IEEE Transactions on Information Theory最新文献

英文中文

A New Upper Bound for Linear Codes and Vanishing Partial Weight Distributions 线性编码和消失部分权重分布的新上限

IF 2.5 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-26 DOI: 10.1109/tit.2024.3449899

Hao Chen, Conghui Xie

引用次数: 0

Self-orthogonal codes from p-divisible codes 来自 p 分码的自正交码

IF 2.5 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-26 DOI: 10.1109/tit.2024.3449921

Xiaoru Li, Ziling Heng

引用次数: 0

Phase Retrieval With Background Information: Decreased References and Efficient Methods 带背景信息的相位检索：减少参考文献和高效方法

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-26 DOI: 10.1109/TIT.2024.3449554

Ziyang Yuan;Haoxing Yang;Ningyi Leng;Hongxia Wang

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

$1/2$

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

$left ({{2^{frac {d+1}{d}}-1}}right)$

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.

傅立叶相位检索（PR）是一个在各种应用中出现的严重求解困难的逆问题。为了保证唯一解并减轻对初始化的依赖，可以利用背景信息作为结构先验。然而，在转向高分辨率成像时，对背景信息的要求可能具有挑战性。同时，之前提出的投影梯度下降（PGD）方法也需要很多背景信息。在本文中，我们提出了一个关于背景信息需求的改进理论结果，以及两种基于 Douglas Rachford（DR）的方法。我们通过分析证明，与一维信号相比，二维信号为确保唯一解所需的背景信息可减少近 1/2$。通过将结果推广到 d 维，我们证明背景信息的长度超过信号的 $/left ({{2^{frac {d+1}{d}}-1}}/right)$ folds 就足以确保唯一性。同时，我们还分析了当测量和背景信息受到噪声干扰时模型的稳定性和鲁棒性。此外，我们还提出了两种方法，即背景道格拉斯拉赫福德（BDR）和凸背景道格拉斯拉赫福德（CBDR）。BDR 是一种非凸方法，已被证明在温和的假设条件下具有局部 R 线性收敛率。相反，CBDR 方法使用了凸化技术，只要背景信息充足，就能证明它具有全局收敛性保证。为了支持这一点，我们建立了一个名为 F-RIP 的新属性。我们通过模拟和实际实验测量测试了所提方法的性能，并证明与 PGD 方法相比，这些方法在背景信息较少的情况下实现了更高的恢复率。

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引用次数: 0

On the Noise Sensitivity of the Randomized SVD 关于随机 SVD 的噪声敏感性

IF 2.5 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-26 DOI: 10.1109/tit.2024.3450412

Elad Romanov

引用次数: 0

Repairing Reed-Solomon Codes over Prime Fields via Exponential Sums 通过指数和修复素域上的里德-所罗门码

IF 2.5 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-23 DOI: 10.1109/tit.2024.3449041

Roni Con, Noah Shutty, Itzhak Tamo, Mary Wootters

引用次数: 0

Improved Field Size Bounds for Higher Order MDS Codes 改进高阶 MDS 代码的字段大小界限

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-23 DOI: 10.1109/TIT.2024.3449030

Joshua Brakensiek;Manik Dhar;Sivakanth Gopi

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

$rm {MDS}(ell)$

where

$ell $

denotes the order of generality,

$rm {MDS}(2)$

codes are equivalent to the usual MDS codes. The best prior lower bound on the field size of an

${[}n,k{]}$

$rm {MDS}(ell)$

codes is

$Omega _{ell } (n^{ell -1})$

, whereas the best known (non-explicit) upper bound is

$O_{ell } (n^{k(ell -1)})$

which is exponential in the dimension. In this work, we nearly close this exponential gap between upper and lower bounds. We show that an

${[}n,k{]}$

$rm {MDS}(3)$

codes requires a field of size

$Omega _{k}(n^{k-1})$

, 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

${[}n,k{]}$

$rm {MDS}(ell)$

code over fields of size

$n^{(ell k)^{O(ell k)}}$

. The smallest non-trivial case where we still do not have optimal constructions is

${[}n,3{]}$

$rm {MDS}(3)$

. In this case, the known lower bound on the field size is

$Omega (n^{2})$

and the best known upper bounds are

$O(n^{5})$

for a non-explicit construction and

$O(n^{32})$

for an explicit construction. In this paper, we give an explicit construction over fields of size

$O(n^{3})$

which comes very close to being optimal.

