Pub Date : 2025-10-17DOI: 10.1109/TIT.2025.3622930
Chih Wei Ling;Cheuk Ting Li
We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6,..., 48, and also has a smaller mean squared error compared to known lattice quantizers with the same entropy for dimensions 35,..., 47, in the high resolution limit. Moreover, our randomized quantizer has a desirable property that the quantization error is always uniform over the ball and independent of the input. Our construction is based on applying rejection sampling on universal quantization, which allows us to shape the error distribution to be any continuous distribution, not only uniform distributions over basic cells of a lattice as in conventional dithered quantization. We also characterize the high SNR limit of one-shot channel simulation for any additive noise channel under a mild assumption (e.g., the AWGN channel), up to an additive constant of 1.45 bits.
{"title":"Rejection-Sampled Universal Quantization for Smaller Quantization Errors","authors":"Chih Wei Ling;Cheuk Ting Li","doi":"10.1109/TIT.2025.3622930","DOIUrl":"https://doi.org/10.1109/TIT.2025.3622930","url":null,"abstract":"We construct a randomized vector quantizer which has a smaller maximum error compared to all known lattice quantizers with the same entropy for dimensions 5, 6,..., 48, and also has a smaller mean squared error compared to known lattice quantizers with the same entropy for dimensions 35,..., 47, in the high resolution limit. Moreover, our randomized quantizer has a desirable property that the quantization error is always uniform over the ball and independent of the input. Our construction is based on applying rejection sampling on universal quantization, which allows us to shape the error distribution to be any continuous distribution, not only uniform distributions over basic cells of a lattice as in conventional dithered quantization. We also characterize the high SNR limit of one-shot channel simulation for any additive noise channel under a mild assumption (e.g., the AWGN channel), up to an additive constant of 1.45 bits.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9784-9803"},"PeriodicalIF":2.9,"publicationDate":"2025-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595133","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 : 2025-10-16DOI: 10.1109/TIT.2025.3622405
Aristomenis Tsopelakos;Georgios Fellouris
The problem of sequential anomaly identification is considered, where multiple data sources are simultaneously monitored and the goal is to identify in real time those, if any, that exhibit “anomalous” statistical behavior. An upper bound is postulated on the number of data sources that can be sampled at each sampling instant, but the decision maker selects which ones to sample based on the already collected data. In this context, a policy consists not only of a stopping rule and a decision rule but also of a sampling rule that determines which sources to sample at each instant. Two distinct formulations are considered, which require control of different generalized error metrics. The first one tolerates a certain user-specified number of errors of any kind, whereas the second tolerates distinct, user-specified numbers of false positives and false negatives. For each formulation and as the error probabilities go to 0, a universal asymptotic lower bound on the expected time for stopping is established in terms of a deterministic max-min problem, and it is shown to be attained by a policy with a probabilistic sampling rule that achieves a specific long-run sampling frequency for each source which comes from the solution of each max-min problem. In certain cases, it is optimal to disregard some of the sources with the most difficult testing problems, introducing a need for forced exploration that is absent in the case of classical error control. In simulation study, the expected time for stopping is plotted in a finite regime, under various scenarios, and the impact of the sampling constraint and tolerance to errors is assessed.
{"title":"Sequential Anomaly Identification Under Sampling Constraints for Generalized Error Metrics","authors":"Aristomenis Tsopelakos;Georgios Fellouris","doi":"10.1109/TIT.2025.3622405","DOIUrl":"https://doi.org/10.1109/TIT.2025.3622405","url":null,"abstract":"The problem of sequential anomaly identification is considered, where multiple data sources are simultaneously monitored and the goal is to identify in real time those, if any, that exhibit “anomalous” statistical behavior. An upper bound is postulated on the number of data sources that can be sampled at each sampling instant, but the decision maker selects which ones to sample based on the already collected data. In this context, a policy consists not only of a stopping rule and a decision rule but also of a sampling rule that determines which sources to sample at each instant. Two distinct formulations are considered, which require control of different generalized error metrics. The first one tolerates a certain user-specified number of errors of any kind, whereas the second tolerates distinct, user-specified numbers of false positives and false negatives. For each formulation and as the error probabilities go to 0, a universal asymptotic lower bound on the expected time for stopping is established in terms of a deterministic max-min problem, and it is shown to be attained by a policy with a probabilistic sampling rule that achieves a specific long-run sampling frequency for each source which comes from the solution of each max-min problem. In certain cases, it is optimal to disregard some of the sources with the most difficult testing problems, introducing a need for forced exploration that is absent in the case of classical error control. In simulation study, the expected time for stopping is plotted in a finite regime, under various scenarios, and the impact of the sampling constraint and tolerance to errors is assessed.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9753-9783"},"PeriodicalIF":2.9,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11205356","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595109","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 : 2025-10-14DOI: 10.1109/TIT.2025.3621494
Yinghao Liang;Zihui Liu
The symbol-pair simplex codes were introduced by the authors recently, and these codes play a similar role as simplex codes with respect to the Hamming metric. Among other things, the concatenations of the symbol-pair simplex codes are symbol-pair constant-weight codes which are a family of codes achieving the Plotkin-type upper bound of the generalized symbol-pair weight, and thus provide optimal security in the data transmission with the symbol-pair metric in the wire-tap channel with the coset coding scheme. Motivated by the mentioned applications, we present new constructions of symbol-pair simplex codes over any finite field.
