On the Multiple Description Coding Problem with One Semi-Deterministic Distortion Measure

In this paper, we revisit the multiple description coding problem with one semi-deterministic distortion measure, which we term as the Fu- Yeung problem (Fu and Yeung, 2002). We present the properties of optimal test channels for the minimum sum-rate function, a non- asymptotic converse bound and second-order asymptotics for discrete memoryless sources. Since the successive refinement problem is a special case of the Fu-Yeung problem, as a by-product, we obtain a non-asymptotic converse bound for the successive refinement problem, which turns out to be a strict generalization of the non-asymptotic converse bound for successively refinable sources (Zhou, Tan and Motani, 2017).