IEEE Transactions on Information Theory最新文献

IEEE Transactions on Information Theory Publication Information

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-25 DOI: 10.1109/TIT.2024.3493733

引用次数: 0

IEEE Transactions on Information Theory Information for Authors 电气和电子工程师学会《信息论导刊》（IEEE Transactions on Information Theory）作者须知

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-25 DOI: 10.1109/TIT.2024.3493737

引用次数: 0

Reliable Computation by Large-Alphabet Formulas in the Presence of Noise 在有噪声的情况下通过大字母公式进行可靠计算

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-11-01 DOI: 10.1109/TIT.2024.3486278

Andrew K. Tan;Matthew H. Ho;Isaac L. Chuang

{"title":"Reliable Computation by Large-Alphabet Formulas in the Presence of Noise","authors":"Andrew K. Tan;Matthew H. Ho;Isaac L. Chuang","doi":"10.1109/TIT.2024.3486278","DOIUrl":"https://doi.org/10.1109/TIT.2024.3486278","url":null,"abstract":"We present two new positive results for reliable computation using formulas over physical alphabets of size \u0000<inline-formula> <tex-math>$q gt 2$ </tex-math></inline-formula>\u0000. First, we show that for logical alphabets of size \u0000<inline-formula> <tex-math>$ell = q$ </tex-math></inline-formula>\u0000 the threshold for denoising using gates subject to q-ary symmetric noise with error probability \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000 is strictly larger than that for Boolean computation, and we show that reliable computation is possible as long as signals remain distinguishable, i.e. \u0000<inline-formula> <tex-math>$epsilon lt (q - 1) / q$ </tex-math></inline-formula>\u0000, in the limit of large fan-in \u0000<inline-formula> <tex-math>$k rightarrow infty $ </tex-math></inline-formula>\u0000. We also determine the point at which generalized majority gates with bounded fan-in fail, and show in particular that reliable computation is possible for \u0000<inline-formula> <tex-math>$epsilon lt (q - 1) / (q (q + 1))$ </tex-math></inline-formula>\u0000 in the case of q prime and fan-in \u0000<inline-formula> <tex-math>$k = 3$ </tex-math></inline-formula>\u0000. Secondly, we provide an example where \u0000<inline-formula> <tex-math>$ell lt q$ </tex-math></inline-formula>\u0000, showing that reliable Boolean computation, \u0000<inline-formula> <tex-math>$ell = 2$ </tex-math></inline-formula>\u0000, can be performed using 2-input ternary, \u0000<inline-formula> <tex-math>$q = 3$ </tex-math></inline-formula>\u0000, logic gates subject to symmetric ternary noise of strength \u0000<inline-formula> <tex-math>$varepsilon lt 1/6$ </tex-math></inline-formula>\u0000 by using the additional alphabet element for error signaling.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9152-9164"},"PeriodicalIF":2.2,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713880","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}

引用次数: 0

Capacity Results for the Wiretapped Oblivious Transfer 窃听遗忘转移的能力结果

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-28 DOI: 10.1109/TIT.2024.3487218

Tianyou Pei;Wei Kang;Nan Liu

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IEEE Transactions on Information Theory Information for Authors 电气和电子工程师学会《信息论导刊》（IEEE Transactions on Information Theory）作者须知

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-25 DOI: 10.1109/TIT.2024.3477754

引用次数: 0

IEEE Transactions on Information Theory Publication Information 电气和电子工程师学会《信息论学报》出版信息

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-25 DOI: 10.1109/TIT.2024.3477756

引用次数: 0

A Recursive Construction for Projective Reed-Muller Codes

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-21 DOI: 10.1109/TIT.2024.3483998

Rodrigo San-José

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Characterizations of the Minimum Weights of LCD Codes of Large Dimensions 大尺寸液晶编码的最小权重特征

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-18 DOI: 10.1109/TIT.2024.3483218

Makoto Araya;Masaaki Harada;Keita Ishizuka;Yuto Tanaka

引用次数: 0

Universality in Block Dependent Linear Models With Applications to Nonlinear Regression 块依赖线性模型中的普遍性及其在非线性回归中的应用

