A single-shot approach to lossy source coding under logarithmic loss

This paper studies the problem of lossy source coding with a specific distortion measure: logarithmic loss. The focus of this paper is on the single-shot approach which exposes the connection between lossy source coding with log-loss and lossless source coding. Point-to-point bounds, including the single-shot fundamental limit for average as well as excess distortion, are presented. Two multi-terminal problems are addressed: coding with side information (Wyner-Ziv), and multiple descriptions coding. In both cases, the application of the Shannon-McMillan Theorem to the single-shot bounds immediately yields the rate-distortion function and the rate distortion-region for stationary and ergodic sources.