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Maximal-Capacity Discrete Memoryless Channel Identification
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-24 DOI: 10.1109/TIT.2024.3522132
Maximilian Egger;Rawad Bitar;Antonia Wachter-Zeh;Deniz Gündüz;Nir Weinberger
{"title":"Maximal-Capacity Discrete Memoryless Channel Identification","authors":"Maximilian Egger;Rawad Bitar;Antonia Wachter-Zeh;Deniz Gündüz;Nir Weinberger","doi":"10.1109/TIT.2024.3522132","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522132","url":null,"abstract":"The problem of identifying the channel with the highest capacity among several discrete memoryless channels (DMCs) is considered. The problem is cast as a pure-exploration multi-armed bandit problem, which follows the practical use of training sequences to sense the communication channel statistics. A gap-elimination algorithm termed <monospace>BestChanID</monospace> is proposed, which is oblivious to the capacity-achieving input distributions, and is guaranteed to output the DMC with the largest capacity, with a desired confidence. Furthermore, two additional algorithms <monospace>NaiveChanSel</monospace> and <monospace>MedianChanEl</monospace>, which output with certain confidence a DMC with capacity close to the maximal, are also presented. Each of these algorithms is shown to be beneficial in a different regime and can be used as a subroutine of <monospace>BestChanID</monospace>. To analyze the algorithms’ guarantees, a capacity estimator is proposed and tight confidence bounds on the estimator error are derived. Based on this estimator, the sample complexity of all the proposed algorithms is analyzed as a function of the desired confidence parameter, the number of channels, and the channels’ input and output alphabet sizes. The cost of best channel identification is shown to scale quadratically with the alphabet size, and a fundamental lower bound is derived on the number of channel senses required to identify the best channel with a certain confidence.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1248-1265"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10813602","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361252","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}
引用次数: 0
A Two-Stage Solution to Quantum Process Tomography: Error Analysis and Optimal Design
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-24 DOI: 10.1109/TIT.2024.3522005
Shuixin Xiao;Yuanlong Wang;Jun Zhang;Daoyi Dong;Gary J. Mooney;Ian R. Petersen;Hidehiro Yonezawa
{"title":"A Two-Stage Solution to Quantum Process Tomography: Error Analysis and Optimal Design","authors":"Shuixin Xiao;Yuanlong Wang;Jun Zhang;Daoyi Dong;Gary J. Mooney;Ian R. Petersen;Hidehiro Yonezawa","doi":"10.1109/TIT.2024.3522005","DOIUrl":"https://doi.org/10.1109/TIT.2024.3522005","url":null,"abstract":"Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography. Utilizing a tensor structure, our algorithm exhibits a computational complexity of <inline-formula> <tex-math>$O(MLd^{2})$ </tex-math></inline-formula> where d is the dimension of the quantum system and <inline-formula> <tex-math>$M, L~(Mgeq d^{2}, Lgeq d^{2})$ </tex-math></inline-formula> represent the numbers of different input states and measurement operators, respectively. We establish an analytical error upper bound and then design the optimal input states and the optimal measurement operators, which are both based on minimizing the error upper bound and maximizing the robustness characterized by the condition number. Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1803-1823"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465588","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
Alpha-NML Universal Predictors
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-23 DOI: 10.1109/TIT.2024.3521221
Marco Bondaschi;Michael Gastpar
{"title":"Alpha-NML Universal Predictors","authors":"Marco Bondaschi;Michael Gastpar","doi":"10.1109/TIT.2024.3521221","DOIUrl":"https://doi.org/10.1109/TIT.2024.3521221","url":null,"abstract":"Inspired by the connection between classical regret measures employed in universal prediction and Rényi divergence, we introduce a new class of universal predictors that depend on a real parameter <inline-formula> <tex-math>$alpha geq 1$ </tex-math></inline-formula>. This class interpolates two well-known predictors, the mixture estimators, that include the Laplace and the Krichevsky-Trofimov predictors, and the Normalized Maximum Likelihood (NML) estimator. We point out some advantages of this new class of predictors and study its benefits from two complementary viewpoints: 1) we prove its optimality when the maximal Rényi divergence is considered as a regret measure, which can be interpreted operationally as a middle ground between the standard average and worst-case regret measures; 2) we discuss how it can be employed when NML is not a viable option, as an alternative to other predictors such as Luckiness NML. Finally, we apply the <inline-formula> <tex-math>$alpha $ </tex-math></inline-formula>-NML predictor to the class of discrete memoryless sources (DMS), where we derive simple formulas to compute the predictor and analyze its asymptotic performance in terms of worst-case regret.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1171-1183"},"PeriodicalIF":2.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106853","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
Information-Theoretic Thresholds for Planted Dense Cycles
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-23 DOI: 10.1109/TIT.2024.3521305