高阶 MDS 码是 Brakensiek 等人（2023 年）最近提出的 MDS 码的有趣概括。在后来的研究中，它们被证明与最优列表可解码码和最大可恢复张量码密切相关。因此，（显式）构造小域上的高阶 MDS 码是一个重要的开放性问题。高阶 MDS 码用 $rm {MDS}(ell)$ 表示，其中 $ell $ 表示一般阶，$rm {MDS}(2)$ 码等价于通常的 MDS 码。关于${[}n,k{]}$ - $rm {MDS}(ell)$ 代码的字段大小的最佳先验下限是$Omega _{ell } (n^{ell -1})$ ，而已知的最佳（非显式）上限是$O_{ell } (n^{k(ell -1)})$ ，它的维数是指数级的。在这项工作中，我们几乎缩小了上界和下界之间的指数差距。我们证明，${[}n,k{]}$ - $rm {MDS}(3)$ 代码需要一个大小为 $Omega _{k}(n^{k-1})$ 的域，这接近已知的上限。利用高阶 MDS 代码和最优列表可解码代码之间的联系，我们证明了即使列表大小为 2，满足最优列表解码 Singleton 约束的代码也需要指数级的字段大小；这解决了上官和 Tamo (2020) 提出的一个未决问题。我们还给出了在大小为 $n^{(ell k)^{O(ell k)}}$ 的字段上的 ${[}n,k{]}$ - $rm {MDS}(ell)$ 代码的明确构造。在这种情况下，已知的字段大小下限是 $Omega (n^{2})$，已知的最佳上限是非显式构造的 $O(n^{5})$和显式构造的 $O(n^{32})$。在本文中，我们给出了在大小为 $O(n^{3})$ 的域上的显式构造，它非常接近最优。

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引用次数: 0

On Confidence Sequences for Bounded Random Processes via Universal Gambling Strategies 通过通用赌博策略论有界随机过程的置信序列

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-23 DOI: 10.1109/TIT.2024.3448461

J. Jon Ryu;Alankrita Bhatt

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.

本文探讨了构建置信序列的问题，置信序列是在时间上均匀成立的置信区间序列，用于估计有界实值随机过程的均值。本文从自然双马赛跑的角度重新审视了近期文献中建立的基于赌博的方法，并展示了由 Cover (1991) 的通用组合所诱导的算法的新特性。本文的主要成果是一种基于混合下限的新算法，它以恒定的每轮时间复杂度近似于 Cover 的通用投资组合的性能。Fan 等人，2015）中关于对数函数下界的高阶泛化，作为所提算法的关键技术被开发出来，可能会引起人们的兴趣。

引用次数: 0

Achieving the Exactly Optimal Privacy-Utility Trade-Off With Low Communication Cost via Shared Randomness 通过共享随机性，以较低通信成本实现恰好最优的隐私-效用权衡

IF 2.2 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-23 DOI: 10.1109/TIT.2024.3448475

Seung-Hyun Nam;Hyun-Young Park;Si-Hyeon Lee

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.

我们考虑的是在共享随机性存在的情况下，局部差分隐私（LDP）约束下的离散分布估计问题。针对这一问题，我们提出了一类新的 LDP 方案，该方案可实现完全最优的隐私-效用权衡（PUT），且通信成本小于或等于输入数据的大小。此外，一个简单的推论表明，如果输入数据的大小是偶数，那么一个比特的通信就足以实现高隐私机制下的完全最优 PUT。其主要思路是根据称为 "解析 "的组合概念，分解 Park 等人（2023 年）提出的分块设计方案。我们把分解后的具有共享随机性的 LDP 方案称为原始块设计方案的分辨率。分块设计方案的分辨率的通信成本小于或等于原始分块设计方案的通信成本。此外，只要原始块设计方案是完全最优的，那么块设计方案的分辨率就是完全最优的。因此，我们提供了 Ye 和 Barg（2018）提出的完全最优子集选择方案的两种分辨率，分别称为 Baranyai 分辨率和循环移位分辨率。我们证明，在所有精确最优的块设计方案决议中，Baranyai决议实现了最小的通信成本。Baranyai 解析的一个缺点是，它的显式结构在一般情况下是未知的。相比之下，循环移位决议具有明确的结构，但其通信成本可能大于巴兰奈决议。作为补充，我们还提出了其他区块设计方案的解决方案，这些方案可以在一定的输入数据大小和隐私预算条件下实现完全最优的 PUT。这些方案与巴兰亚决议一样，需要最小的通信成本，与循环移位决议一样，具有明确的结构。

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引用次数: 0

Optimal Trace Distance and Fidelity Estimations for Pure Quantum States 纯量子态的最佳轨迹距离和保真度估计

IF 2.5 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-22 DOI: 10.1109/tit.2024.3447915

Qisheng Wang

引用次数: 0

Improving explicit constructions of r-PD-sets for Z p s -linear generalized Hadamard codes 改进 Z p s 线性广义哈达玛德码 r-PD 集的显式构造

IF 2.5 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory

Pub Date : 2024-08-22 DOI: 10.1109/tit.2024.3448230

Josep Rifâ, Adrián Torres-Martín, Mercè Villanueva

引用次数: 0

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IEEE Transactions on Information Theory

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