We study the problem of maximizing the broadcast rate in peer-to-peer (P2P) systems under node degree bounds, i.e., the number of neighbors a node can simultaneously connect to is upper-bounded. The problem is critical for supporting highquality video streaming in P2P systems, and is challenging due to its combinatorial nature. In this paper, we address this problem by providing the first distributed solution that achieves nearoptimal broadcast rate under arbitrary node degree bounds, and over arbitrary overlay graph. It runs on individual nodes and utilizes only the measurement from their one-hop neighbors, making the solution easy to implement and adaptable to peer churn and network dynamics. Our solution consists of two distributed algorithms proposed in this paper that can be of independent interests: a network-coding based broadcasting algorithm that optimizes the broadcast rate given a topology, and a Markov-chain guided topology hopping algorithm that optimizes the topology. Our...