math></inline-formula>-Galois cases. This paper focuses on constructing new and improved classical codes and quantum codes within the framework of the <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> inner product. We derive some general properties of linear codes, including matrix-product (MP) codes, with respect to the <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> inner product. We develop general methods and design effective routes involving certain optimization problems for constructing <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> self-orthogonal (SO) and <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> dual-containing (DC) MP codes. Our schemes efficiently generate numerous such codes with new or optimal parameters. We establish the <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> construction of quantum stabilizer codes from classical codes. We propose a unified method for constructing two general classes of entanglement-assisted quantum error-correcting codes (EAQECCs) based on the <inline-formula> <tex-math>$sigma $ </tex-math></inline-formula> hulls of general linear codes. This further yields six types of EAQECCs with flexible parameters based on propagation rules using MP codes under the Euclidean and Hermitian cases. Compared to the best-known ternary EAQECCs, we obtain 17 new ones and 13 of them have improved parameters. Finally, we present two infinite families of <italic>q</i>-ary EAQECCs with lengths <inline-formula> <tex-math>$(q^{2}-1)(q+2)$ </tex-math></inline-formula> and <inline-formula> <tex-math>$q^{2}(q+2)$ </tex-math></inline-formula>, respectively. These families include many <italic>q</i>-ary QECCs that are not only new according to Grassl’s online database but also surpass those listed in Edel’s online database.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7649-7669"},"PeriodicalIF":2.9,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110300","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":"Improved Decoding Algorithms for MDS and Almost-MDS Codes From Twisted GRS Codes","authors":"Guodong Wang;Hongwei Liu;Jinquan Luo","doi":"10.1109/TIT.2025.3594174","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594174","url":null,"abstract":"In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further study decoding of almost-MDS TGRS codes and provide a decoding algorithm. These two decoding algorithms are more efficient in terms of performance compared with the decoding algorithms presented in [Sun et al., IEEE-TIT, 2024] and [Sui et al., IEEE-TIT, 2023] respectively. Moreover, these two optimized decoding algorithms can be applied to the decoding of a more general class of twisted Goppa codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7688-7698"},"PeriodicalIF":2.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110254","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":"Low-SNR Asymptotic Capacity of Two Types of Optical Wireless Channels Under Average-Intensity Constraints","authors":"Longguang Li","doi":"10.1109/TIT.2025.3593888","DOIUrl":"https://doi.org/10.1109/TIT.2025.3593888","url":null,"abstract":"In this paper, we study two types of optical wireless channels under average-intensity constraints. One is called the Gaussian optical intensity channel, where the channel output models the converted electrical current corrupted by additive white Gaussian noise. The other one is the Poisson optical intensity channel, where the channel output models the number of received photons whose arrival rates are corrupted by a dark current. When the average input intensity <inline-formula> <tex-math>$mathcal {E}$ </tex-math></inline-formula> is small, the capacity of the Gaussian optical intensity channel is shown to scale as <inline-formula> <tex-math>$mathcal {E}sqrt {frac {log frac {1}{mathcal {E}}}{2}}$ </tex-math></inline-formula>, and the capacity of the Poisson optical intensity channel as <inline-formula> <tex-math>$mathcal {E}log log frac {1}{mathcal {E}}$ </tex-math></inline-formula>. This closes the gaps between previously-derived upper and lower bounds on the asymptotic capacity of these two types of channels.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7504-7517"},"PeriodicalIF":2.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110268","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":"Capacity Bounds for Broadcast Channels With Bidirectional Conferencing Decoders","authors":"Reza K. Farsani;Wei Yu","doi":"10.1109/TIT.2025.3594183","DOIUrl":"https://doi.org/10.1109/TIT.2025.3594183","url":null,"abstract":"The two-user broadcast channel (BC) with receivers connected by bidirectional cooperation links of finite capacities, known as conferencing decoders, is considered. A novel capacity region outer bound is established based on multiple applications of the Csiszár-Körner identity. Achievable rate regions are derived by using Marton’s coding as the transmission scheme, together with different combinations of decode-and-forward and quantize-bin-and-forward strategies at the receivers. It is shown that the outer bound coincides with the achievable rate region for a new class of semi-deterministic BCs with degraded message sets; for this class of channels, one-round cooperation is sufficient to achieve the capacity. Capacity result is also derived for a class of more capable semi-deterministic BCs with both common and private messages and one-sided conferencing. For the Gaussian BC with conferencing decoders, if the noises at the decoders are perfectly correlated (i.e., the correlation is either 1 or −1), the new outer bound yields exact capacity region for two cases: 1) BC with degraded message sets; 2) BC with one-sided conferencing from the weaker receiver to the stronger receiver. When the noises have arbitrary correlation, the outer bound is shown to be within half a bit from the capacity region for these same two cases. Finally, for the general Gaussian BC, a one-sided cooperation scheme based on decode-and-forward from the stronger receiver to the weaker receiver is shown to achieve the capacity region to within <inline-formula> <tex-math>$frac {1}{2}log left ({{frac {2}{1-|lambda |}}}right)$ </tex-math></inline-formula> bits, where <inline-formula> <tex-math>$lambda $ </tex-math></inline-formula> is the noise correlation. An interesting implication of these results is that for a Gaussian BC with perfectly negatively correlated noises and conferencing decoders with finite cooperation link capacities, it is possible to achieve a strictly positive rate using only an infinitesimal amount of transmit power.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7484-7503"},"PeriodicalIF":2.9,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110335","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":"Difficulties Constructing Lattices With Exponential Kissing Number From Codes","authors":"Huck Bennett;Alexander Golovnev;Noah Stephens-Davidowitz","doi":"10.1109/TIT.2025.3593195","DOIUrl":"https://doi.org/10.1109/TIT.2025.3593195","url":null,"abstract":"In this note, we present examples showing that several natural ways of constructing lattices from error-correcting codes do not in general yield a correspondence between minimum-weight non-zero codewords and shortest non-zero lattice vectors. From these examples, we conclude that the main results in two works of Vlăduţ (Moscow J. Comb. Number Th., 2019 and Discrete Comput. Geom., 2021) on constructing lattices with exponential kissing number from error-correcting codes are invalid. A more recent preprint (arXiv, 2024) that Vlăduţ posted after an initial version of this work was made public is also invalid. Exhibiting a family of lattices with exponential kissing number therefore remains an open problem (as of July 2025).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7644-7648"},"PeriodicalIF":2.9,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110193","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}