{"title":"New Constructions of Symbol-Pair Simplex Codes","authors":"Yinghao Liang;Zihui Liu","doi":"10.1109/TIT.2025.3621494","DOIUrl":"https://doi.org/10.1109/TIT.2025.3621494","url":null,"abstract":"The symbol-pair simplex codes were introduced by the authors recently, and these codes play a similar role as simplex codes with respect to the Hamming metric. Among other things, the concatenations of the symbol-pair simplex codes are symbol-pair constant-weight codes which are a family of codes achieving the Plotkin-type upper bound of the generalized symbol-pair weight, and thus provide optimal security in the data transmission with the symbol-pair metric in the wire-tap channel with the coset coding scheme. Motivated by the mentioned applications, we present new constructions of symbol-pair simplex codes over any finite field.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9563-9568"},"PeriodicalIF":2.9,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595124","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 : 2025-10-09DOI: 10.1109/TIT.2025.3619905
Yifeng Fan;Zhizhen Zhao
The emerging problem of joint community detection and group synchronization, with applications in signal processing and machine learning, has been extensively studied in recent years. Previous research on this topic has focused predominantly on a statistical model that extends the stochastic block model (SBM) by incorporating additional group transformations. In its simplest form, a random network of size n is generated with two communities of equal size, where each node i is associated with a group element $g_{i}^{*} in {mathcal {G}}_{M}$ for some finite group ${mathcal {G}}_{M}$ of order M. The nodes are connected with probability p if they are in the same community, and q otherwise. In addition, a group transformation $g_{ij}$ is observed at each edge, where $g_{ij} = g_{i}^{*}(g_{j}^{*})^{-1}$ if the nodes i and j are in the same community, and $g_{ij} sim text {Unif}({mathcal {G}}_{M})$ otherwise. The goal is to recover both the underlying communities and group elements. When $p = frac {alog n}{n}$ and $q = frac {blog n}{n} $ with $a, b gt 0$ , we establish the sharp information-theoretic threshold for exact recovery: mathfonts $(i):enspace frac {a + b}{2} -sqrt {frac {ab}{M}} gt 1 quad text {and} quad (ii):enspace a gt 2$ where exact recovery of communities is possible only if $(i)$ is satisfied, and recovery of group elements is achieved only if both $(i)$ and $(ii)$ hold. Our theory indicates the recovery of communities greatly benefits from the group elements, and demonstrates a significant performance gap between the information limit and existing approaches.
