This paper considers the application of network coding to reduce the number of retransmission by combining the lost packets from different receivers with network coding in a wireless broadcast network. In particular, the study propses an algebraic expression to define the coding conditions of retransmission packets by matrix and vector operations. According to the graph constructed by correlation matrix, an algorithm is presented to find more coding opportunity based on maximum matches in graph theory. The proposed algorithm has the ability to find the maximum pairwise coding opportunities, meanwhile, it takes into account the probability of coding the lost packets as possible to more than one retransmission packet to minimize the number of retransmissions by coding optimization, and increase the network bandwidth efficiency and throughput.%针对成批数据在无线广播过程中发生丢包后的重传策略,利用网络编码技术,研究尽可能多地减少重传次数的方法.首先通过矩阵及向量的运算给出了待重传数据满足编码条件的代数表达形式,再根据关联矩阵构造相应的图,最后通过图论中的最佳匹配理论给出了一种寻找编码机会的优化算法.此算法中不但能够找出最多的两两编码机会,而且还考虑了将尽可能多的数据包编在一起的可能性,从而尽可能地减少了重传次数,实现了编码的优化,有效提高了网络带宽效率和吞吐量.
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