CIF: Small: Fundamental Analysis and Design of Repair-Efficient Cloud Storage Systems: a Linear Perspective

云存储系统正越来越多地被广泛的数据密集型应用所采用，例如网络搜索、云计算、分布式文件共享以及具有高访问需求的各种类型的数据网络，包括社交网络、健康和医疗数据库以及银行系统。云存储系统由多个数据中心和通过互联网连接的计算机服务器组成。虽然系统的各个组件会遇到多种类型的故障，但在数据可用性方面的可靠性和重新生成故障存储节点的能力是设计云存储系统的两个关键特征。随着存储数据的大小和访问数据的用户数量不断增加，设计健壮、高效和可扩展的系统是一个具有挑战性但至关重要的问题。该研究为高效云存储系统的设计和分析奠定了坚实的理论基础。在技术方面，本研究将侧重于（1）研究云存储系统中存储开销和修复需求之间的权衡，以及（2）开发有效的编码方案，保证数据恢复和故障节点再生。虽然表征一般信息理论的权衡似乎是棘手的，但可以通过将问题限制在实际相关和低复杂度的线性代码类，并利用有限域上线性代码和多维子空间之间的对偶性来取得进展。一个优化问题，制定了这个问题，其中智能的最佳解决方案的解释提供了有见地的指导方针，设计代码的建设机制。最后，提出了一个统一的框架代码建设，不仅包括几个特设的设计，但也概括建设的所有最佳操作点的系统。

Cloud storage systems are increasingly being adopted by a wide spectrum of data intensive applications such as web search, cloud computing, distributed file sharing, and various types of data networks with high access demand, including social networks, health and medical databases, and banking system. A cloud storage system consists of several data centers and computer servers that are connected through Internet. While individual components of the system are subject to several types of failure, reliability, in the sense of data availability, and ability of regenerating failed storage nodes are two key features to design cloud storage systems. As the size of stored data and the number of users accessing the data continues to increase, designing robust, efficient, and scalable systems is a challenging and yet critically important problem. This research will develop a solid theoretical foundation for design and analysis of efficient cloud storage systems. On the technical side, this research will focus on (1) studying the tradeoff between storage overhead and repair requirements in cloud storage systems, and (2) development of efficient coding schemes with guarantees on data recovery and failed node regeneration. While characterizing the general information-theoretic tradeoff appears to be intractable, progress can be made by limiting the problem to the class of practically relevant and low-complexity linear codes, and exploiting the duality between linear codes and multi-dimensional subspaces over finite fields. An optimization problem is formulated for this question, where an intelligent interpretation of the optimum solution provides insightful guidelines to devise code construction mechanisms. Lastly, a unified framework is proposed for code construction, to not only encompass several ad-hoc designs, but also generalize construction to all optimum operating points of the system.