Tradeoffs between the excess-code-length exponent and the excess-distortion exponent in lossy source coding

Lossy compression of a discrete memoryless source (DMS) with respect to a single-letter distortion measure is considered. We study the best attainable tradeoff between the exponential rates of the probabilities that the codeword length and that the cumulative distortion exceed respective thresholds for two main cases. The first scenario examined is that where the source is corrupted by a discrete memoryless channel (DMC) prior to reaching the coder. In the second part of this work, we examine the universal setting, where the (noise-free) source is an unknown member P_θ of a given family {P _θ,θ∈Θ}. Here, inspired by an approach which was proven fruitful previously in the context of composite hypothesis testing, we allow the constraint on the excess-code-length exponent to be θ-dependent. Corollaries are derived for some special cases of interest, including Marton´s (1974) classical source coding exponent and its generalization to the case where the constraint on the rate of the code is relaxed from an almost sure constraint to a constraint on the excess-code-length exponent