Abstract
We derive the optimal second-order coding region for the lossy Gray-Wyner source coding problem for discrete memoryless sources under mild conditions. To do so, we leverage the properties of an appropriate generalization of the conditional distortion-tilted information density, which was first introduced by Kostina and Verdu (2012). The converse part uses the perturbation argument by Gu and Effros (2009) in their strong converse proof of the discrete Gray-Wyner problem. The achievability part uses a generalization of type covering lemmas and the uniform continuity of the conditional rate-distortion function in both the source joint distribution and the distortion level.
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