IEEE Transactions on Information Theory最新文献

{"title":"Two Families of Linear Codes With Desirable Properties From Some Functions Over Finite Fields","authors":"Ziling Heng;Xiaoru Li;Yansheng Wu;Qi Wang","doi":"10.1109/TIT.2024.3439408","DOIUrl":"10.1109/TIT.2024.3439408","url":null,"abstract":"Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic. In this paper, based on the augmentation technique, we present two families of linear codes from some functions over finite fields. The first family of linear codes is constructed from monomial functions over finite fields. The weight distribution of the codes is determined in some cases. The codes are proved to be both optimally or almost optimally extendable and self-orthogonal under certain conditions. The localities of the codes and their duals are also studied and we obtain an infinite family of optimal or almost optimal locally recoverable codes. The second family of linear codes is constructed from weakly regular bent functions over finite fields and its weight distribution is explicitly determined. This family of codes is also proved to be both optimally or almost optimally extendable and self-orthogonal. Besides, this family of codes has been proven to have locality 2 or 3 under certain conditions. Particularly, we derive two infinite families of optimal locally recoverable codes. Some infinite families of 2-designs are obtained from the codes in this paper as byproducts.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"8320-8342"},"PeriodicalIF":2.2,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947531","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":"Detection of Correlated Random Vectors","authors":"Dor Elimelech, Wasim Huleihel","doi":"10.1109/tit.2024.3435008","DOIUrl":"https://doi.org/10.1109/tit.2024.3435008","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"62 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947534","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":"Uniform Convergence of Deep Neural Networks With Lipschitz Continuous Activation Functions and Variable Widths","authors":"Yuesheng Xu;Haizhang Zhang","doi":"10.1109/TIT.2024.3439136","DOIUrl":"10.1109/TIT.2024.3439136","url":null,"abstract":"We consider deep neural networks (DNNs) with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in which sufficient conditions on weight matrices and bias vectors together with the Lipschitz constant are provided to ensure uniform convergence of DNNs to a meaningful function as the number of their layers tends to infinity. In the framework, special results on uniform convergence of DNNs with a fixed width, bounded widths and unbounded widths are presented. In particular, as convolutional neural networks are special DNNs with weight matrices of increasing widths, we put forward conditions on the mask sequence which lead to uniform convergence of the resulting convolutional neural networks. The Lipschitz continuity assumption on the activation functions allows us to include in our theory most of commonly used activation functions in applications.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"7125-7142"},"PeriodicalIF":2.2,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10623495","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947533","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":"The Weight Enumerator Polynomials of the Lifted Codes of the Projective Solomon-Stiffler Codes","authors":"Minjia Shi;Shitao Li;Tor Helleseth","doi":"10.1109/TIT.2024.3436923","DOIUrl":"10.1109/TIT.2024.3436923","url":null,"abstract":"Determining the weight distribution of a code is an old and fundamental topic in coding theory that has been thoroughly studied. In 1977, Helleseth, Kløve, and Mykkeltveit presented a weight enumerator polynomial of the lifted code over \u0000<inline-formula> <tex-math>${mathbb {F}}_{q^{ell } }$ </tex-math></inline-formula>\u0000 of a q-ary linear code with significant combinatorial properties, which can determine the support weight distribution of this linear code. The Solomon-Stiffler codes are a family of famous Griesmer codes, which were proposed by Solomon and Stiffler in 1965. In this paper, we determine the weight enumerator polynomials of the lifted codes of the projective Solomon-Stiffler codes using some combinatorial properties of subspaces. As a result, we determine the support weight distributions of the projective Solomon-Stiffler codes. In particular, we determine the weight hierarchies of the projective Solomon-Stiffler codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6316-6325"},"PeriodicalIF":2.2,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886463","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":"Error-Correction Performance of Regular Ring-Linear LDPC Codes Over Lee Channels","authors":"Jessica Bariffi;Hannes Bartz;Gianluigi Liva;Joachim Rosenthal","doi":"10.1109/TIT.2024.3436938","DOIUrl":"10.1109/TIT.2024.3436938","url":null,"abstract":"Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their error-correction performance is studied over two channel models, in the Lee metric. The first channel model is a discrete memoryless channel, whereas in the second channel model an error vector is drawn uniformly at random from all vectors of a fixed Lee weight. It is known that the two channel laws coincide in the asymptotic regime, meaning that their marginal distributions match. For both channel models, we derive upper bounds on the block error probability in terms of a random coding union bound as well as sphere packing bounds that make use of the marginal distribution of the considered channels. We estimate the decoding error probability of regular LDPC code ensembles over the channels using the marginal distribution and determining the expected Lee weight distribution of a random LDPC code over a finite integer ring. By means of density evolution and finite-length simulations, we estimate the error-correction performance of selected LDPC code ensembles under belief propagation decoding and a low-complexity symbol message passing decoding algorithm and compare the performances. The analysis developed in this paper may serve to design regular low-density parity-check (LDPC) codes over integer residue rings for storage and cryptographic application.