A New Approach to Lossy Compression and Applications to Security

Abstract

In this thesis, rate-distortion theory is studied in the context of lossy compression communication systems with and without security concerns. A new source coding proof technique using the ``likelihood encoder" is proposed that achieves the best known compression rate in various lossy compression settings. It is demonstrated that the use of the likelihood encoder together with Wyner's soft-covering lemma yields simple achievability proofs for classical source coding problems. We use the likelihood encoder technique to show the achievability parts of the point-to-point rate-distortion function, the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the Berger-Tung problem). Furthermore, a non-asymptotic analysis is used for the point-to-point case to examine the upper bound on the excess distortion provided by this method. The likelihood encoder is also compared, both in concept and performance, to a recent alternative random-binning based technique.

Also, the likelihood-encoder source coding technique is further used to obtain new results in rate-distortion based secrecy systems. Several secure source coding settings, such as using shared secret key and correlated side information, are investigated. It is shown that the rate-distortion based formulation for secrecy fully generalizes the traditional equivocation-based secrecy formulation. The extension to joint source-channel security is also considered using similar encoding techniques. The rate-distortion based secure source-channel analysis is applied to optical communication for reliable and secure delivery of an information source through a multimode fiber channel subject to eavesdropping.