近年来，群体联合检测和群体同步问题在信号处理和机器学习等领域得到了广泛的研究。先前对该主题的研究主要集中在一个统计模型上，该模型通过加入额外的群变换来扩展随机块模型（SBM）。在其最简单的形式中，一个大小为n的随机网络由两个大小相等的群体生成，其中每个节点i与某个m阶有限群体${mathcal {G}}_{M}$的组元素$g_{i}^{*} in {mathcal {G}}_{M}$相关联，如果节点在同一群体中，节点连接的概率为p，否则为q。此外，在每条边观察到一个群体变换$g_{ij}$，如果节点i和j在同一社区，则为$g_{ij} = g_{i}^{*}(g_{j}^{*})^{-1}$，否则为$g_{ij} sim text {Unif}({mathcal {G}}_{M})$。目标是恢复潜在的社区和群体元素。当$p = frac {alog n}{n}$和$q = frac {blog n}{n} $与$a, b gt 0$相结合时，我们为精确恢复建立了明确的信息理论阈值：mathfonts $(i):enspace frac {a + b}{2} -sqrt {frac {ab}{M}} gt 1 quad text {and} quad (ii):enspace a gt 2$，其中只有$(i)$满足时才能精确恢复社区，只有$(i)$和$(ii)$都满足时才能恢复组元素。我们的理论表明，群体元素极大地促进了社区的恢复，并证明了信息限制与现有方法之间存在显著的性能差距。
{"title":"Information Limits of Joint Community Detection and Finite Group Synchronization","authors":"Yifeng Fan;Zhizhen Zhao","doi":"10.1109/TIT.2025.3619905","DOIUrl":"https://doi.org/10.1109/TIT.2025.3619905","url":null,"abstract":"The emerging problem of joint community detection and group synchronization, with applications in signal processing and machine learning, has been extensively studied in recent years. Previous research on this topic has focused predominantly on a statistical model that extends the stochastic block model (SBM) by incorporating additional group transformations. In its simplest form, a random network of size <italic>n</i> is generated with two communities of equal size, where each node <italic>i</i> is associated with a group element <inline-formula> <tex-math>$g_{i}^{*} in {mathcal {G}}_{M}$ </tex-math></inline-formula> for some finite group <inline-formula> <tex-math>${mathcal {G}}_{M}$ </tex-math></inline-formula> of order <italic>M</i>. The nodes are connected with probability <italic>p</i> if they are in the same community, and <italic>q</i> otherwise. In addition, a group transformation <inline-formula> <tex-math>$g_{ij}$ </tex-math></inline-formula> is observed at each edge, where <inline-formula> <tex-math>$g_{ij} = g_{i}^{*}(g_{j}^{*})^{-1}$ </tex-math></inline-formula> if the nodes <italic>i</i> and <italic>j</i> are in the same community, and <inline-formula> <tex-math>$g_{ij} sim text {Unif}({mathcal {G}}_{M})$ </tex-math></inline-formula> otherwise. The goal is to recover both the underlying communities and group elements. When <inline-formula> <tex-math>$p = frac {alog n}{n}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$q = frac {blog n}{n} $ </tex-math></inline-formula> with <inline-formula> <tex-math>$a, b gt 0$ </tex-math></inline-formula>, we establish the sharp information-theoretic threshold for exact recovery: mathfonts <inline-formula> <tex-math>$(i):enspace frac {a + b}{2} -sqrt {frac {ab}{M}} gt 1 quad text {and} quad (ii):enspace a gt 2$ </tex-math></inline-formula> where exact recovery of communities is possible only if <inline-formula> <tex-math>$(i)$ </tex-math></inline-formula> is satisfied, and recovery of group elements is achieved only if both <inline-formula> <tex-math>$(i)$ </tex-math></inline-formula> and <inline-formula> <tex-math>$(ii)$ </tex-math></inline-formula> hold. Our theory indicates the recovery of communities greatly benefits from the group elements, and demonstrates a significant performance gap between the information limit and existing approaches.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 1","pages":"542-570"},"PeriodicalIF":2.9,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145808583","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 : 2025-10-09DOI: 10.1109/TIT.2025.3619813
Dong Huang;Xianwen Song;Pengkun Yang
This paper studies the problem of recovering hidden vertex correspondences between two correlated random graphs. We introduce the partially correlated Erdős-Rényi model and the partially correlated Gaussian Wigner model, where a pair of induced subgraphs is correlated. We investigate the information-theoretic thresholds for recovering these latent correlated subgraphs and their hidden vertex correspondences. For the partially correlated Erdős-Rényi model, we establish the optimal rate for partial recovery: above this threshold, a positive fraction of vertices can be correctly matched, while below it, matching any positive fraction is impossible. We also determine the optimal rate for exact recovery. In the partially correlated Gaussian Wigner model, the optimal rates for partial and exact recovery coincide. To prove the achievability results, we introduce correlated functional digraphs to partition the edges and bound error probabilities using lower-order cumulant generating functions. Our impossibility results rely on a generalized Fano’s inequality and the recovery thresholds for correlated Erdős-Rényi graphs.
