A Single-Shot Approach to Lossy Source Coding Under Logarithmic Loss

This paper considers 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 crisply the connection between lossless source coding with list decoding and lossy source coding with log-loss. Fixed-length and variable-length bounds are presented. Fixed-length bounds include the single-shot fundamental limit for average as well as excess distortion. Variable-length bounds include the single-shot fundamental limit for average as well as excess length. Two multi-terminal problems are addressed: coding with side information (Wyner-Ziv) and multiple descriptions coding. In both the cases, the application of the Shannon-McMillan theorem to the single-shot bounds yields the rate-distortion function and the rate distortion-region for stationary ergodic sources.