CIF: Small: Computer assisted rate regions for multi-source distributed storage and network coding

分布式信息存储体系结构对驱动器故障具有恢复能力，并以允许自身高效修复的方式进行组织，是大数据系统新兴领域的关键组件。此外，公司和个人向云存储数据的过渡正在实现巨大的规模经济，而分布式存储体系结构是如此大规模的计算服务系统中最重要的组件之一。从所使用的编码的角度来看，现代分布式存储系统正在使用的体系结构仍然是过时的。更高效的分布式存储体系结构将以更低的长期总成本向客户提供更好、更具响应性的服务，包括更快的访问、更好的可靠性和更快速的处理。为了获得这些长期利益，必须发展新的科学来理解和确定这些系统的基本极限。这些基本极限可以用网络编码下的网络容量区域来表示，这些网络编码本身只是隐含地描述了除了最对称和最简化的形式之外的所有形式。本项目将研究网络和分布式存储系统的容量区域，以及实现它们的代码类。将开发用于小型网络的计算这些速率区域的自动化方法，该方法利用问题对称性的检测、专门的多面体计算以及与最优码相关联的拟阵的类的列举。更大的网络和存储系统也将通过引入网络嵌入操作来研究，这些操作保留了代码类别的充分性，以实现整个容量区域。

Distributed information storage architectures that are resilient against drive failures and organized in a manner that allow themselves to heal efficiently are a key component of the emerging area of big data systems. Moreover, the transition by companies and individuals to storing data in the cloud are enabling gigantic economies of scale, and distributed storage architectures are one of the most important components of such a large scale computing services system. The architectures modern distributed storage systems are using are still, from the standpoint of the coding utilized, archaic. More efficient distributed storage architectures would deliver better, more responsive, services to customers including faster access, better reliability, and more responsive processing, and at a lower aggregate long term cost. To reap these long term benefits, new science has to be developed to understand and determine the fundamental limits for these systems. These fundamental limits can be expressed in terms of the capacity regions of networks under network coding, which are themselves as of yet only implicitly characterized in all but the most symmetrized and simplified forms.This project will study the capacity regions of networks and distributed storage systems, and the classes of codes that achieve them. Automated methods of computing these rate regions for small networks will be developed that harness the detection of problem symmetries, specialized polyhedral computation, and the enumeration of classes of matroids associated with optimal codes. Larger networks and storage systems will also be studied via the introduction of network embedding operations that preserve the sufficiency of classes of codes to achieve the entire capacity region.