{"title":"Information-Theoretic Thresholds for the Alignments of Partially Correlated Graphs","authors":"Dong Huang;Xianwen Song;Pengkun Yang","doi":"10.1109/TIT.2025.3619813","DOIUrl":"https://doi.org/10.1109/TIT.2025.3619813","url":null,"abstract":"This paper studies the problem of recovering hidden vertex correspondences between two correlated random graphs. We introduce the partially correlated Erdős-Rényi model and the partially correlated Gaussian Wigner model, where a pair of induced subgraphs is correlated. We investigate the information-theoretic thresholds for recovering these latent correlated subgraphs and their hidden vertex correspondences. For the partially correlated Erdős-Rényi model, we establish the optimal rate for partial recovery: above this threshold, a positive fraction of vertices can be correctly matched, while below it, matching any positive fraction is impossible. We also determine the optimal rate for exact recovery. In the partially correlated Gaussian Wigner model, the optimal rates for partial and exact recovery coincide. To prove the achievability results, we introduce correlated functional digraphs to partition the edges and bound error probabilities using lower-order cumulant generating functions. Our impossibility results rely on a generalized Fano’s inequality and the recovery thresholds for correlated Erdős-Rényi graphs.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9674-9697"},"PeriodicalIF":2.9,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595138","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 : 2025-10-07DOI: 10.1109/TIT.2025.3618595
Adel Javanmard;Mohammad Mehrabi
Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable Y and another variable X, while controlling for the effect of a high-dimensional confounding variable Z. In this paper, we introduce a novel test, called ‘Pearson Chi-squared Conditional Randomization’ (PCR) test, which uses the distributional information on covariates $X,Z$ and constructs randomizations to test conditional independence. PCR leverages the i.i.d-ness property of the observations to obtain high-resolution p-values with a very small number of conditional randomizations. We also provide a power analysis of the PCR test, which captures the effect of various parameters of the test, the sample size and the distance of the alternative from the set of null distributions, measured in terms of a notion called ‘conditional relative density’. In addition, we propose two extensions of the PCR test, with important practical implications: $(i)$ parameter-free PCR, which uses Bonferroni’s correction to decide on a tuning parameter in the test; $(ii)$ robust PCR, which avoids inflations in the size of the test when there is slight error in estimating the conditional law $P_{X|Z}$ .
{"title":"Pearson Chi-Squared Conditional Randomization Test","authors":"Adel Javanmard;Mohammad Mehrabi","doi":"10.1109/TIT.2025.3618595","DOIUrl":"https://doi.org/10.1109/TIT.2025.3618595","url":null,"abstract":"Conditional independence (CI) testing arises naturally in many scientific problems and applications domains. The goal of this problem is to investigate the conditional independence between a response variable <italic>Y</i> and another variable <italic>X</i>, while controlling for the effect of a high-dimensional confounding variable <italic>Z</i>. In this paper, we introduce a novel test, called ‘Pearson Chi-squared Conditional Randomization’ (PCR) test, which uses the distributional information on covariates <inline-formula> <tex-math>$X,Z$ </tex-math></inline-formula> and constructs randomizations to test conditional independence. PCR leverages the i.i.d-ness property of the observations to obtain high-resolution p-values with a very small number of conditional randomizations. We also provide a power analysis of the PCR test, which captures the effect of various parameters of the test, the sample size and the distance of the alternative from the set of null distributions, measured in terms of a notion called ‘conditional relative density’. In addition, we propose two extensions of the PCR test, with important practical implications: <inline-formula> <tex-math>$(i)$ </tex-math></inline-formula> parameter-free PCR, which uses Bonferroni’s correction to decide on a tuning parameter in the test; <inline-formula> <tex-math>$(ii)$ </tex-math></inline-formula> robust PCR, which avoids inflations in the size of the test when there is slight error in estimating the conditional law <inline-formula> <tex-math>$P_{X|Z}$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9617-9646"},"PeriodicalIF":2.9,"publicationDate":"2025-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595139","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 : 2025-10-01DOI: 10.1109/TIT.2025.3616035
Yongqiang Li;Fangzhen Wang;Xingwei Ren;Fen Liu;Xichao Hu;Lin Jiao;Ya Han
Permutations with low multiplication depth over prime fields are highly valuable in the design of symmetric ciphers that are compatible with fully homomorphic encryption (FHE). Quadratic permutations, which have the lowest depth, have been widely used in prior designs. In this paper, we propose a construction method that can give new quadratic permutations over $mathbb {F}_{p}^{m}$ , and cryptographic properties such as differential uniformity and Walsh spectrum of these permutations are also characterized. We give sufficient conditions for permutations over $mathbb {F}_{p}^{n}$ to attain a differential uniformity of $p^{n-1}$ for $nge 3$ . Furthermore, it is proven that for these permutations, the maximal 2-norm of Walsh coefficients remains bounded by $p^{n-1}$ , provided either the last $n-1$ entries of the input mask or the last $n-1$ entries of the output mask form a nonzero vector. As an application, we design a new FHE-friendly stream cipher named $textsf {YuS}$ based on a new quadratic permutation over $mathbb {F}_{p}^{3}$ and a fixed linear mapping. According to our implementation, $textsf {YuS}$ achieves faster evaluation times and higher throughput compared to Masta, Pasta, $text {Pasta}_{mathrm {v2}}$ and HERA in almost all instances for both BGV and BFV schemes at 80-bit and 128-bit security levels.
