CIF: Small: Service Rates of Codes

分布式存储平台支持在高度不确定性下运行但具有严格的低延迟要求的主要系统。这些系统包括健康（远程手术）、金融（电子交易）、商业（在线购物）、云游戏、自动驾驶汽车和增强现实。在大多数这些新兴的应用程序中，用户的瞬时和预期的数量和他们的数据兴趣广泛波动。因此，为满足特定预期需求而设计和配置的传统存储解决方案是不够的。该项目首先假设了一个新的指标，该指标应该是设计高效分布式存储的重要考虑因素，必须为时间敏感的应用程序提供低延迟，并在高度不确定性下保持稳定。它提供了最佳的存储解决方案。此外，它还发展了编码理论、图的优化、真实的和有限几何等基础知识，增强了存储系统的鲁棒性。相比之下，纠删编码可以有效地服务于数据访问中不断变化的动态和需求。因此，确定冗余存储方案可以支持哪些数据访问速率是至关重要的。这些费率构成其服务费率区域。该项目有两个主要目标：1）对于给定的（已实现的）冗余方案，它询问其服务速率区域是什么。2)对于一个给定的（期望的）服务速率区域，它要求的冗余方案的服务速率区域，包括在一些最佳的成本或一些所需的属性。关于第一个问题，该项目正在确定众所周知的各类代码的服务费率区域，以及在储存系统中使用的那些代码的服务费率区域，以提供其他所需的功能。关于第二个问题，该项目正在设计准则，以支持在资源有限的情况下所需的服务费率，这一奖项反映了国家科学基金会的法定使命，并已被认为值得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的支持。

Distributed storage platforms support major systems that operate under high uncertainty but have strict, low-latency requirements. Such systems include health (remote surgery), finance (electronic trading), commerce (online shopping), cloud gaming, self-driving cars, and augmented reality. In most of these emerging applications, users’ instantaneous and expected numbers and their data interests extensively fluctuate. Therefore, traditional storage solutions, designed and provisioned to satisfy specific expected demands, are inadequate. This project first postulates a new metric that should be an essential consideration in designing efficient distributed storage that must provide low latency for time-sensitive applications and remain stable under high uncertainty. It then offers optimal storage solutions. Besides that, it advances fundamentals of coding theory, optimization on graphs, and real and finite geometry.Redundancy increases the robustness of storage systems. Comparatively, erasure coding can efficiently service changing dynamics and requirements in data access. It is therefore essential to determine which data-access rates a redundant storage scheme can support. These rates make up its service-rate region. This project has two primary objectives: 1) For a given (implemented) redundancy scheme, it asks what its service-rate region is. 2) For a given (desired) service-rate region, it asks which redundancy scheme has the service-rate region that includes the desired one under some optimal cost or some required properties. In connection with the first question, the project is characterizing the service-rate regions of well-known classes of codes, as well as of those in use in storage systems to provide other desirable features. In connection with the second question, the project is designing codes to support desired service rates in resource-constrained settings.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.