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-16 DOI: 10.1109/TIT.2024.3481956

Samriddha Lahiry;Pragya Sur

{"title":"Universality in Block Dependent Linear Models With Applications to Nonlinear Regression","authors":"Samriddha Lahiry;Pragya Sur","doi":"10.1109/TIT.2024.3481956","DOIUrl":"https://doi.org/10.1109/TIT.2024.3481956","url":null,"abstract":"Over the past decade, characterizing the precise asymptotic risk of regularized estimators in high-dimensional regression has emerged as a prominent research area. This literature focuses on the proportional asymptotics regime, where the number of features and samples diverge proportionally. Much of this work assumes i.i.d. Gaussian entries in the design. Concurrently, researchers have explored the universality of these findings, discovering that results based on the i.i.d. Gaussian assumption extend to other settings, including i.i.d. sub-Gaussian designs. However, universality results examining dependent covariates have predominanatly focused on correlation-based dependence or structured forms of dependence allowed by right-rotationally-invariant designs. In this paper, we challenge this limitation by investigating dependence structures beyond these established classes. We identify a class of designs characterized by a block dependence structure where results based on i.i.d. Gaussian designs persist. Formally, we establish that the optimal values of regularized empirical risk and the risk associated with convex regularized estimators, such as the Lasso and the ridge, converge to the same limit under block-dependent designs as for i.i.d. Gaussian entry designs. Our dependence structure differs significantly from correlation-based dependence and enables, for the first time, asymptotically exact risk characterization in prevalent high-dimensional nonlinear regression problems.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"8975-9000"},"PeriodicalIF":2.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713761","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}

引用次数: 0

The Local Landscape of Phase Retrieval Under Limited Samples 有限样本下的相位检索局部景观

IF 2.2 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2024-10-15 DOI: 10.1109/TIT.2024.3481269

Kaizhao Liu;Zihao Wang;Lei Wu

{"title":"The Local Landscape of Phase Retrieval Under Limited Samples","authors":"Kaizhao Liu;Zihao Wang;Lei Wu","doi":"10.1109/TIT.2024.3481269","DOIUrl":"https://doi.org/10.1109/TIT.2024.3481269","url":null,"abstract":"We present a fine-grained analysis of the local landscape of phase retrieval under the regime of limited samples. Specifically, we aim to ascertain the minimal sample size required to guarantee a benign local landscape surrounding global minima in high dimensions. Let n and d denote the sample size and input dimension, respectively. We first explore the local convexity and establish that when \u0000<inline-formula> <tex-math>$n=o(dlog d)$ </tex-math></inline-formula>\u0000, for almost every fixed point in the local ball, the Hessian matrix has negative eigenvalues, provided d is sufficiently large. We next consider the one-point convexity and show that, as long as \u0000<inline-formula> <tex-math>$n=omega (d)$ </tex-math></inline-formula>\u0000, with high probability, the landscape is one-point strongly convex in the local annulus: \u0000<inline-formula> <tex-math>${win mathbb {R}^{d}: o_{d}({1})leqslant |w-w^{*}|leqslant c}$ </tex-math></inline-formula>\u0000, where \u0000<inline-formula> <tex-math>$w^{*}$ </tex-math></inline-formula>\u0000 is the ground truth and c is an absolute constant. This implies that gradient descent, initialized from any point in this domain, can converge to an \u0000<inline-formula> <tex-math>$o_{d}({1})$ </tex-math></inline-formula>\u0000-loss solution exponentially fast. Furthermore, we show that when \u0000<inline-formula> <tex-math>$n=o(dlog d)$ </tex-math></inline-formula>\u0000, there is a radius of \u0000<inline-formula> <tex-math>$widetilde {Theta } left ({{sqrt {1/d}}}right)$ </tex-math></inline-formula>\u0000 such that one-point convexity breaks down in the corresponding smaller local ball. This indicates an impossibility to establish a convergence to the exact \u0000<inline-formula> <tex-math>$w^{*}$ </tex-math></inline-formula>\u0000 for gradient descent under limited samples by relying solely on one-point convexity.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 12","pages":"9012-9035"},"PeriodicalIF":2.2,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142713915","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}

引用次数: 0