{"title":"YuS: A FHE-Friendly Stream Cipher Based on New Quadratic Permutations","authors":"Yongqiang Li;Fangzhen Wang;Xingwei Ren;Fen Liu;Xichao Hu;Lin Jiao;Ya Han","doi":"10.1109/TIT.2025.3616035","DOIUrl":"https://doi.org/10.1109/TIT.2025.3616035","url":null,"abstract":"Permutations with low multiplication depth over prime fields are highly valuable in the design of symmetric ciphers that are compatible with fully homomorphic encryption (FHE). Quadratic permutations, which have the lowest depth, have been widely used in prior designs. In this paper, we propose a construction method that can give new quadratic permutations over <inline-formula> <tex-math>$mathbb {F}_{p}^{m}$ </tex-math></inline-formula>, and cryptographic properties such as differential uniformity and Walsh spectrum of these permutations are also characterized. We give sufficient conditions for permutations over <inline-formula> <tex-math>$mathbb {F}_{p}^{n}$ </tex-math></inline-formula> to attain a differential uniformity of <inline-formula> <tex-math>$p^{n-1}$ </tex-math></inline-formula> for <inline-formula> <tex-math>$nge 3$ </tex-math></inline-formula>. Furthermore, it is proven that for these permutations, the maximal 2-norm of Walsh coefficients remains bounded by <inline-formula> <tex-math>$p^{n-1}$ </tex-math></inline-formula>, provided either the last <inline-formula> <tex-math>$n-1$ </tex-math></inline-formula> entries of the input mask or the last <inline-formula> <tex-math>$n-1$ </tex-math></inline-formula> entries of the output mask form a nonzero vector. As an application, we design a new FHE-friendly stream cipher named <inline-formula> <tex-math>$textsf {YuS}$ </tex-math></inline-formula> based on a new quadratic permutation over <inline-formula> <tex-math>$mathbb {F}_{p}^{3}$ </tex-math></inline-formula> and a fixed linear mapping. According to our implementation, <inline-formula> <tex-math>$textsf {YuS}$ </tex-math></inline-formula> achieves faster evaluation times and higher throughput compared to Masta, <sc>Pasta</small>, <inline-formula> <tex-math>$text {Pasta}_{mathrm {v2}}$ </tex-math></inline-formula> and HERA in almost all instances for both BGV and BFV schemes at 80-bit and 128-bit security levels.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9714-9731"},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595135","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 : 2025-10-01DOI: 10.1109/TIT.2025.3616817
Georg Tauböck;Shristi Rajbamshi;Peter Balazs
We investigate the applicability of frame multipliers as compressive sensing measurements. We show that, under certain conditions, subsampled frame multipliers yield measurement matrices with desirable properties. To that end, we prove a general probabilistic nullspace property for arbitrary nonempty sets, that accounts for the special measurement structure induced by subsampled frame multipliers. Conditions for uniqueness of reconstruction of signals that are sparse with respect to dictionaries or, more generally, to non-linear locally Lipschitz mappings are obtained as special cases. Furthermore, we show that a frame multiplier matrix is full superregular, i.e., that all its minors are nonzero, for almost all frame symbol vectors, provided that the underlying frames are full spark and sufficiently redundant. Since Gabor frames are full spark for almost all windows, we study Gabor multipliers in more detail and are able to derive improved constants for some scenarios. Finally, our simulation results reveal that, in many instances, subsampled frame multiplier matrices exhibit the same $ell _{1}$ -reconstruction performance as i.i.d. Gaussian measurement matrices.
