稀疏网络编码译码概率的马尔可夫链模型
A Markov Chain Model for the Decoding Probability of Sparse Network Coding
摘要：
随机线性网络编码（RLNC）已被证明提供了一种有效的通信方案，利用一个有趣的鲁棒性对数据包丢失。然而，它具有较高的计算复杂性，最近提出了一些遵循相同思想的新方法。这种解决方案之一是可调稀疏网络编码（TSNC），其中在每次传输中仅组合很少的分组。要在每次传输中组合的数据分组的量可以根据密度参数/分布来设置，其最终可以被适配。在这项工作中，我们提出了一个分析模型，捕捉SNC的性能上一个准确的方式。我们利用一个吸收马尔可夫过程，其中的状态定义的解码器，即解码矩阵秩，在这样的矩阵的非零列的数量接收到的有用的数据包的数量。该模型是通过一个全面的仿真活动进行验证，模型和仿真之间的差异可以忽略不计。最差情况下均方误差小于$4 \cdot 10^{-4}$。我们还包括在比较中的一些更一般的界限，最近使用的，表明他们的准确性是相当差的。所提出的模型将能够更精确地评估稀疏网络编码技术的行为。最后的结果表明，所提出的分析模型可以利用TSNC技术，以选择由编码器的最佳密度作为传输的演变。
英文摘要：
Random Linear Network Coding (RLNC) has been proved to offer an efficient communication scheme, leveraging an interesting robustness against packet losses. However, it suffers from a high computational complexity and some novel approaches, which follow the same idea, have been recently proposed. One of such solutions is Tunable Sparse Network Coding (TSNC), where only few packets are combined in each transmissions. The amount of data packets to be combined in each transmissions can be set from a density parameter/distribution, which could be eventually adapted. In this work we present an analytical model that captures the performance of SNC on an accurate way. We exploit an absorbing Markov process where the states are defined by the number of useful packets received by the decoder, i.e the decoding matrix rank, and the number of non-zero columns at such matrix. The model is validated by means of a thorough simulation campaign, and the difference between model and simulation is negligible. A mean square error less than $4 \cdot 10^{-4}$ in the worst cases. We also include in the comparison some of more general bounds that have been recently used, showing that their accuracy is rather poor. The proposed model would enable a more precise assessment of the behavior of sparse network coding techniques. The last results show that the proposed analytical model can be exploited by the TSNC techniques in order to select by the encoder the best density as the transmission evolves.
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