Principal Investigators: Giuseppe Caire and Sergio Verd'u University of Southern California Princeton University Summary This 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 the missing 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 redesign compression, 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.
