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

分布式信息存储架构能够抵御驱动器故障，并以一种允许自身有效修复的方式组织起来，是大数据系统新兴领域的关键组成部分。此外，公司和个人向云存储数据的转变正在实现巨大的规模经济，分布式存储架构是这种大规模计算服务系统的最重要组成部分之一。从所使用的编码的角度来看，现代分布式存储系统所使用的架构仍然是陈旧的。更高效的分布式存储体系结构将为客户提供更好、响应更快的服务，包括更快的访问、更好的可靠性和响应更快的处理，并且长期总成本更低。为了获得这些长期的好处，必须发展新的科学来理解和确定这些系统的基本限制。这些基本限制可以用网络编码下的网络容量区域来表示，这些容量区域本身除了最对称和简化的形式外，还只能以隐含的形式表现出来。该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别。小型网络计算这些速率区域的自动化方法将被开发出来，这些方法将利用问题对称性的检测、专门的多面体计算以及与最优代码相关的拟阵类的枚举。还将通过引入网络嵌入操作来研究更大的网络和存储系统，以保持代码类别的充分性，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.