Cheng Mao;Alexander S. Wein;Shenduo Zhang
{"title":"Information-Theoretic Thresholds for Planted Dense Cycles","authors":"Cheng Mao;Alexander S. Wein;Shenduo Zhang","doi":"10.1109/TIT.2024.3521305","DOIUrl":"https://doi.org/10.1109/TIT.2024.3521305","url":null,"abstract":"We study a random graph model for small-world networks which are ubiquitous in social and biological sciences. In this model, a dense cycle of expected bandwidth <inline-formula> <tex-math>$n tau $ </tex-math></inline-formula>, representing the hidden one-dimensional geometry of vertices, is planted in an ambient random graph on n vertices. For both detection and recovery of the planted dense cycle, we characterize the information-theoretic thresholds in terms of n, <inline-formula> <tex-math>$tau $ </tex-math></inline-formula>, and an edge-wise signal-to-noise ratio <inline-formula> <tex-math>$lambda $ </tex-math></inline-formula>. In particular, the information-theoretic thresholds differ from the computational thresholds established in a recent work for low-degree polynomial algorithms, thereby justifying the existence of statistical-to-computational gaps for this problem.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1266-1282"},"PeriodicalIF":2.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361253","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
Covering b-Symbol Metric Codes and the Generalized Singleton Bound
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-23 DOI: 10.1109/TIT.2024.3521328
Hao Chen
{"title":"Covering b-Symbol Metric Codes and the Generalized Singleton Bound","authors":"Hao Chen","doi":"10.1109/TIT.2024.3521328","DOIUrl":"https://doi.org/10.1109/TIT.2024.3521328","url":null,"abstract":"Symbol-pair codes were proposed for the application in high density storage systems, where it is not possible to read individual symbols. Yaakobi, Bruck and Siegel proved that the minimum pair-distance <inline-formula> <tex-math>$d_{2}$ </tex-math></inline-formula> of binary linear cyclic codes satisfies <inline-formula> <tex-math>$d_{2} geq lceil 3d_{H}/2 rceil $ </tex-math></inline-formula> and introduced b-symbol metric codes in 2016. In this paper, covering codes in b-symbol metrics are considered. Some examples are given to show that the Delsarte bound and the Norse bound for covering codes in the Hamming metric do not hold true for covering codes in the pair metric. We give the redundancy bound on covering radius of linear codes in the b-symbol metric and give some optimal codes attaining this bound. Then we prove that there is no perfect linear symbol-pair code with the minimum pair-distance 7 and there is no perfect b-symbol metric code if <inline-formula> <tex-math>$bgeq frac {n+4}{2}$ </tex-math></inline-formula>. Moreover a lot of cyclic and algebraic-geometric codes are proved non-perfect in the b-symbol metric. The covering radius of the Reed-Solomon code in the b-symbol metric is determined. As an application, the generalized Singleton bound on the sizes of list-decodable b-symbol metric codes is also presented. Then an upper bound on lengths of general MDS symbol-pair codes is proved.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1585-1592"},"PeriodicalIF":2.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465640","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
Linear Complementary Dual Codes and Linear Complementary Pairs of AG Codes in Function Fields
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-23 DOI: 10.1109/TIT.2024.3521094
Alonso S. Castellanos;Adler V. Marques;Luciane Quoos
{"title":"Linear Complementary Dual Codes and Linear Complementary Pairs of AG Codes in Function Fields","authors":"Alonso S. Castellanos;Adler V. Marques;Luciane Quoos","doi":"10.1109/TIT.2024.3521094","DOIUrl":"https://doi.org/10.1109/TIT.2024.3521094","url":null,"abstract":"In recent years, linear complementary pairs (LCPs) of codes and linear complementary dual (LCD) codes have gained significant attention due to their applications in coding theory and cryptography. In this work, we construct explicit LCPs of codes and LCD codes from function fields of genus <inline-formula> <tex-math>$g geq 1$ </tex-math></inline-formula>. To accomplish this, we present pairs of suitable divisors that give rise to non-special divisors of degree <inline-formula> <tex-math>$g-1$ </tex-math></inline-formula> in the function field. The results are applied in constructing LCPs of algebraic geometry codes and LCD algebraic geometry (AG) codes in Kummer extensions, hyperelliptic function fields, and elliptic curves.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 3","pages":"1676-1688"},"PeriodicalIF":2.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465669","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
On Constructing Bent Functions From Cyclotomic Mappings
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-23 DOI: 10.1109/TIT.2024.3521236
Xi Xie;Nian Li;Qiang Wang;Xiangyong Zeng
