论文标题
稀疏随机线性网络编码多播的解码成功概率
The Decoding Success Probability of Sparse Random Linear Network Coding for Multicast
论文作者
论文摘要
可靠和低延迟的多播通信对于将来的车辆通信很重要。广泛研究了用于确保多播通信可靠性的稀疏随机线性网络编码方法。这种交流的一个基本问题是表征解码的成功概率，这是由有限字段的稀疏随机矩阵（全等级）的概率给出的。但是，稀疏随机矩阵的概率的确切表达仍然未知，现有的近似值是递归或不一致的。在本文中，我们通过呈现简化的行梯形梯形矩阵的显式结构并使用乘积定理来提供稀疏随机矩阵的概率紧密而封闭形式的近似。仿真结果表明，无论发电大小，编码数据包的数量，场的大小和稀疏度如何，我们提出的近似值都具有很高的精度，并且比最新参数的最新近似值更紧密。
Reliable and low latency multicast communication is important for future vehicular communication. Sparse random linear network coding approach used to ensure the reliability of multicast communication has been widely investigated. A fundamental problem of such communication is to characterize the decoding success probability, which is given by the probability of a sparse random matrix over a finite field being full rank. However, the exact expression for the probability of a sparse random matrix being full rank is still unknown, and existing approximations are recursive or not consistently tight. In this paper, we provide a tight and closed-form approximation to the probability of a sparse random matrix being full rank, by presenting the explicit structure of the reduced row echelon form of a full rank matrix and using the product theorem. Simulation results show that our proposed approximation is of high accuracy regardless of the generation size, the number of coded packets, the field size and the sparsity, and tighter than the state-of-the-art approximations for a large range of parameters.
