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This paper extends rate-distortion optimized streaming techniques to operate on a general class of coding formats that explicitly support redundancy in their coding structure. Examples include multiple description layered coding (MDLC) and multiple independently encoded versions of a video source. Such source codecs usually produce multiple decoding paths, while previous work on video streaming has mostly focused on those encoding techniques that only generate a single decoding path. A new source model called directed acyclic hypergraph is introduced to describe the dependency and redundancy relationship between different video data units with multiple decoding paths. Based on this model, we then propose two rate-distortion based packet scheduling algorithms, i.e., Lagrangian optimization and a greedy algorithm, to dynamically adjust the system's real-time redundancy to match the channel behavior. The proposed streaming system introduces two types of redundancies, namely, source redundancy and transport redundancy. This paper presents a detailed performance analysis of the individual benefits for error robustness provided by these redundancies and their interplay. Experimental results show that our proposed system with both redundancies achieves the best end-to-end performance on real-time video communication over a wide range of network scenarios.