CIF: Small: Distributed Function Computation and Multiterminal Data Compression

本研究致力于理论和算法的设计，为一个有效的本地计算，由多个网络终端的共享功能的所有他们观察到的相关数据。终端之间的有效通信有助于有效计算。应用包括：计算进行相关测量的无线传感器托管网络中观察到的数据的平均值、方差、最大值、最小值和奇偶性。这一目标与为存储和传输目的有效压缩数据的算法设计以及确保数据安全的算法设计密切相关。该项目的一个主要目标是明确地描述这些连接，从而导致新的和有效的算法的数据压缩，功能计算和网络安全的发展。技术方法涉及的基本问题的制定和分析，使用信息理论框架。这将使网络模型中的“熵分解总共享随机性”的原则的发展，以解决多用户信息理论中的困难问题，其中率效率函数计算是一个领先的例子。特别地，将研究信源编码算法在分布式函数计算中的应用。特定组的开放性问题选择调查地址的一般类的多端模型的功能计算和数据压缩。这种选择的动机，是令人信服的兴趣，网络功能计算和源代码的理论和工程实践，以及网络安全。

This research addresses the theory and design of algorithms for an efficient local computation by multiple network terminals of shared functions of all their observed correlated data. Efficient communication among the terminals facilitates efficient computation. Applications include: computing the average, variance, maximum, minimum and parity of observed data in a colocated network of wireless sensors that make correlated measurements. This objective is connected closely to the design of algorithms for the efficient compression of data for storage and transmission purposes, as well as of algorithms for assuring data security. A main goal of the project is to characterize explicitly these connections, thereby leading to the development of new and efficient algorithms for data compression, function computation and network security.The technical approach involves a formulation of the underlying problems and their analysis, using an information theoretic framework. This will enable the development of a principle of "entropy decomposition of total shared randomness" in a network model to address difficult problems in multiuser information theory of which rate-efficient function computation is a leading example. In particular, an application of source coding algorithms in distributed function computation will be studied. Specific groups of open problems chosen for investigation address a general class of multiterminal models for function computation and data compression. This choice is motivated by, and is of compelling interest to, the theory and engineering practice of network function computation and source coding, as well as network security.