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 11","pages":"7820-7839"},"PeriodicalIF":2.2,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886462","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":"Average Probability of Error for Single Uniprior Index Coding Over Binary-Input Continuous-Output Channels","authors":"Anjana A. Mahesh;Charul Rajput;Bobbadi Rupa;B. Sundar Rajan","doi":"10.1109/TIT.2024.3435849","DOIUrl":"10.1109/TIT.2024.3435849","url":null,"abstract":"Ong and Ho developed optimal linear index codes for single uniprior index coding problems (ICPs) by finding a spanning tree for each strongly connected component of their information-flow graphs, following which Thomas et al. considered the same class of ICPs over Rayleigh fading channels. They developed the min-max probability of error criterion for choosing an index code from the set of bandwidth-optimal linear index codes. Motivated by the above works, this paper deals with single uniprior ICPs over binary-input continuous-output channels. Minimizing the average probability of error is introduced as a criterion for further selection of index codes which is shown to be equivalent to minimizing the total number of transmissions used for decoding the message requests at all the receivers. An algorithm that generates a spanning tree with a lower value of this metric than the optimal star graph is also presented. A couple of lower bounds for the total number of transmissions, used by any optimal index code, are derived, and two classes of ICPs for which these bounds are tight are identified. An improvement of the proposed algorithm for information-flow graphs with bridges and a generalization of the improved algorithm for information-flow graphs obtainable as the union of strongly connected sub-graphs are presented, and some optimality results are derived.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6297-6315"},"PeriodicalIF":2.2,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864887","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":"Locally Repairable Convertible Codes With Optimal Access Costs","authors":"Xiangliang Kong","doi":"10.1109/TIT.2024.3435346","DOIUrl":"10.1109/TIT.2024.3435346","url":null,"abstract":"Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time, and leads to changes of the ideal code parameters. To maintain the storage efficiency, this requires the system to adjust parameters of the currently used codes. The changing process of code parameters on encoded data is called code conversion. As an important class of storage codes, locally repairable codes (LRCs) can repair any codeword symbol using a small number of other symbols. This feature makes LRCs highly efficient for addressing single node failures in the storage systems. In this paper, we investigate the code conversions for locally repairable codes in the merge regime. We establish a lower bound on the access cost of code conversion for general LRCs and propose a construction of LRCs that can perform code conversions with access cost matching this bound. This construction yields a family of LRCs with optimal conversion processes over a field size linear in the code length. As a special case, it provides a family of RS codes with optimal conversion processes, which could be of particular practical interest.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6239-6257"},"PeriodicalIF":2.2,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The existence of distinguishable bases in three-dimensional subspaces of qutrit-qudit systems under one-way local projective measurements and classical communication","authors":"Zhiwei Song, Lin Chen, Dragomir Ž Ðoković","doi":"10.1109/tit.2024.3435412","DOIUrl":"https://doi.org/10.1109/tit.2024.3435412","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"49 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864890","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":"Global Optimality of the EM Algorithm for Mixtures of Two-Component Linear Regressions","authors":"Jeongyeol Kwon;Wei Qian;Yudong Chen;Constantine Caramanis;Damek Davis;Nhat Ho","doi":"10.1109/TIT.2024.3435522","DOIUrl":"10.1109/TIT.2024.3435522","url":null,"abstract":"Recent results established that EM enjoys global convergence for Gaussian Mixture Models. For Mixed Linear Regression, however, only local convergence results have been established, and those only for the high signal-to-noise ratio (SNR) regime. In this work, we completely characterize the global optimality of EM: we show that starting from any randomly initialized point, the EM algorithm converges to the true parameter \u0000<inline-formula> <tex-math>${beta }^{*}$ </tex-math></inline-formula>\u0000 at the minimax statistical rates under all SNR regimes. Toward this goal, we first show the global convergence of the EM algorithm at the population level. Then we provide a complete characterization of statistical and computational behaviors of EM under all SNR regimes with finite samples. In particular: (i) When the SNR is sufficiently large, the EM updates converge to the true parameter \u0000<inline-formula> <tex-math>$ {beta }^{*}$ </tex-math></inline-formula>\u0000 at the standard parametric convergence rate \u0000<inline-formula> <tex-math>$O((d/n)^{1/2})$ </tex-math></inline-formula>\u0000 after \u0000<inline-formula> <tex-math>$O(log (n/d))$ </tex-math></inline-formula>\u0000 iterations. (ii) In the regime where the SNR is above \u0000<inline-formula> <tex-math>$O((d/n)^{1/4})$ </tex-math></inline-formula>\u0000 and below some constant, the EM iterates converge to a \u0000<inline-formula> <tex-math>$O({mathrm { SNR}}^{-1} (d/n)^{1/2})$ </tex-math></inline-formula>\u0000 neighborhood of the true parameter, when the number of iterations is of the order \u0000<inline-formula> <tex-math>$O({mathrm { SNR}}^{-2} log (n/d))$ </tex-math></inline-formula>\u0000. (iii) In the low SNR regime where the SNR is below \u0000<inline-formula> <tex-math>$O((d/n)^{1/4})$ </tex-math></inline-formula>\u0000, we show that EM converges to a \u0000<inline-formula> <tex-math>$O((d/n)^{1/4})$ </tex-math></inline-formula>\u0000 neighborhood of the true parameters, after \u0000<inline-formula> <tex-math>$O((n/d)^{1/2})$ </tex-math></inline-formula>\u0000 iterations. By providing tight convergence guarantees of the EM algorithm in middle-to-low SNR regimes, we reveal that in low SNR, EM changes rate, matching the \u0000<inline-formula> <tex-math>$n^{-1/4}$ </tex-math></inline-formula>\u0000 rate of the MLE, a behavior that previous work had been unable to show.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 9","pages":"6519-6546"},"PeriodicalIF":2.2,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864889","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":"Vectorial bent functions with non-weakly regular components","authors":"Ayça Çeşmelioğlu, Wilfried Meidl","doi":"10.1109/tit.2024.3434481","DOIUrl":"https://doi.org/10.1109/tit.2024.3434481","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"10 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864891","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}