NSF-BSF:CIF:Small:Reliable Data Storage on Sampling Channels

爆炸性的数据增长和对数据处理和计算的永不满足的需求，迫切需要开发能够及时处理高级数据处理请求的复杂信息系统。新兴的解决方案越来越多地采用更复杂、超大规模、分散的数据存储系统和子系统，从多云到区块链辅助网络。对付数据存储系统中的错误和故障的常见方法是在用户数据块存储之前增加冗余。描述这些操作的现有数学解决方案本质上假设存储的数据块可以以集中的方式完整地访问。为了满足具有新型数据任务和分散数据组织的新兴系统的需求，现在需要开发新的数学模型和抽象，为分散数据存储系统提供相关的理论基础和实际设计原则。该项目通过引入采样通道的概念来解决这一需求，该通道用于从数学上捕获用户数据与其可用于处理的表示之间的关系。抽样概念的关键特征是，它既不假设集中访问，也不假设全块可用性，这是由现代数据系统的特性所激发的。然后，该项目将开发适用于不同类型采样通道的数学工具和技术。除了技术和科学贡献外，该项目还具有减少资源消耗和增强未来信息系统中敌对参与者的稳健性的潜力。该项目将开发一个以采样通道为中心的新数学框架，重点是它们在分散数据存储系统中的应用。超越了基本的和被充分研究的非受控抽样的案例，新兴的分布式系统和应用激发了受控抽样的使用，根据是否对抽样有精确的控制或仅通过其分布将其分为两个级别。信道编码是一门旨在通过有原则的数学框架最大化用户数据鲁棒性和最小化系统冗余的科学学科。在此背景下，研究人员将把注意力集中在稀疏图形表示的有效可解码代码的理论和实践上。这种代码提供了足够的灵活性，可用于新兴系统所需的抽样类别和系统任务。有了最初的令人信服的发现，这些发现指出了代码设计原则，这些原则与在传统环境中证明成功的方法不同，研究者将严格分析现有的代码族，并提供如何使它们适应所研究的环境的技术，以及开发新的代码族。该项目将包括从理论上建立相关的代码属性、性能保证和权衡，以及实际的评估和比较。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Explosive data growth and insatiable demand for data processing and computing have created an urgent need to develop sophisticated information systems able to timely handle advanced data processing requests. Emerging solutions increasingly employ more complex, hyper-scaled, decentralized data storage systems and sub-systems, ranging from the multi-cloud to block-chain assisted networks. Common approaches to combatting errors and failures in data storage systems add redundancy to blocks of user data before they are stored. Existing mathematical solutions that describe these operations intrinsically assume that the stored data block can be accessed in its entirety and in a centralized manner. To meet the requirements of emerging systems that have both new types of data tasks and a decentralized data organization, there is now an identified need to develop new mathematical models and abstractions that will provide relevant theoretical foundations and practical design principles for decentralized data storage systems. The project addresses this need by introducing the concept of a sampling channel, which serves to mathematically capture the relationship between the user data and its representation that is available for processing. The key feature of the sampling concept, motivated by the properties of modern data systems, is that it assumes neither centralized access nor full-block availability. The project will then develop mathematical tools and techniques that are suitable for sampling channels of different types. In addition to technical and scientific contributions, this project also has a potential to reduce resource consumption and increase robustness to adversarial participants in future information systems. This project will develop a new mathematical framework centered around sampling channels, with the focus on their applications to decentralized data storage systems. Moving beyond the basic and well-studied case of uncontrolled sampling, emerging distributed systems and applications motivate the usage of controlled sampling, which is classified into two levels depending on whether one has the exact control on the sampling or only through its distribution. Channel coding is a scientific discipline aimed at maximizing the user-data robustness and minimizing system redundancy through principled mathematical frameworks. In this context, the investigators will focus their attention on the theory and practice of efficiently decodable codes with sparse graphical representations. Such codes offer sufficient flexibility to be utilized for the sampling categories and system tasks that are needed in emerging systems. Equipped with initial compelling findings that point to code-design principles that depart from the methods proven successful in conventional settings, the investigators will rigorously analyze existing code families, and offer techniques on how to adapt them to the studied setting, as well as develop new code families. The project will involve theoretically establishing relevant code properties, performance guarantees and trade-offs, and practical evaluations and comparisons.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.