我们研究帧乘法器作为压缩感知测量的适用性。我们证明，在一定条件下，下采样帧乘法器产生具有理想性质的测量矩阵。为此，我们证明了任意非空集的一般概率零空间性质，这解释了由下采样帧乘法器引起的特殊测量结构。对于相对于字典或更一般的非线性局部Lipschitz映射的稀疏信号，作为特例得到了其重构的唯一性条件。进一步，我们证明了一个帧乘法器矩阵是完全超正则的，即，对于几乎所有的帧符号向量，它的所有子矩阵都是非零的，只要底层帧是完全火花和足够冗余的。由于Gabor帧对几乎所有窗口都是满火花的，我们更详细地研究了Gabor乘子，并能够为某些场景导出改进的常数。最后，我们的仿真结果表明，在许多情况下，下采样帧乘法器矩阵表现出与i.i.d高斯测量矩阵相同的$ well _{1}$ -重建性能。
{"title":"Frame Multipliers and Compressive Sensing","authors":"Georg Tauböck;Shristi Rajbamshi;Peter Balazs","doi":"10.1109/TIT.2025.3616817","DOIUrl":"https://doi.org/10.1109/TIT.2025.3616817","url":null,"abstract":"We investigate the applicability of frame multipliers as compressive sensing measurements. We show that, under certain conditions, subsampled frame multipliers yield measurement matrices with desirable properties. To that end, we prove a general probabilistic nullspace property for arbitrary nonempty sets, that accounts for the special measurement structure induced by subsampled frame multipliers. Conditions for uniqueness of reconstruction of signals that are sparse with respect to dictionaries or, more generally, to non-linear locally Lipschitz mappings are obtained as special cases. Furthermore, we show that a frame multiplier matrix is full superregular, i.e., that all its minors are nonzero, for almost all frame symbol vectors, provided that the underlying frames are full spark and sufficiently redundant. Since Gabor frames are full spark for almost all windows, we study Gabor multipliers in more detail and are able to derive improved constants for some scenarios. Finally, our simulation results reveal that, in many instances, subsampled frame multiplier matrices exhibit the same <inline-formula> <tex-math>$ell _{1}$ </tex-math></inline-formula>-reconstruction performance as i.i.d. Gaussian measurement matrices.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1393-1410"},"PeriodicalIF":2.9,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11187356","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015949","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}
In this article, we study bent functions on <inline-formula> <tex-math>$ mathbb {F}_{2}^{2m} $ </tex-math></inline-formula> of the form <inline-formula> <tex-math>$ f(x,y) = x cdot phi (y) + h(y) $ </tex-math></inline-formula>, where <inline-formula> <tex-math>$ x in mathbb {F}_{2}^{m-1} $ </tex-math></inline-formula> and <inline-formula> <tex-math>$ y in mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula>, which form the generalized Maiorana-McFarland class (denoted by <inline-formula> <tex-math>$ {mathcal {GMM}}_{m+1} $ </tex-math></inline-formula>) and are referred to as almost Maiorana-McFarland bent functions. We provide a complete characterization of the bent property for such functions and determine their duals. Specifically, we show that <inline-formula> <tex-math>$f$ </tex-math></inline-formula> is bent if and only if the mapping <inline-formula> <tex-math>$ phi $ </tex-math></inline-formula> partitions <inline-formula> <tex-math>$ mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula> into 2-dimensional affine subspaces, on each of which the function <inline-formula> <tex-math>$ h $ </tex-math></inline-formula> has odd weight. While the partition of <inline-formula> <tex-math>$mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula> into 2-dimensional affine subspaces is crucial for the bentness, we demonstrate that the algebraic structure of these subspaces plays an even greater role in ensuring that the constructed bent functions <inline-formula> <tex-math>$f$ </tex-math></inline-formula> are excluded from the completed Maiorana-McFarland class <inline-formula> <tex-math>$ mathcal {M}^{#} $ </tex-math></inline-formula> (the set of bent functions that are extended-affine equivalent to bent functions from the Maiorana-McFarland class <inline-formula> <tex-math>$mathcal {M}$ </tex-math></inline-formula>). Consequently, we investigate which properties of mappings <inline-formula> <tex-math>$ phi colon mathbb {F}_{2}^{m+1} to mathbb {F}_{2}^{m-1} $ </tex-math></inline-formula> lead to bent functions of the form <inline-formula> <tex-math>$ f(x,y) = x cdot phi (y) + h(y) $ </tex-math></inline-formula> both inside and outside <inline-formula> <tex-math>$ mathcal {M}^{#} $ </tex-math></inline-formula> and provide construction methods for suitable Boolean functions <inline-formula> <tex-math>$ h $ </tex-math></inline-formula> on <inline-formula> <tex-math>$ mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula>. As part of this framework, we present a simple algorithm for constructing partitions of the vector space <inline-formula> <tex-math>$ mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula> together with appropriate Boolean functions <inline-formula> <tex-math>$ h $ </tex-math></inline-formula> that generate bent functions outside <inline-formula> <tex-math>$ mathcal {M}^{#} $ </tex-math></inline-formula>. When <inline-formula> <tex-math>$ 2m = 8 $ </tex-math></inline-formula>, we explicitly identify many such partitions that produce at least <inline
