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

NSF计算机和通信基础分部：理论基础项目征集NSF 07-525：观测缺失信道的信息论主要研究者：Giuseppe Caire和Sergio Verd'u南加州大学普林斯顿大学摘要该项目采用统一的信息论方法来解决传输、压缩、估计和感知中观测可能从可用数据中缺失的问题。在当前实际感兴趣的许多应用中，由于衰落和/或干扰，数据经受随机擦除（在无线中），由于缓冲区大小有限而导致的数据包丢弃（在网络中），脉冲噪声（在电源和用户环路中），有缺陷的介质（在磁记录中），传感器故障（在传感器网络中），降低了复杂性（在压缩感知中），链路故障（在蜂窝系统的有线基础设施中），机会信令（在非平稳信道中），评估丢失数据对可靠压缩和传输的基本Shannon理论极限的影响具有重要的理论和实际意义，以及估计理论极限。此外，新的实际问题出现在如何最好地重新设计压缩，编码，调制和滤波方案，以获得性能接近基本极限的缺失观测的存在。该项目解决了一些具体的挑战性和技术相关的研究问题，涉及各种模型与缺失观测：当擦除位置在压缩器处已知/未知时，丢失数据的无损和有损压缩;遭受擦除的噪声信道的容量，特别是输出擦除对具有存储器的信道的容量的影响;最小均方误差估计和预测与丢失的意见;喷泉码同时广播到几个接收机有很大的不同丢失信息率;多用户信息理论的网络受到擦除，包括基本范例，如多址信道和广播信道;具有集中处理和不可靠有线链路的蜂窝网络（“光纤无线电”受链路中断影响）;收发机技术的鲁棒化，例如正交频分复用、反馈方案和脏纸编码，这些技术对擦除非常敏感;重新审视压缩感知的基本限制（这可以解释为一个满秩随机投影的串联，然后是投影系数的随机擦除）。本项目旨在促进对与当前技术相关的通信和信号处理系统的发现和理解，在几个研究社区的十字路口，并提供了一个肥沃的土壤，培养研究生的学科信息论，编码理论，估计，信号处理，随机矩阵理论和网络。

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.