{"title":"On Constructing Bent Functions From Cyclotomic Mappings","authors":"Xi Xie;Nian Li;Qiang Wang;Xiangyong Zeng","doi":"10.1109/TIT.2024.3521236","DOIUrl":"https://doi.org/10.1109/TIT.2024.3521236","url":null,"abstract":"We propose to study the construction of Boolean bent functions from cyclotomic mappings. By considering Dillon functions, Niho functions and Kasami functions as different branch functions respectively, we obtain three generic constructions from this new perspective. As a result, several infinite classes of bent functions belonging to the <inline-formula> <tex-math>${mathcal {PS}}_{ap}$ </tex-math></inline-formula> class, class <inline-formula> <tex-math>$mathcal {H}$ </tex-math></inline-formula> and the completed <inline-formula> <tex-math>$mathcal {MM}$ </tex-math></inline-formula> class are derived, thereby providing simple representations of known classes of bent functions through cyclotomic mappings. In addition, computer experiments show that examples of bent functions outside these three well-known classes can also be obtained by selecting other branch functions.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1389-1399"},"PeriodicalIF":2.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361257","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
Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-23 DOI: 10.1109/TIT.2024.3521638
Jens Niklas Eberhardt;Vincent Steffan
{"title":"Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes","authors":"Jens Niklas Eberhardt;Vincent Steffan","doi":"10.1109/TIT.2024.3521638","DOIUrl":"https://doi.org/10.1109/TIT.2024.3521638","url":null,"abstract":"Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of surface codes even with near-term hardware. The question of how to implement logical gates fault-tolerantly for these codes is still open. We present new examples of high-rate bivariate bicycle (BB) codes with enhanced symmetry properties. These codes feature explicit nice bases of logical operators (similar to toric codes) and support fold-transversal Clifford gates. As examples, we construct <inline-formula> <tex-math>$[[{98,6,12}]]$ </tex-math></inline-formula> and <inline-formula> <tex-math>$[[{162, 8, 12}]]$ </tex-math></inline-formula> BB codes which admit interesting fault-tolerant Clifford gates. Our work also lays the mathematical foundations for explicit bases of logical operators and fold-transversal gates in quantum two-block group algebra codes, which might be of independent interest.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1140-1152"},"PeriodicalIF":2.2,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106907","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
Optimal Few-SSW Linear Codes and Their Subcode Support Weight Distributions
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-18 DOI: 10.1109/TIT.2024.3519672
Xu Pan;Hao Chen;Hongwei Liu;Shengwei Liu
{"title":"Optimal Few-SSW Linear Codes and Their Subcode Support Weight Distributions","authors":"Xu Pan;Hao Chen;Hongwei Liu;Shengwei Liu","doi":"10.1109/TIT.2024.3519672","DOIUrl":"https://doi.org/10.1109/TIT.2024.3519672","url":null,"abstract":"Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight <inline-formula> <tex-math>$left [{{frac {q^{k}-1}{q-1},k,q^{k-1}}}right ]_{q}$ </tex-math></inline-formula>-linear codes and they meet all Griesmer bounds on the generalized Hamming weights of linear codes. All the subcodes with dimension r of a <inline-formula> <tex-math>$left [{{frac {q^{k}-1}{q-1},k,q^{k-1}}}right ]_{q}$ </tex-math></inline-formula>-simplex code have the same subcode support weight <inline-formula> <tex-math>$frac {q^{k-r}(q^{r}-1)}{q-1}$ </tex-math></inline-formula> for <inline-formula> <tex-math>$1leq rleq k$ </tex-math></inline-formula>. In this paper, we construct linear codes meeting the Griesmer bound of the r-generalized Hamming weight, such codes do not meet the Griesmer bound of the j-generalized Hamming weight for <inline-formula> <tex-math>$1leq jlt r$ </tex-math></inline-formula>. Moreover these codes have only few subcode support weights (few-SSW). The weight distributions and the subcode support weight distributions of these distance-optimal codes are determined. Linear codes constructed in this paper are natural generalizations of distance-optimal few-weight codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"1028-1042"},"PeriodicalIF":2.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106962","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
Information Rates Over Multi-View Channels
IF 2.2 3区 计算机科学
IEEE Transactions on Information Theory Pub Date : 2024-12-16 DOI: 10.1109/TIT.2024.3518760
V. Arvind Rameshwar;Nir Weinberger
{"title":"Information Rates Over Multi-View Channels","authors":"V. Arvind Rameshwar;Nir Weinberger","doi":"10.1109/TIT.2024.3518760","DOIUrl":"https://doi.org/10.1109/TIT.2024.3518760","url":null,"abstract":"We investigate the fundamental limits of reliable communication over multi-view channels, in which the channel output is comprised of a large number of independent noisy views of a transmitted symbol. We consider first the setting of multi-view discrete memoryless channels and then extend our results to general multi-view channels (using multi-letter formulas). We argue that the channel capacity and dispersion of such multi-view channels converge exponentially fast in the number of views to the entropy and varentropy of the input distribution, respectively. We identify the exact rate of convergence as the smallest Chernoff information between two conditional distributions of the output, conditioned on unequal inputs. For the special case of the deletion channel, we compute upper bounds on this Chernoff information. Finally, we present a new channel model we term the Poisson approximation channel — of possible independent interest — whose capacity closely approximates the capacity of the multi-view binary symmetric channel for any fixed number of views.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 2","pages":"847-861"},"PeriodicalIF":2.2,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143106997","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
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