CIF: Small: New Approaches to the Design and Analysis of Graphical Models for Linear Codes and Secret Sharing Schemes
CIF:小:线性码和秘密共享方案图形模型设计和分析的新方法
基本信息
- 批准号:0916919
- 负责人:
- 金额:$ 35.07万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2009
- 资助国家:美国
- 起止时间:2009-08-15 至 2013-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
NSF Proposal 0916919 New approaches to the design and analysis of graphical models for linear codes and secret sharing schemesAbstractError-correcting coding enables one to design reliable systems of transmission and storage of information and is used universally for sending packets over the web, in writing data on CD's and flash memory devices, and other similar means of modern communication. A very efficient method of encoding information for error protection is the so-called "iterative decoding," which assumes that every binary digit of transmission is recovered based on its realiblity and the realibility of a few other, carefully selected bits of the encoded message. This method of error correction is analyzed based on the representation of the encoding as a graph in the plane in which recovery from errors proceeds by successive exchange of information between the nodes of the graph in an iterative procedure performed in a number of rounds. One of the main goals of this research is to reduce complexity (the number of rounds) needed for reliable recovery of the transmission from errors in the communication medium.Graphical models of linear codes have so far been restricted to trellises, i.e., cycle-free graphs, and graphs with exactly one cycle (tail-biting trellises). This research studies complexity of realization of codes and iterative decoding algorithms on connected graphs with cycles, deriving complexity estimates from the tree-decomposition of graphs. One of the goals of this research is to find methods of constructing low-complexity realizations of codes for such well-known code families as Reed-Muller and Reed-Solomon codes, and explore the optimality gap of these representations. Methods of matroid theory used in the study of graphical models will also be explored in the analysis of access structures of secret sharing schemes and secure multi-party computation protocols.
NSF提案0916919设计和分析线性代码的图形模型和秘密共享shemesabstracterror-correct recretting编码使人们能够设计可靠的信息传输和存储系统,并在CD和闪光设备以及其他类似的通信方式上通过网络编写数据,用于通过网络发送数据包。 一种非常有效的编码信息以进行错误保护的方法是所谓的“迭代解码”,它假设每个传输的每个二进制数字都是根据其实质性恢复的,并且是编码消息的其他一些,精心选择的位置的可实现性。根据在平面中编码为图的表示,对这种误差校正方法进行了分析,在该平面中,从错误中恢复从错误进行了恢复,以在图形的迭代过程中连续交换图表的节点,以多回合进行。 这项研究的主要目标之一是降低从通信介质中的错误恢复传输所需的复杂性(回合数)。迄今为止,线性代码的质量模型仅限于格子,即无周期的图形,以及具有一个循环的图形(尾部折线)。这项研究研究了与周期的连接图上的代码实现和迭代解码算法的复杂性,从图的树分解中得出了复杂性估计。这项研究的目标之一是找到针对诸如Reed-Muller和Reed-Solomon代码等著名的代码家族构建低复杂性实现的方法,并探讨这些表示形式的最佳差距。在图形模型研究中使用的原始理论方法还将在秘密共享方案和安全多方计算方案的访问结构的分析中进行探讨。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

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数据更新时间:2024-06-01
Alexander Barg其他文献
Rényi divergence guarantees for hashing with linear codes
Rényi 散度保证线性码散列
- DOI:
- 发表时间:20242024
- 期刊:
- 影响因子:0
- 作者:Madhura Pathegama;Alexander BargMadhura Pathegama;Alexander Barg
- 通讯作者:Alexander BargAlexander Barg
Anatomic bundle reconstruction of the deltoid ligament
- DOI:10.1016/j.orthtr.2013.07.01310.1016/j.orthtr.2013.07.013
- 发表时间:2013-09-012013-09-01
- 期刊:
- 影响因子:
- 作者:Matthias D. Wimmer;Patrick Vavken;Alexander Barg;Victor Valderrabano;Geert I. PagenstertMatthias D. Wimmer;Patrick Vavken;Alexander Barg;Victor Valderrabano;Geert I. Pagenstert
- 通讯作者:Geert I. PagenstertGeert I. Pagenstert
A family of permutationally invariant quantum codes
一系列排列不变的量子码
- DOI:
- 发表时间:20232023
- 期刊:
- 影响因子:6.4
- 作者:Arda Aydin;Max A. Alekseyev;Alexander BargArda Aydin;Max A. Alekseyev;Alexander Barg
- 通讯作者:Alexander BargAlexander Barg
A bound on Grassmannian codes
- DOI:10.1016/j.jcta.2006.03.02510.1016/j.jcta.2006.03.025
- 发表时间:2006-11-012006-11-01
- 期刊:
- 影响因子:
- 作者:Alexander Barg;Dmitry NoginAlexander Barg;Dmitry Nogin
- 通讯作者:Dmitry NoginDmitry Nogin
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Alexander Barg的其他基金
CIF: Small: Quantum LDPC codes: structure and logical operations
CIF:小:量子 LDPC 码:结构和逻辑运算
- 批准号:23309092330909
- 财政年份:2023
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CIF: Small: Coding-theoretic methods in discrepancy and energy optimization, with applications
CIF:小:差异和能量优化中的编码理论方法及其应用
- 批准号:21044892104489
- 财政年份:2021
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
NSF-BSF: CIF: Small: From storage codes to recoverable systems
NSF-BSF:CIF:小型:从存储代码到可恢复系统
- 批准号:21101132110113
- 财政年份:2021
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CIF: Small: Information Recovery Under Connectivity and Communication Constraints
CIF:小:连接和通信限制下的信息恢复
- 批准号:18144871814487
- 财政年份:2018
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CCF-BSF: CIF: Small: Collaborative Research: Coding and Information - Theoretic Aspects of Local Data Recovery
CCF-BSF:CIF:小型:协作研究:编码和信息 - 本地数据恢复的理论方面
- 批准号:16186031618603
- 财政年份:2016
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CIF: Small: Collaborative Research: Efficient Codes and their Performance Limits for Distributed Storage Systems
CIF:小型:协作研究:分布式存储系统的高效代码及其性能限制
- 批准号:14229551422955
- 财政年份:2014
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CIF: Small: Ordered Metrics and Their Applications
CIF:小:有序指标及其应用
- 批准号:12172451217245
- 财政年份:2012
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CIF: Small: Collaborative Research: A General Theory of Group Testing for Genotyping
CIF:小型:协作研究:基因分型群体测试的一般理论
- 批准号:12178941217894
- 财政年份:2012
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
Collaborative Research: Positive definite functions in distance geometry and combinatorics
合作研究:距离几何和组合学中的正定函数
- 批准号:11016871101687
- 财政年份:2011
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
CIF: Small: 2010 IEEE Information Theory Workshop
CIF:小型:2010 IEEE 信息论研讨会
- 批准号:10180121018012
- 财政年份:2010
- 资助金额:$ 35.07万$ 35.07万
- 项目类别:Standard GrantStandard Grant
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相似海外基金
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- 批准号:23112742311274
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- 资助金额:$ 35.07万$ 35.07万
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合作研究:CIF:小:非光滑和非Lipschitz黎曼优化的新理论和应用
- 批准号:23085972308597
- 财政年份:2022
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- 批准号:22410572241057
- 财政年份:2022
- 资助金额:$ 35.07万$ 35.07万
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- 批准号:21328152132815
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