稀疏网络编码中秩分布分析模型研究

针对现有稀疏网络编码研究中线性相关概率性能指标精准度较低的问题，提出基于马尔可夫链的性能分析模型。对线性相关概率、秩的概率分布等性能指标及其复杂度进行分析，并通过该性能分析模型分析编码包传输后期的译码成功概率;基于吸收马尔可夫链计算编码包传输过程中的瞬态、吸收态以及各状态间的状态转移概率，并对状态转移概率中蒙特卡罗模拟误差较大的问题进行改进，由状态转移概率构建吸收马尔可夫链基本矩阵，得出信宿端收到非再生包的线性相关概率，进而推导出秩的概率分布和译码成功概率性能指标。仿真结果表明，在相同条件下所提模型性能指标精确度均优于对比模型，且能精确地评估信宿端解码矩阵秩的概率分布、译码成功概率等稀疏网络编码的译码行为。

Research on rank distribution analysis model in sparse network coding

To address the low accuracy of linear correlation probability performance indicators in current sparse network coding research, we propose a performance analysis model based on Markov chain. The performance indicators such as linear correlation probability and rank probability distribution and their complexity are analyzed, and the decoding success probability in the later stage of encoding packet transmission is analyzed through this performance analysis model. The model is based on absorbing Markov chain to compute the transient state, absorbing state and state transition probabilities during encoding packet transmission. Monte Carlo simulation errors in state transition probabilities are improved. Further, the basic matrix of absorbing Markov chain is constructed from state transition probabilities, and the linear correlation probability of non-innovative packets at receiver is obtained. The rank probability distribution and the decoding probability are deduced. Simulation results indicate that the performance metrics of this model are more accurate than those of other research models under the same conditions, and the decoding behavior of sparse network coding, such as the probability of rank distribution of the decoded matrix and the probability of decoding success, can be evaluated accurately.