The likelihood encoder with applications to lossy compression and secrecy

A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on a soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma recovers the point-to-point rate-distortion function, the rate-distortion function with side information at the decoder, and several other important inner bounds for multi-user lossy compression. The likelihood encoder also provides a way for analyzing rate-distortion based secrecy systems. Coupled with hybrid coding, new achievability results are obtained for a joint source-channel secrecy model that outperform an operationally separate source-channel coding scheme.