中文摘要：

网络编码技术为无线报文重传问题研究提供了新思路．分析并证明了完全无线报文重传问题最优策略所需重传报文数量等于节点请求报文数量的最大值；基于随机网络编码技术提出了最优重传策略RNCOPT（Random Network Coding based OPTimal Scheme），其编码系数从某选定有限域中随机选取（0除外）；利用网络编码矩阵重新生成机制以保证100％解码成功率；描述了RNCOPT组合报文结构及发送节点操作过程．仿真表明：当接收节点数量为30而报文总数为30时，RNCOPT相对于传统非网络编码方案节省重传报文数量可达32％，而此时现有某典型策略CliqueNC却无明显效果．

英文摘要：

Network coding （NC） provides a new approach to solve wireless packet retransmission problems （WPRTPs）. The property that the number of retransmitted packets of optimal NC-based schemes for a perfect WPRTP （P-WPRTP） equals to the maximum number of requested packets of a receiver was proposed and proved. Based on random network coding （RNC） technology, an optimal scheme for P-WPRTPs named as random network coding based optimal scheme（RNCOPT） was proposed where coefficients in network coding matrix are randomly selected from a pre-determined Galois field except for its element zero. Network coding matrix re-creation mechanism was used to guarantee a 100% success probability of decoding. Format of assem- bled packets and operation process of senders in RNCOPT were described. Simulation results show that, when receiver number and packet number are both 30, number of retransmitted packets in RNCOPT reduces about 32% when compared with traditional scheme where NC is not used, but meanwhile a typical NC-based scheme CliqueNC shows little performance gain.