Pub Date : 2025-08-07DOI: 10.1109/TIT.2025.3595144
Yongxiang Li;Yuanyuan Li;Di Wang
Existing periodic Gaussian process (PGP) modeling methods rely on the regularly-spaced-signal assumption (i.e., signals are evenly spaced) and the integer-period assumption for the sake of computational feasibility. However, such an assumption prevents conventional efficient modeling approaches from working properly on irregularly (unevenly) spaced signals, such as evenly spaced signals with missing data. Moreover, without the integer-period assumption, it is computationally prohibitive to accurately search the decimal period of PGP due to the severe non-convexity of its likelihood function. To address these issues, this study proposes a PGP-controlled B-spline for scalable modeling of irregularly spaced signals with a decimal period. The proposed model integrates PGP with B-spline basis functions, allowing for nonlinear and nonparametric modeling of periodic signals. An explore-exploit optimization is developed to overcome the non-convexity of the likelihood, enabling effective and efficient decimal period estimation. The proposed PGP modeling approach has a linear time complexity. Asymptotic properties of the proposed method are studied, which shed light on the period estimation of other PGP models. Simulation and real case studies are conducted to demonstrate the superiority of the proposed method.
{"title":"Periodic Gaussian Process Controlled B-Spline for Scalable Modeling of Irregularly Spaced Signals","authors":"Yongxiang Li;Yuanyuan Li;Di Wang","doi":"10.1109/TIT.2025.3595144","DOIUrl":"https://doi.org/10.1109/TIT.2025.3595144","url":null,"abstract":"Existing periodic Gaussian process (PGP) modeling methods rely on the regularly-spaced-signal assumption (i.e., signals are evenly spaced) and the integer-period assumption for the sake of computational feasibility. However, such an assumption prevents conventional efficient modeling approaches from working properly on irregularly (unevenly) spaced signals, such as evenly spaced signals with missing data. Moreover, without the integer-period assumption, it is computationally prohibitive to accurately search the decimal period of PGP due to the severe non-convexity of its likelihood function. To address these issues, this study proposes a PGP-controlled B-spline for scalable modeling of irregularly spaced signals with a decimal period. The proposed model integrates PGP with B-spline basis functions, allowing for nonlinear and nonparametric modeling of periodic signals. An explore-exploit optimization is developed to overcome the non-convexity of the likelihood, enabling effective and efficient decimal period estimation. The proposed PGP modeling approach has a linear time complexity. Asymptotic properties of the proposed method are studied, which shed light on the period estimation of other PGP models. Simulation and real case studies are conducted to demonstrate the superiority of the proposed method.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7842-7855"},"PeriodicalIF":2.9,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110191","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}
Pub Date : 2025-08-06DOI: 10.1109/TIT.2025.3596305
Daniel Escudero;Cheng Hong;Hongqing Liu;Chaoping Xing;Chen Yuan
Reverse multiplication-friendly embeddings have played a crucial role in secure multiparty computation and zero-knowledge proofs. In this work, we generalize the notion of RMFEs to degree-D RMFEs. We present a general construction of degree-D RMFEs by generalizing the ideas on algebraic geometry used to construct traditional degree-2 RMFEs. Furthermore, our theory is given in a unified manner for general Galois rings, which include both rings of the form $mathbb {Z}_{p^{k}}$ and fields like $mathbb {F}_{p^{k}}$ , which have been treated separately in prior works. We present multiple concrete sets of parameters for degree-D RMFEs (including $D=2$ ), which can be useful for future works. In the recent work of (Cheon & Lee, Eurocrypt’22), the concept of a degree-D packing method was formally introduced, which captures the idea of embedding multiple elements of a smaller ring into a larger ring. We show that the generalized notion of RMFEs to degree-D RMFEs which, in spite of being “more algebraic” than packing methods, turn out to be essentially equivalent. Thus, our constructions of degree-D RMFEs are also degree-D packing methods.
{"title":"Degree-D Reverse Multiplication-Friendly Embeddings","authors":"Daniel Escudero;Cheng Hong;Hongqing Liu;Chaoping Xing;Chen Yuan","doi":"10.1109/TIT.2025.3596305","DOIUrl":"https://doi.org/10.1109/TIT.2025.3596305","url":null,"abstract":"Reverse multiplication-friendly embeddings have played a crucial role in secure multiparty computation and zero-knowledge proofs. In this work, we generalize the notion of RMFEs to <italic>degree-D RMFEs</i>. We present a general construction of degree-<italic>D</i> RMFEs by generalizing the ideas on algebraic geometry used to construct traditional degree-2 RMFEs. Furthermore, our theory is given in a unified manner for general Galois rings, which include both rings of the form <inline-formula> <tex-math>$mathbb {Z}_{p^{k}}$ </tex-math></inline-formula> and fields like <inline-formula> <tex-math>$mathbb {F}_{p^{k}}$ </tex-math></inline-formula>, which have been treated separately in prior works. We present multiple concrete sets of parameters for degree-<italic>D</i> RMFEs (including <inline-formula> <tex-math>$D=2$ </tex-math></inline-formula>), which can be useful for future works. In the recent work of (Cheon & Lee, Eurocrypt’22), the concept of a <italic>degree-D packing method</i> was formally introduced, which captures the idea of embedding multiple elements of a smaller ring into a larger ring. We show that the generalized notion of RMFEs to <italic>degree-D RMFEs</i> which, in spite of being “more algebraic” than packing methods, turn out to be essentially equivalent. Thus, our constructions of degree-<italic>D</i> RMFEs are also degree-<italic>D</i> packing methods.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7990-8001"},"PeriodicalIF":2.9,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110243","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}
Pub Date : 2025-08-06DOI: 10.1109/TIT.2025.3596479
Mahir Bilen Can;Roy Joshua
We show that it is possible to break up Higher Grassmann codes we constructed in earlier work to a sequence of affine Reed-Muller codes so that various operations can be reduced to performing these operations for the component affine Reed-Muller codes. Then we consider quantum codes produced from a pair of Higher Grassmann codes and discuss also their implementation aspects in detail.
