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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 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-10-25 DOI: 10.1109/TIT.2024.3477754
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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 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-10-25 DOI: 10.1109/TIT.2024.3477756
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引用次数: 0
Derivatives of Entropy and the MMSE Conjecture 熵的衍生物和 MMSE 猜想
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-25 DOI: 10.1109/TIT.2024.3466566
Paul Mansanarez;Guillaume Poly;Yvik Swan
We investigate the properties of the entropy of a probability measure along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided that the measure admits moments of any order, it has been proved in Guo et al. (2010) that this functional is smooth, and in Ledoux (2016) that its derivatives at zero can be expressed into multivariate polynomials evaluated in the moments (or cumulants) of the underlying measure. Moreover, these algebraic expressions are derived through $Gamma $ -calculus techniques which provide implicit recursive formulas for these polynomials. Our main contribution consists in a fine combinatorial analysis of these inductive relations and for the first time to derive closed formulas for the leading coefficients of these polynomials expressions. Building upon these explicit formulas we revisit the so-called “MMSE conjecture” from Ledoux (2016) which asserts that two distributions on the real line with the same entropy along the heat flow must coincide up to translation and symmetry. Our approach enables us to provide new conditions on the source distributions ensuring that the MMSE conjecture holds and to refine several criteria proved in Ledoux (2016). As illustrating examples, our findings cover the cases of uniform and Rademacher distributions, for which previous results in the literature were inapplicable.
我们研究热流沿线概率度量的熵的性质,更确切地说,我们寻求其导数的封闭代数表示。郭等人(2010)证明了这个函数是平滑的,而勒杜(2016)则证明了它的零点导数可以用多变量多项式来表示,以底层量度的矩(或积)来求值。此外,这些代数表达式是通过 $Gamma $ 微积分技术推导出来的,这些技术为这些多项式提供了隐式递归公式。我们的主要贡献在于对这些归纳关系进行了精细的组合分析,并首次推导出了这些多项式表达式前导系数的封闭公式。在这些明确公式的基础上,我们重新审视了勒杜(Ledoux,2016 年)提出的所谓 "MMSE 猜想",该猜想认为在实线上沿热流方向具有相同熵的两个分布必须在平移和对称的范围内重合。我们的方法使我们能够为源分布提供新的条件,确保 MMSE 猜想成立,并完善了 Ledoux(2016 年)中证明的几个标准。作为示例,我们的发现涵盖了均匀分布和拉德马赫分布的情况,而之前文献中的结果并不适用于这些情况。
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引用次数: 0
Large and Small Deviations for Statistical Sequence Matching 统计序列匹配的大偏差和小偏差
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-25 DOI: 10.1109/TIT.2024.3464586
Lin Zhou;Qianyun Wang;Jingjing Wang;Lin Bai;Alfred O. Hero
We revisit the problem of statistical sequence matching between two databases of sequences initiated by Unnikrishnan, (2015) and derive theoretical performance guarantees for the generalized likelihood ratio test (GLRT). We first consider the case where the number of matched pairs of sequences between the databases is known. In this case, the task is to accurately find the matched pairs of sequences among all possible matches between the sequences in the two databases. We analyze the performance of the GLRT by Unnikrishnan and explicitly characterize the tradeoff between the mismatch and false reject probabilities under each hypothesis in both large and small deviations regimes. Furthermore, we demonstrate the optimality of Unnikrishnan’s GLRT test under the generalized Neyman-Person criterion for both regimes and illustrate our theoretical results via numerical examples. Subsequently, we generalize our achievability analyses to the case where the number of matched pairs is unknown, and an additional error probability needs to be considered. When one of the two databases contains a single sequence, the problem of statistical sequence matching specializes to the problem of multiple classification introduced by Gutman, (1989). For this special case, our result for the small deviations regime strengthens previous result of Zhou et al., (2020) by removing unnecessary conditions on the generating distributions.
我们重温了 Unnikrishnan(2015 年)提出的两个序列数据库之间的统计序列匹配问题,并推导出广义似然比检验(GLRT)的理论性能保证。我们首先考虑数据库之间匹配的序列对数量已知的情况。在这种情况下,任务是在两个数据库中所有可能匹配的序列中准确找到匹配的序列对。我们分析了 Unnikrishnan 提出的 GLRT 的性能,并明确描述了在大偏差和小偏差两种情况下,每种假设下的错配概率和错误拒绝概率之间的权衡。此外,我们还证明了 Unnikrishnan 的 GLRT 检验在广义 Neyman-Person 准则下在两种情况下的最优性,并通过数值示例说明了我们的理论结果。随后,我们将可实现性分析推广到配对数量未知的情况,并需要考虑额外的错误概率。当两个数据库中的一个包含单一序列时,统计序列匹配问题就会特殊化为 Gutman(1989 年)提出的多重分类问题。对于这种特殊情况,我们的小偏差机制结果通过消除生成分布的不必要条件,加强了 Zhou 等人(2020)之前的结果。
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引用次数: 0
Combinatorial Constructions of Optimal Quaternary Additive Codes 最优四元加法码的组合构造
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-24 DOI: 10.1109/TIT.2024.3467123
Chaofeng Guan;Jingjie Lv;Gaojun Luo;Zhi Ma
This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive $[n,3.5,n-t]_{4}$ codes for all t with variable n, except for $t=6,7,12$ .