在本文中，我们研究了$ mathbb {F}_{2}^{2m} $上的弯曲函数，其形式为$ F (x,y) = x cdot phi (y) + h(y) $，其中$ x In mathbb {F}_{2}^{m-1} $和$ y In mathbb {F}_{2}^{m+1} $，它们构成广义Maiorana-McFarland类（表示为$ {mathcal {GMM}}_{m+1} $），称为几乎Maiorana-McFarland弯曲函数。我们提供了这类函数弯曲性质的完整表征，并确定了它们的对偶。具体地说，我们证明$f$是弯曲的当且仅当映射$ phi $将$ mathbb {f}_{2}^{m+1} $分割成二维仿射子空间，其中每个子空间上的函数$ h $具有奇数权值。虽然$mathbb {F}_{2}^{m+1} $划分为二维仿射子空间对弯曲性至关重要，但我们证明了这些子空间的代数结构在确保构造的弯曲函数$ F $被排除在完成的Maiorana-McFarland类$mathcal {m}$（扩展仿射等价于Maiorana-McFarland类$mathcal {m}$的弯曲函数集合）之外方面发挥了更大的作用。因此，我们研究了映射$ phi 冒号mathbb {F}_ b{2}^{m+1} 到$ mathbb {F}_{2}^{m-1} $的哪些性质导致$ F (x,y) = x cdot phi (y) + h(y) $在$ mathcal {m}^{#} $内外的弯曲函数，并提供了在$ mathbb {F}_{2}^{m+1} $上合适的布尔函数$ h $的构造方法。作为这个框架的一部分，我们提出了一个简单的算法，用于构造向量空间$ mathbb {F}_{2}^{m+1} $的分区，以及在$ mathcal {m}^{#} $之外生成弯曲函数的适当的布尔函数$ h $。当$ 2m = 8 $时，我们显式地识别出许多这样的分区，这些分区在$ mathbb {F}_{2}^{8} $上产生至少$2^{78}$不同的弯曲函数，这些函数不属于$ mathcal {M}^{#} $，从而在$ mathcal {M}^{#} $之外生成的弯曲函数比$ mathcal {M}^{#} $中8变量弯曲函数的总数还多（其基数大约为$2^{77}$）。此外，我们证明了在$ mathcal {M}^{#} $之外连接四个几乎Maiorana-McFarland弯曲函数，即定义$ f = f_{1} || f_{2} || f_{3} || f_{4} $，其中$ f_{i} M}^{#} $中可以得到$ f 在mathcal {M}^{#} $中的弯曲函数。这一发现基本上回答了Kudin等人最近提出的一个开放性问题。参考文献31(5):3999- 4011,2025)。相反，使用类似的方法连接四个函数$ f_{1} || f_{2} || f_{3} || f_{4} $，其中每个$ f_{i} 在mathcal {M}^{#} $中，我们生成可证明在$ mathcal {M}^{#} $之外的弯曲函数。
{"title":"Almost Maiorana-McFarland Bent Functions","authors":"Sadmir Kudin;Enes Pasalic;Alexandr Polujan;Fengrong Zhang;Haixia Zhao","doi":"10.1109/TIT.2025.3614379","DOIUrl":"https://doi.org/10.1109/TIT.2025.3614379","url":null,"abstract":"In this article, we study bent functions on <inline-formula> <tex-math>$ mathbb {F}_{2}^{2m} $ </tex-math></inline-formula> of the form <inline-formula> <tex-math>$ f(x,y) = x cdot phi (y) + h(y) $ </tex-math></inline-formula>, where <inline-formula> <tex-math>$ x in mathbb {F}_{2}^{m-1} $ </tex-math></inline-formula> and <inline-formula> <tex-math>$ y in mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula>, which form the generalized Maiorana-McFarland class (denoted by <inline-formula> <tex-math>$ {mathcal {GMM}}_{m+1} $ </tex-math></inline-formula>) and are referred to as almost Maiorana-McFarland bent functions. We provide a complete characterization of the bent property for such functions and determine their duals. Specifically, we show that <inline-formula> <tex-math>$f$ </tex-math></inline-formula> is bent if and only if the mapping <inline-formula> <tex-math>$ phi $ </tex-math></inline-formula> partitions <inline-formula> <tex-math>$ mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula> into 2-dimensional affine subspaces, on each of which the function <inline-formula> <tex-math>$ h $ </tex-math></inline-formula> has odd weight. While the partition of <inline-formula> <tex-math>$mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula> into 2-dimensional affine subspaces is crucial for the bentness, we demonstrate that the algebraic structure of these subspaces plays an even greater role in ensuring that the constructed bent functions <inline-formula> <tex-math>$f$ </tex-math></inline-formula> are excluded from the completed Maiorana-McFarland class <inline-formula> <tex-math>$ mathcal {M}^{#} $ </tex-math></inline-formula> (the set of bent functions that are extended-affine equivalent to bent functions from the Maiorana-McFarland class <inline-formula> <tex-math>$mathcal {M}$ </tex-math></inline-formula>). Consequently, we investigate which properties of mappings <inline-formula> <tex-math>$ phi colon mathbb {F}_{2}^{m+1} to mathbb {F}_{2}^{m-1} $ </tex-math></inline-formula> lead to bent functions of the form <inline-formula> <tex-math>$ f(x,y) = x cdot phi (y) + h(y) $ </tex-math></inline-formula> both inside and outside <inline-formula> <tex-math>$ mathcal {M}^{#} $ </tex-math></inline-formula> and