IEEE Transactions on Information Theory最新文献

{"title":"A New Upper Bound for Linear Codes and Vanishing Partial Weight Distributions","authors":"Hao Chen, Conghui Xie","doi":"10.1109/tit.2024.3449899","DOIUrl":"https://doi.org/10.1109/tit.2024.3449899","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"44 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194875","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":"Self-orthogonal codes from p-divisible codes","authors":"Xiaoru Li, Ziling Heng","doi":"10.1109/tit.2024.3449921","DOIUrl":"https://doi.org/10.1109/tit.2024.3449921","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"85 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194877","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":"Phase Retrieval With Background Information: Decreased References and Efficient Methods","authors":"Ziyang Yuan;Haoxing Yang;Ningyi Leng;Hongxia Wang","doi":"10.1109/TIT.2024.3449554","DOIUrl":"10.1109/TIT.2024.3449554","url":null,"abstract":"Fourier phase retrieval (PR) is a severely ill-posed inverse problem that arises in various applications. To guarantee a unique solution and relieve the dependence on the initialization, background information can be exploited as a structural prior. However, the requirement for the background information may be challenging when moving to high-resolution imaging. At the same time, the previously proposed projected gradient descent (PGD) method also demands much background information. In this paper, we present an improved theoretical result about the demand for the background information, along with two Douglas Rachford (DR) based methods. Analytically, we demonstrate that the background information required to ensure a unique solution can be decreased by nearly \u0000<inline-formula> <tex-math>$1/2$ </tex-math></inline-formula>\u0000 for the 2-D signals compared to the 1-D signals. By generalizing the results into d-dimension, we show that the length of the background information more than \u0000<inline-formula> <tex-math>$left ({{2^{frac {d+1}{d}}-1}}right)$ </tex-math></inline-formula>\u0000 folds of the signal is sufficient to ensure uniqueness. At the same time, we also analyze the stability and robustness of the model when the measurements and background information are corrupted by noise. Furthermore, two methods called Background Douglas Rachford (BDR) and Convex Background Douglas Rachford (CBDR) are proposed. BDR, which is a kind of non-convex method, is proven to have the local R-linear convergence rate under mild assumptions. Instead, the CBDR method uses the techniques of convexification and can be proven to have a global convergence guarantee as long as the background information is sufficient. To support this, a new property called F-RIP is established. We test the performance of the proposed methods through simulations as well as real experimental measurements, and demonstrate that they achieve a higher recovery rate with less background information compared to the PGD method.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"7498-7520"},"PeriodicalIF":2.2,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194876","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":"On the Noise Sensitivity of the Randomized SVD","authors":"Elad Romanov","doi":"10.1109/tit.2024.3450412","DOIUrl":"https://doi.org/10.1109/tit.2024.3450412","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"15 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194878","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":"Repairing Reed-Solomon Codes over Prime Fields via Exponential Sums","authors":"Roni Con, Noah Shutty, Itzhak Tamo, Mary Wootters","doi":"10.1109/tit.2024.3449041","DOIUrl":"https://doi.org/10.1109/tit.2024.3449041","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"32 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Improved Field Size Bounds for Higher Order MDS Codes","authors":"Joshua Brakensiek;Manik Dhar;Sivakanth Gopi","doi":"10.1109/TIT.2024.3449030","DOIUrl":"10.1109/TIT.2024.3449030","url":null,"abstract":"Higher order MDS codes are an interesting generalization of MDS codes recently introduced by Brakensiek et al., (2023). In later works, they were shown to be intimately connected to optimally list-decodable codes and maximally recoverable tensor codes. Therefore (explicit) constructions of higher order MDS codes over small fields is an important open problem. Higher order MDS codes are denoted by \u0000<inline-formula> <tex-math>$rm {MDS}(ell)$ </tex-math></inline-formula>\u0000 where \u0000<inline-formula> <tex-math>$ell $ </tex-math></inline-formula>\u0000 denotes the order of generality, \u0000<inline-formula> <tex-math>$rm {MDS}(2)$ </tex-math></inline-formula>\u0000 codes are equivalent to the usual MDS codes. The best prior lower bound on the field size of an \u0000<inline-formula> <tex-math>${[}n,k{]}$ </tex-math></inline-formula>\u0000-\u0000<inline-formula> <tex-math>$rm {MDS}(ell)$ </tex-math></inline-formula>\u0000 codes is \u0000<inline-formula> <tex-math>$Omega _{ell } (n^{ell -1})$ </tex-math></inline-formula>\u0000, whereas the best known (non-explicit) upper bound is \u0000<inline-formula> <tex-math>$O_{ell } (n^{k(ell -1)})$ </tex-math></inline-formula>\u0000 which is exponential in the dimension. In this work, we nearly close this exponential gap between upper and lower bounds. We show that an \u0000<inline-formula> <tex-math>${[}n,k{]}$ </tex-math></inline-formula>\u0000-\u0000<inline-formula> <tex-math>$rm {MDS}(3)$ </tex-math></inline-formula>\u0000 codes requires a field of size \u0000<inline-formula> <tex-math>$Omega _{k}(n^{k-1})$ </tex-math></inline-formula>\u0000, which is close to the known upper bound. Using the connection between higher order MDS codes and optimally list-decodable codes, we show that even for a list size of 2, a code which meets