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In this paper, we present the design of an unstructured peer-to-peer (P2P) streaming system employing Scalable Video Coding (SVC) and Network Coding (NC). The proposed design enables the customizations of video streams to support heterogeneous receivers, high churn rates, and quick adaptation to network and peers dynamics. Peers with various network conditions, displays and computational capabilities in this P2P streaming system can enjoy different video qualities during the same streaming period. In order to combine the two techniques SVC and NC, a novel packetization method and a new coding scheme is discussed in detail. The simulation results show that the proposed scheme yields a superior visual quality, smoother streaming rates, as well as robustness against high churn rates.