中文摘要：

本文分析了基于随机线性网络编码（random linear network coding,RLNC）的无线广播系统的性能。该系统的一个源节点需要将N个信息包广播给以其为圆心的多个均匀分布用户。通过利用随机几何分析我们推导了该系统中的近似平均传输次数和平均成功译码用户百分比。仿真结果表明,理论近似推导和实际仿真结果十分接近以及RLNC方案相比LT码（Luby Transform codes）方案有很大的性能提升。同时,一个用户接收到N个RLNC编码包即可以极高概率恢复出源信息包。

英文摘要：

In this paper,we analyze the performances of the random linear network coding（ RLNC） based wireless broadcasting system,where a source wants to broadcast N packets to a large number of users with uniform distribution. By resorting to stochastic geometry analysis,we deduce the approximate average number of transmissions and the average percent of successful decoding users in the RLNC based wireless broadcasting system. Simulation results are given to demonstrate the accuracy of our theoretical analyses and the performance improvement of using RLNC scheme when compared with LT codes（ Luby Transform codes）. Meanwhile,we show that a user can recover all the original packets with high probability by receiving N out of all the transmitted RLNC combined packets.