the optimal list-decoding Singleton bound requires exponential field size; this resolves an open question by Shangguan and Tamo, (2020). We also give explicit constructions of \u0000<inline-formula> <tex-math>${[}n,k{]}$ </tex-math></inline-formula>\u0000-\u0000<inline-formula> <tex-math>$rm {MDS}(ell)$ </tex-math></inline-formula>\u0000 code over fields of size \u0000<inline-formula> <tex-math>$n^{(ell k)^{O(ell k)}}$ </tex-math></inline-formula>\u0000. The smallest non-trivial case where we still do not have optimal constructions is \u0000<inline-formula> <tex-math>${[}n,3{]}$ </tex-math></inline-formula>\u0000-\u0000<inline-formula> <tex-math>$rm {MDS}(3)$ </tex-math></inline-formula>\u0000. In this case, the known lower bound on the field size is \u0000<inline-formula> <tex-math>$Omega (n^{2})$ </tex-math></inline-formula>\u0000 and the best known upper bounds are \u0000<inline-formula> <tex-math>$O(n^{5})$ </tex-math></inline-formula>\u0000 for a non-explicit construction and \u0000<inline-formula> <tex-math>$O(n^{32})$ </tex-math></inline-formula>\u0000 for an explicit construction. In this paper, we give an explicit construction over fields of size \u0000<inline-formula> <tex-math>$O(n^{3})$ </tex-math></inline-formula>\u0000 which comes very close to being optimal.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"6950-6960"},"PeriodicalIF":2.2,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194879","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":"On Confidence Sequences for Bounded Random Processes via Universal Gambling Strategies","authors":"J. Jon Ryu;Alankrita Bhatt","doi":"10.1109/TIT.2024.3448461","DOIUrl":"10.1109/TIT.2024.3448461","url":null,"abstract":"This paper considers the problem of constructing a confidence sequence, which is a sequence of confidence intervals that hold uniformly over time, for estimating the mean of bounded real-valued random processes. This paper revisits the gambling-based approach established in the recent literature from a natural two-horse race perspective, and demonstrates new properties of the resulting algorithm induced by Cover (1991)’s universal portfolio. The main result of this paper is a new algorithm based on a mixture of lower bounds, which closely approximates the performance of Cover’s universal portfolio with constant per-round time complexity. A higher-order generalization of a lower bound on a logarithmic function in (Fan et al., 2015), which is developed as a key technique for the proposed algorithm, may be of independent interest.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"7143-7161"},"PeriodicalIF":2.2,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194881","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":"Achieving the Exactly Optimal Privacy-Utility Trade-Off With Low Communication Cost via Shared Randomness","authors":"Seung-Hyun Nam;Hyun-Young Park;Si-Hyeon Lee","doi":"10.1109/TIT.2024.3448475","DOIUrl":"10.1109/TIT.2024.3448475","url":null,"abstract":"We consider a discrete distribution estimation problem under a local differential privacy (LDP) constraint in the presence of shared randomness. For this problem, we propose a new class of LDP schemes achieving the exactly optimal privacy-utility trade-off (PUT), with the communication cost less than or equal to the size of the input data. Moreover, it is shown as a simple corollary that one-bit communication is sufficient for achieving the exactly optimal PUT for a high privacy regime if the input data size is an even number. The main idea is to decompose a block design scheme proposed by Park et al. (2023), based on the combinatorial concept called resolution. We call the resultant decomposed LDP scheme with shared randomness as a resolution of the original block design scheme. A resolution of a block design scheme has a communication cost less than or equal to that of the original block design scheme. Also, the resolution of a block design scheme is exactly optimal whenever the original block design scheme is exactly optimal. Accordingly, we provide two resolutions of the exactly optimal subset selection scheme proposed by Ye and Barg (2018), called the Baranyai’s resolution and the cyclic shift resolution. We show that the Baranyai’s resolution achieves the minimum communication cost among all exactly optimal resolutions of block design schemes. One drawback of the Baranyai’s resolution is that its explicit structure is unknown in general. In contrast, the cyclic shift resolution has an explicit structure, but its communication cost can be larger than that of the Baranyai’s resolution. To complement this, we also suggest resolutions of other block design schemes achieving the exactly optimal PUT for some input data size and privacy budget. Those require the minimum communication cost as the Baranyai’s resolution and have explicit structures as the cyclic shift resolution.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"70 10","pages":"7447-7462"},"PeriodicalIF":2.2,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194883","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":"Optimal Trace Distance and Fidelity Estimations for Pure Quantum States","authors":"Qisheng Wang","doi":"10.1109/tit.2024.3447915","DOIUrl":"https://doi.org/10.1109/tit.2024.3447915","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"26 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194950","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":"Improving explicit constructions of r-PD-sets for Z p s -linear generalized Hadamard codes","authors":"Josep Rifâ, Adrián Torres-Martín, Mercè Villanueva","doi":"10.1109/tit.2024.3448230","DOIUrl":"https://doi.org/10.1109/tit.2024.3448230","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"85 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194891","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}