本文旨在构建非整数维的最优四元加法码。首先,我们提出了四元加法恒重码的组合构造,以及加法广义反码构造。随后,我们提出了广义构造 X,它有助于从线性码构造非整数维最优加法码。然后,我们通过这两种方法构建了十类最优四元非整数维加法码。作为应用,我们还确定了除 $t=6,7,12$ 外,所有 t 的可变 n 的最优加法码 $[n,3.5,n-t]_{4}$ 。
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引用次数: 0
Two New Classes of MDS Symbol-Pair Codes 两类新的 MDS 符号对代码
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-23 DOI: 10.1109/TIT.2024.3466523
Xiaoshan Kai;Yajing Zhou;Shixin Zhu
Due to the application of high density data storage systems, symbol-pair codes are proposed to combat errors of the overlapping symbol pairs output over symbol-pair read channels. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they have the highest pair error-correcting capability. In this paper, we construct two new classes of MDS symbol-pair codes with minimum pair distance seven based on simple-root cyclic codes. Our technique is through the decomposition of cyclic codes and the dual of each component code.
由于高密度数据存储系统的应用,人们提出了符号对编码来消除符号对读取通道上输出的重叠符号对的错误。最大距离可分(MDS)符号对编码是最佳编码,因为它们具有最高的符号对纠错能力。在本文中,我们以单根循环码为基础,构建了两类具有最小对距七的 MDS 符号对码。我们的技术是通过分解循环码和每个组成码的对偶来实现的。
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引用次数: 0
Consistent Estimation of a Class of Distances Between Covariance Matrices 协方差矩阵间一类距离的一致性估计
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-20 DOI: 10.1109/TIT.2024.3464678
Roberto Pereira;Xavier Mestre;David Gregoratti
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. This family of distances is particularly useful as it takes into consideration the fact that covariance matrices lie in the Riemannian manifold of positive definite matrices, thereby including a variety of commonly used metrics, such as the Euclidean distance, Jeffreys’ divergence, and the log-Euclidean distance. Moreover, a statistical analysis of the asymptotic behavior of this class of distance estimators has also been conducted. Specifically, we present a central limit theorem that establishes the asymptotic Gaussianity of these estimators and provides closed form expressions for the corresponding means and variances. Empirical evaluations demonstrate the superiority of our proposed consistent estimator over conventional plug-in estimators in multivariate analytical contexts. Additionally, the central limit theorem derived in this study provides a robust statistical framework to assess of accuracy of these estimators.
本研究考虑的问题是直接从数据中估计两个协方差矩阵之间的距离。特别是,我们对可以表示为分别应用于每个协方差矩阵的函数迹之和的距离族感兴趣。这个距离族特别有用,因为它考虑到了协方差矩阵位于正定矩阵的黎曼流形中这一事实,从而包含了各种常用度量,如欧氏距离、杰弗里斯发散和对数欧氏距离。此外,我们还对这类距离估计器的渐近行为进行了统计分析。具体来说,我们提出了一个中心极限定理,该定理确定了这些估计值的渐近高斯性,并提供了相应均值和方差的封闭式表达式。经验评估表明,在多元分析背景下,我们提出的一致估计器优于传统的插入式估计器。此外,本研究中得出的中心极限定理为评估这些估计器的准确性提供了一个稳健的统计框架。
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引用次数: 0
Efficient Algorithms for Constructing Minimum-Weight Codewords in Some Extended Binary BCH Codes 在某些扩展二进制 BCH 码中构建最小权码的高效算法
IF 2.2 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-20 DOI: 10.1109/TIT.2024.3465218
Amit Berman;Yaron Shany;Itzhak Tamo
We present <inline-formula> <tex-math>$O(m^{3})$ </tex-math></inline-formula> algorithms for specifying the support of minimum-weight codewords of extended binary BCH codes of length <inline-formula> <tex-math>$n=2^{m}$ </tex-math></inline-formula> and designed distance <inline-formula> <tex-math>$d(m,s,i):=2^{m-1-s}-2^{m-1-i-s}$ </tex-math></inline-formula> for some values of <inline-formula> <tex-math>$m,i,s$ </tex-math></inline-formula>, where m may grow to infinity. Here, the support is specified as the sum of two sets: a set of <inline-formula> <tex-math>$2^{2i-1}-2^{i-1}$ </tex-math></inline-formula> elements, and a subspace of dimension <inline-formula> <tex-math>$m-2i-s$ </tex-math></inline-formula>, specified by a basis. In some detail, for designed distance <inline-formula> <tex-math>$6cdot 2^{j}$ </tex-math></inline-formula>, <inline-formula> <tex-math>$jin {0,ldots ,m-4}$ </tex-math></inline-formula>, we have a deterministic algorithm for even <inline-formula> <tex-math>$mgeq 4$ </tex-math></inline-formula>, and a probabilistic algorithm with success probability <inline-formula> <tex-math>$1-O(2^{-m})$ </tex-math></inline-formula> for odd <inline-formula> <tex-math>$mgt 4$ </tex-math></inline-formula>. For designed distance <inline-formula> <tex-math>$28cdot 2^{j}$ </tex-math></inline-formula>, <inline-formula> <tex-math>$jin {0,ldots , m-6}$ </tex-math></inline-formula>, we have a probabilistic algorithm with success probability <inline-formula> <tex-math>$geq frac {1}{3}-O(2^{-m/2})$ </tex-math></inline-formula> for even <inline-formula> <tex-math>$mgeq 6$ </tex-math></inline-formula>. Finally, for designed distance <inline-formula> <tex-math>$120cdot 2^{j}$ </tex-math></inline-formula>, <inline-formula> <tex-math>$jin {0,ldots , m-8}$ </tex-math></inline-formula>, we have a deterministic algorithm for <inline-formula> <tex-math>$mgeq 8$ </tex-math></inline-formula> divisible by 4. We also show how Gold functions can be used to find the support of minimum-weight words for designed distance <inline-formula> <tex-math>$d(m,s,i)$ </tex-math></inline-formula> (for <inline-formula> <tex-math>$iin {0,ldots ,lfloor m/2rfloor }$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$sleq m-2i$ </tex-math></inline-formula>) whenever <inline-formula> <tex-math>$2i|m$ </tex-math></inline-formula>. Our construction builds on results of Kasami and Lin, who proved that for extended binary BCH codes of designed distance <inline-formula> <tex-math>$d(m,s,i)$ </tex-math></inline-formula> (for integers <inline-formula> <tex-math>$mgeq 2$ </tex-math></inline-formula>, <inline-formula> <tex-math>$0leq ileq lfloor m/2rfloor $ </tex-math></inline-formula>, and <inline-formula> <tex-math>$0leq sleq m-2i$ </tex-math></inline-formula>), the minimum distance equals the designed distance. The proof of Kasami and Lin makes use of a non-constructive existence result of Berlekamp, and a constructive “dow
我们提出了$O(m^{3})$算法,用于指定长度为$n=2^{m}$、设计距离为$d(m,s,i):=2^{m-1-s}-2^{m-1-i-s}$的扩展二进制 BCH 码的最小权编码词的支持,其中 m 可以增长到无穷大。在这里,支持度被指定为两个集合的总和:一个是包含 2^{2i-1}-2^{i-1}$ 元素的集合,另一个是维度为 $m-2i-s$ 的子空间,由一个基础指定。详细来说,对于设计距离为 $6cdot 2^{j}$, $jin {0,ldots ,m-4}$的问题,我们有一个针对偶数$mgeq 4$的确定性算法,以及一个针对奇数$mgt 4$的成功概率为$1-O(2^{-m})$的概率算法。对于设计距离 $28cdot 2^{j}$ , $jin {0,ldots , m-6}$ , 我们有一个概率算法,对于偶数 $mgeq 6$,成功概率为 $geq frac {1}{3}-O(2^{-m/2})$ 。最后,对于设计距离为 $120cdot 2^{j}$ , $jin {0,ldots , m-8}$的情况,我们有一个可被 4 整除的 $mgeq 8$ 的确定性算法。我们还展示了如何使用 Gold 函数为设计的距离 $d(m,s,i)$(对于 $iin {0,ldots ,lfloor m/2rfloor }$,以及 $sleq m-2i$ )找到最小权重词的支持,只要 $2i|m$。我们的结构建立在 Kasami 和 Lin 的结果之上,他们证明了对于设计距离为 $d(m,s,i)$ 的扩展二进制 BCH 码(对于整数 $mgeq 2$ , $0leq ileq lfloor m/2rfloor $ , 和 $0leq sleq m-2i$ ),最小距离等于设计距离。Kasami 和 Lin 的证明利用了 Berlekamp 的一个非构造性存在结果和一个构造性 "向下转换定理",该定理将 BCH 码中的一些词转换为设计距离更小的 BCH 码中的低权重词。我们的主要贡献在于用一种低复杂度算法取代了 Berlekamp 的非构造性计数论证。Grigorescu 和 Kaufman 提出了设计距离正好为 6 的扩展二进制 BCH 码的显式最小权编码字(通过著名的 "上转换定理",设计距离为 $6cdot 2^{j}$的扩展二进制 BCH 码也有显式最小权编码字),本文从一个方面扩展了他们的研究成果,因为我们涵盖了更多的最小距离情况。事实上,我们证明了格里戈列斯库和考夫曼构造的编码是当前构造的特例。然而,我们构造的最小权码字并不生成代码,也不是仿射生成器,可能的话,设计距离为 6 的情况除外。
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引用次数: 0
Support Recovery in Mixture Models with Sparse Parameters 具有稀疏参数的混合模型中的支持恢复
IF 2.5 3区 计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-18 DOI: 10.1109/tit.2024.3462937
Arya Mazumdar, Soumyabrata Pal
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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 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS Pub Date : 2024-09-17 DOI: 10.1109/TIT.2024.3455151
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引用次数: 0
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IEEE Transactions on Information Theory
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