CIF: Small: Collaborative Research: Fundamental Limits of Information Systems: A Computational Approach

信息论提供了一个总体框架，在这个框架中，可以对信息系统（有线和无线网络、密码系统、数据压缩和存储系统等）的基本限制进行有意义的研究。对这些极限的调查传统上是分析性的，在许多情况下需要大量的独创性。随着现代信息系统变得越来越复杂，这种方法变得相当笨拙。该项目的主要目标是建立在应用计算方法的初步成功基础上，以表征某些分布式存储系统的基本限制，并进一步了解所提出的计算方法在大数据基础设施的广泛设置中取得成功所需要的条件。所提出的计算方法是建立在一个有利的观点上，即识别和证明基本极限的整个过程可以被看作是在当前系统的特定约束和信息测量的一般约束下的优化问题。困难在于，对于任何实际相关的问题，这种优化程序通常非常大，并且数值结果难以解释。该项目有三个主要目标：1)使用对称和其他约束找到更有效的问题表示；2)利用领域知识改进优化算法；3)通过对偶对计算结果进行智能解释，以方便工程设计。研究结果预计将对以下两个领域产生可衡量的影响：1)大数据基础设施：正在进行的大数据运动要求具有不同可靠性和功能需求的信息系统。通过确定这些系统的基本限制，可以评估准确的业绩评价和有意义的设计准则；2)信息论：本研究将衔接计算优化与信息论两门学科，为信息论研究注入更多的计算机智能。

Information theory provides a general framework in which the fundamental limits of information systems (wired and wireless networks, cryptographic systems, data compression and storage systems, and others) can be meaningfully investigated. The investigation of such limits is traditionally conducted analytically, requiring in many cases substantial ingenuity. As modern information systems become more and more complex, such an approach becomes rather unwieldy. The main goal of this project is to build upon initial successes in applying a computational approach to characterize the fundamental limits of certain distributed storage systems, and to further understand what it takes for the proposed computational approach to be successful in the broad setting of big-data infrastructure.The proposed computational approach is built upon the vantage point that the overall process of identifying and proving fundamental limits can be alternatively viewed as an optimization problem under the specific constraints of the system at hand and the general constraints of information measures. The difficulty lies in the fact that such optimization programs are usually very large for any practically relevant problems, and numerical results are difficult to interpret. This project pursues three major thrusts: 1) finding more efficient problem representations using symmetry and other constraints; 2) improving the optimization algorithms using domain knowledge; and 3) finding intelligent interpretations of the computed results through duality to facilitate engineering design. The results are expected to have measurable impacts on the following two disciplines: 1) Big-data infrastructure: The ongoing big-data movement calls for information systems with diverse reliability and functionality requirements. By identifying the fundamental limits of such systems, accurate performance evaluations and meaningful design guidelines may be assessed; and 2) Information theory: The proposed study will bridge the disciplines of computational optimization and information theory, and instill more computerized intelligence into information theory research.