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This paper studies Byzantine reliable broadcast (BRB) under asynchronous networks, and improves the state-of-the-art protocols from the following aspects. Near-optimal communication cost: We propose two new BRB protocols for n nodes and input message M that has communication cost O(n|M| +n^2 log n), which is near-optimal due to the lower bound of Ω(n|M| +n^2). The first BRB protocol assumes threshold signature but is easy to understand, while the second BRB protocol is error-free but less intuitive. Improved computation: We propose a new construction that improves the computation cost of the state-of-the-art BRB by avoiding the expensive online error correction on the input message, while achieving the same communication cost. Balanced communication: We propose a technique named balanced multicast that can balance the communication cost for BRB protocols where the broadcaster needs to multicast the message M while other nodes only needs to multicast coded fragments of size O(|M|/n + log n). The balanced multicast technique can be applied to many existing BRB protocols as well as all our new constructions in this paper, and can make every node incur about the same communication cost. Finally, we present a lower bound to show the near optimality of our protocol in termsmore »of communication cost at each node.« less