Second-order coding region for the discrete successive refinement source coding problem

We derive the optimal second-order coding region for the discrete successive refinement source coding problem under the joint excess-distortion event. To do so, we define a generalization of the tilted information density and leverage its properties. In the achievability part, we make use of type covering lemmas by Kanlis and Narayan (1996) and by No, Ingber and Weissman (2015). In the converse proof, we make use of the perturbation approach by Gu and Effros (2009). We also specialize our results to successively refinable sources and provide an alternative converse proof for such sources by generalizing Kostina and Verdú's (2012) one-shot converse bound for point-to-point lossy source coding.

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