provide construction methods for suitable Boolean functions <inline-formula> <tex-math>$ h $ </tex-math></inline-formula> on <inline-formula> <tex-math>$ mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula>. As part of this framework, we present a simple algorithm for constructing partitions of the vector space <inline-formula> <tex-math>$ mathbb {F}_{2}^{m+1} $ </tex-math></inline-formula> together with appropriate Boolean functions <inline-formula> <tex-math>$ h $ </tex-math></inline-formula> that generate bent functions outside <inline-formula> <tex-math>$ mathcal {M}^{#} $ </tex-math></inline-formula>. When <inline-formula> <tex-math>$ 2m = 8 $ </tex-math></inline-formula>, we explicitly identify many such partitions that produce at least <inline","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9698-9713"},"PeriodicalIF":2.9,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11180145","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595099","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 : 2025-09-22DOI: 10.1109/TIT.2025.3613143
Lujia Bai;Weichi Wu
This paper proposes a unified framework for inferring large-scale time-varying correlation networks via data-driven time-varying thresholds that can control uncertainty simultaneously. The framework allows the dimension of time series vectors to be fixed or diverging at a high polynomial rate of the sample size. It also allows the time series to exhibit changing temporal characteristics beyond stationarity without specific structural assumptions. Motivated by the practical issue that the confidence band of non-parametric estimators of correlations can exceed their natural domain $[-1,1]$ , we propose a simple uniform variance reduction technique. When applied to the construction of a correlation network, the new device yields more accurate thresholds, which enhance the probability of recovering the time-varying network structures. We broaden the applicability of our method by developing difference-based estimators of cross-correlations that are robust to structure breaks in the time-varying mean functions, and by allowing both a fixed and a diverging number of lags in the correlation functions. We prove the asymptotic validity of the proposed method, especially in achieving accurate family-wise error control when disclosing flexible time-varying network structures. The effectiveness of our method in finite samples is demonstrated through simulation studies and data analysis.
{"title":"Uniform Variance Reduced Simultaneous Inference of Time-Varying Correlation Networks","authors":"Lujia Bai;Weichi Wu","doi":"10.1109/TIT.2025.3613143","DOIUrl":"https://doi.org/10.1109/TIT.2025.3613143","url":null,"abstract":"This paper proposes a unified framework for inferring large-scale time-varying correlation networks via data-driven time-varying thresholds that can control uncertainty simultaneously. The framework allows the dimension of time series vectors to be fixed or diverging at a high polynomial rate of the sample size. It also allows the time series to exhibit changing temporal characteristics beyond stationarity without specific structural assumptions. Motivated by the practical issue that the confidence band of non-parametric estimators of correlations can exceed their natural domain <inline-formula> <tex-math>$[-1,1]$ </tex-math></inline-formula>, we propose a simple uniform variance reduction technique. When applied to the construction of a correlation network, the new device yields more accurate thresholds, which enhance the probability of recovering the time-varying network structures. We broaden the applicability of our method by developing difference-based estimators of cross-correlations that are robust to structure breaks in the time-varying mean functions, and by allowing both a fixed and a diverging number of lags in the correlation functions. We prove the asymptotic validity of the proposed method, especially in achieving accurate family-wise error control when disclosing flexible time-varying network structures. The effectiveness of our method in finite samples is demonstrated through simulation studies and data analysis.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 12","pages":"9647-9673"},"PeriodicalIF":2.9,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145595106","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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