Collaborative Research: TF: Information Theory of Channels with Missing Observations

美国国家科学基金会计算机和通信基础分部：理论基础计划征集NSF 07-525：缺少观测的信道的信息论主要调查人员：南加州普林斯顿大学的Giuseppe Caire和Sergio Verd‘u概述这个项目采用统一的信息论方法来解决传输、压缩、估计和传感中的问题，在这些问题中，观测可能会从现有数据中丢失。在当前的许多实际应用中，由于衰落和/或干扰(在无线中)、由于有限缓冲区大小而导致的分组丢失(在网络中)、脉冲噪声(在功率和用户环路中)、有缺陷的介质(在磁记录中)、故障换能器(在传感器网络中)、降低的复杂性(在压缩感知中)、链路故障(在蜂窝系统的有线基础设施中)、机会主义信令(在非平稳信道中)等，数据容易受到随机擦除。评估数据丢失对可靠压缩和传输的基本Shannon理论极限以及估计理论极限的影响具有重要的理论和实践意义。此外，在存在缺失观测的情况下，如何最好地重新设计压缩、编码、调制和滤波方案以获得接近基本极限的性能的新的实际问题出现了。该项目解决了涉及各种缺失观测模型的一些具体的挑战性和技术相关的研究问题：当压缩器处的擦除位置已知/未知时，缺失数据的无损和有损压缩；受擦除影响的噪声信道的容量，特别是输出擦除对有记忆的信道容量的影响；丢失观测的最小均方误差估计和预测；同时广播给具有大不同丢失信息率的多个接收器的喷泉码；易被删除的网络的多用户信息理论，包括诸如多路访问信道和广播信道等基本范例；具有集中处理和不可靠有线链路的蜂窝网络(链路中断时的“光纤无线电”)；收发信机技术的罗布斯化，如对删除非常敏感的正交频分多路复用、反馈方案和脏纸编码；从信息论的角度重温压缩感知的基本极限(可以解释为满级随机投影和投影系数的随机擦除的串联)。本项目旨在促进在几个研究社区的十字路口发现和理解与当前技术相关的通信和信号处理系统，并为培养信息论、编码理论、估计、信号处理、随机矩阵理论和网络等学科的研究生提供肥沃的土壤。

NSF Division of Computer and Communications Foundations:Theoretical FoundationsProgram Solicitation NSF 07-525:Information Theory of Channels with Missing ObservationsPrincipal Investigators: Giuseppe Caire and Sergio Verd'uUniversity of Southern California Princeton UniversitySummaryThis project takes a unified information theoretic approach to problems in transmission, compression, estimation and sensing in which observations may be missing from the available data. In many applications of current practical interest, data is subject to random erasures because of fading and/or jamming (in wireless), packet dropping due to finite buffer sizes (in networks), impulse noise (in power and subscriber looplines), defective media (in magnetic recoding), faulty transducers (in sensor networks), reduced complexity(in compressed sensing), link failure (in wired infrastructure of a cellular system), opportunistic signaling(in nonstationary channels), etc. It is of great theoretical and practical interest to assess the impact of themissing data on the fundamental Shannon theoretic limits for reliable compression and transmission, as well as the estimation theoretic limits. Furthermore, new practical questions arise on how to best redesigncompression, coding, modulation, and filtering schemes to attain performance close to the fundamental limits in the presence of missing observations.This project tackles a number of specific challenging and technologically relevant research problems that involve a variety of models with missing observations: Lossless and lossy compression of missing data, when the erasure locations are known/unknown at the compressor; Capacity of noisy channels subject to erasures, and in particular the effect of output erasures on the capacity of channels with memory; Minimum mean square error estimation and prediction with missing observations; Fountain codes for simultaneous broadcast to several receivers with widely different missing information rates; Multiuser information theory for networks subject to erasures, including basic paradigms such as the multiaccess channel and the broadcast channel; Cellular networks with centralized processing and unreliable wired links ("radio on fiber" subject to link outages); Robustification of transceiver techniques such as orthogonal frequency division multiplexing, feedback schemes, and dirty-paper coding which are notoriously sensitive to erasures; Revisiting the fundamental limits of compressed sensing (which can be interpreted as the concatenation of a full-rank random projection followed by random erasures of the projected coefficients) from the viewpoint of information theory.This project aims at advancing discovery and understanding of communication and signal processing systems of relevance to current technology, at the crossroads of several research communities, and provides a fertile ground for training of graduate students in the disciplines of information theory, coding theory, estimation, signal processing, random matrix theory and networks.