Error exponents for source coding under logarithmic loss

In source coding under the logarithmic loss distortion measure, a source is compressed into a message, which is then decompressed into a soft reconstruction (i.e. probability distribution). The distortion is measured by the remaining uncertainty about the source given the message. Shkel and Verdú showed that this lossy source coding setting is intimately related to almost lossless source coding with list decoding, and used this insight to characterize the single-shot excess distortion error probability. In this work, we build upon this connection to list decoding and derive error exponents for source coding under logarithmic loss, without and with side information. The error exponents are closely related to their almost lossless counterparts.