{"title":"Higher Grassmann Codes III: Quantum Variants","authors":"Mahir Bilen Can;Roy Joshua","doi":"10.1109/TIT.2025.3596479","DOIUrl":"https://doi.org/10.1109/TIT.2025.3596479","url":null,"abstract":"We show that it is possible to break up Higher Grassmann codes we constructed in earlier work to a sequence of affine Reed-Muller codes so that various operations can be reduced to performing these operations for the component affine Reed-Muller codes. Then we consider quantum codes produced from a pair of Higher Grassmann codes and discuss also their implementation aspects in detail.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7585-7594"},"PeriodicalIF":2.9,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110253","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}
Pub Date : 2025-08-06DOI: 10.1109/TIT.2025.3596304
Ziyuan Wang;Jin Liu;Jun Shao;Heng Lian;Lei Wang
For a relatively small labeled dataset from high-dimensional generalized linear models with block-wise missing covariates and a large unlabeled dataset, we utilize a model-assisted approach in the labeled dataset to address the issue of block-wise missing covariates and then integrate the unlabeled data to construct estimation equations for the coefficients without any imputation. A lasso-penalized semi-supervised estimator is obtained, and then its debiased estimator is proposed to establish asymptotic normality/confidence intervals. When the labeled data are distributed in multiple machines independently and only some machines have unlabeled data, we further propose a distributed debiased semi-supervised estimator for estimation and inference. The finite sample performance of our proposed two estimators is studied through simulations and further illustrated with a breast cancer dataset.
{"title":"Distributed Semi-Supervised Inference for Generalized Linear Models With Block-Wise Missing Covariates","authors":"Ziyuan Wang;Jin Liu;Jun Shao;Heng Lian;Lei Wang","doi":"10.1109/TIT.2025.3596304","DOIUrl":"https://doi.org/10.1109/TIT.2025.3596304","url":null,"abstract":"For a relatively small labeled dataset from high-dimensional generalized linear models with block-wise missing covariates and a large unlabeled dataset, we utilize a model-assisted approach in the labeled dataset to address the issue of block-wise missing covariates and then integrate the unlabeled data to construct estimation equations for the coefficients without any imputation. A lasso-penalized semi-supervised estimator is obtained, and then its debiased estimator is proposed to establish asymptotic normality/confidence intervals. When the labeled data are distributed in multiple machines independently and only some machines have unlabeled data, we further propose a distributed debiased semi-supervised estimator for estimation and inference. The finite sample performance of our proposed two estimators is studied through simulations and further illustrated with a breast cancer dataset.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7815-7841"},"PeriodicalIF":2.9,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110311","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}
Pub Date : 2025-08-05DOI: 10.1109/TIT.2025.3596103
Dengming Xu;Yihui Song
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 $A_{q}(n,d,k)$ for given parameters $n,d$ and k, where $A_{q}(n,d,k)$ denotes the maximum size of all $(n,M,d,k)_{q}$ 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 ${mathcal {G}}_{q}(n, k)$ . As applications, numerous CDCs with larger size than the previously best known codes are obtained, including $A_{q}(18, 6,9), A_{q}(14, 6, 7), ~A_{q}(12, 4, 6), A_{q}(10, 4, 5),A_{q}(14, 4, 7),$ $A_{q}(16, 4, 8)$ and $A_{q}(n, 4,4)$ for $13leq nleq 16$ .
{"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}
Pub Date : 2025-08-04DOI: 10.1109/TIT.2025.3595488
Bruce Hajek;Xiaohan Kang
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.
{"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}
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.
{"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}
Pub Date : 2025-08-01DOI: 10.1109/TIT.2025.3594999
Holger Boche;Andrea Grigorescu;Rafael F. Schaefer;H. Vincent Poor
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.
{"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}
Pub Date : 2025-07-31DOI: 10.1109/TIT.2025.3594536
Zhaoxing Gao;Ruey S. Tsay
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 $p_{1}times p_{2}$ matrix-variate time series consists of a dynamically dependent, lower-dimensional matrix-variate factor process and a $p_{1}times p_{2}$ 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.
{"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}
Pub Date : 2025-07-31DOI: 10.1109/TIT.2025.3594472
Meng Cao;Yang Li;Shixin Zhu
In 2019, Carlet et al. introduced the concept of $sigma $ duals of linear codes involving the $sigma $ inner product, which generalizes the Euclidean, Hermitian and $ell $ -Galois cases. This paper focuses on constructing new and improved classical codes and quantum codes within the framework of the $sigma $ inner product. We derive some general properties of linear codes, including matrix-product (MP) codes, with respect to the $sigma $ inner product. We develop general methods and design effective routes involving certain optimization problems for constructing $sigma $ self-orthogonal (SO) and $sigma $ dual-containing (DC) MP codes. Our schemes efficiently generate numerous such codes with new or optimal parameters. We establish the $sigma $ 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 $sigma $ 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 q-ary EAQECCs with lengths $(q^{2}-1)(q+2)$ and $q^{2}(q+2)$ , respectively. These families include many q-ary QECCs that are not only new according to Grassl’s online database but also surpass those listed in Edel’s online database.
{"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}
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