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The problem of correlated information multicasting is considered in this paper, i.e., from multiple sources to multiple destinations through a network. It can be solved by jointly optimizing the distributed source coding and network coding. Previous research found that optimal performance can be achieved with unlimited decoding complexity, which cannot be applied in practical implementations. Some practical methods were also presented, which shows sub-optimal performance. To improve the coding performance and keep the low complexity of the algorithm, an adaptive coding and transmission scheme according to the conditional entropy of the sources is proposed. It has been demonstrated that the proposed scheme can achieve better performance compared with the existing ones.