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Although random access operations are desirable for on-demand video streaming in peer-to-peer systems, they are difficult to efficiently achieve due to the asynchronous interactive behaviors of users and the dynamic nature of peers. In this paper, we propose a network coding equivalent content distribution (NCECD) scheme to efficiently handle interactive video-on-demand (VoD) operations in peer-to-peer systems. In NCECD, videos are divided into segments that are then further divided into blocks. These blocks are encoded into independent blocks that are distributed to different peers for local storage. With NCECD, a new client only needs to connect to a sufficient number of parent peers to be able to view the whole video and rarely needs to find new parents when performing random access operations. In most existing methods, a new client must search for parent peers containing specific segments; however, NCECD uses the properties of network coding to cache equivalent content in peers, so that one can pick any parent without additional searches. Experimental results show that the proposed scheme achieves low startup and jump searching delays and requires fewer server resources. In addition, we present the analysis of system parameters to achieve reasonable block loss rates for the proposed scheme.