Lossy compression plays a key role in our information economy. By far, most of the information that we generate as a society represents pictures, sounds, and videos, and for this kind of data, lossy compression yields a tremendous reduction in transmission and storage requirements. The aim of this project is to understand the fundamental limits of lossy compression,especially in the context of networks, which dominate today's communication infrastructure. Previous work on this problem has not led to a fundamental understanding of lossy network compression nor has it had a significant impact on the design of practical systems.
This research overcomes the limitations of prior work using two novel approaches. First, the highly general models of the past are eschewed in favor of canonical, concrete problems that are simultaneously more tractable and more relevant to applications. Building on recent results of the PI, the work develops a comprehensive and conclusive understanding of the fundamental limits of lossy network compression for Gaussian sources under quadratic distortion constraints and discrete sources under erasure distortion constraints. Second, these fundamental limits are studied under more realistic scenarios in which the source, the network, and the allowable distortion all change in unpredictable ways. To help students learn how to create probabilistic and information-theoretic models that are tractable yet also applicable to real systems, existing courses at both the graduate and undergraduate level are being remade to include greater emphasis on modeling. The project also includes significant outreach, involving an interactive tutorial on compression delivered to women and underrepresented-minority engineering undergraduates and rural high-school students.
While much of electrical engineering focuses on how to move around ever-larger amounts of data, this project took an alternative view: how can we reduce the amount of data that we need to move around to achieve our goals? This project focused in particular on lossy data compression. Lossy data compression is the process of reducing the bit-rate of a data source while maintaining an acceptable fidelity to the original. A well-known example of lossy data compression is reducing the size of audio files using the mp3 format, which allows more songs to fit on a handheld device such as an ipod. The project considered how well data can be compressed when it consists of multiple channels that must be compressed separately (such as if the left and right channels in an audio file must be compressed separately). This problem arises as a subproblem in several areas of electrical engineering including how to design wireless relay systems and how to efficiently disseminate a file over a peer-to-peer network. The project determined the ultimate limit of compression for this configuration, i.e., what is the minimum bit rate needed to maintain an acceptable fidelity to the original. This problem had confounded researchers for several decades. During the project, the course developed a new graduate course on the data compression that combined results on the mathematical limits of compression with practical projects designed to teach students how to achieve those limits. Students who pass the class are well-equipped to help society contend with the deluge of data that it is experiencing.
