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In this paper, a proper solution for a capacity-limited lossy wireless sensor network subject to packet loss as a problem has been presented by considering multiple sinks and correlated sources. At first, a joint optimization problem with two objectives, rate allocation and transmission structure, is introduced and solved. Also in the lossy network, a method to allocate the rates to the correlated source nodes is proposed. At the end, the sensitivity of the proposed algorithm to several parameters of the network and the algorithm and the network performance is investigated.