非线性网络编码实例研究

Nonlinear Network Coding:A Case Study

在网络编码研究中,线性编码技术已趋于成熟,但它有着需要大字符表且不适用于非多播网络的弱点,这推动了对非线性编码的研究。本文给出编码函数的新描述,在此基础上将非线性编码分成两类:证明了前者与线性编码等价,能从线性编码中构造出,且具有相同的编码能力;证明了后者的存在性。

In the area of network coding,linear code can achieve the maximum capacity of multicast networks by large alphabets. However, it is insufficient for non-multicast networks. Meanwhile nonlinear code is of interest for its possibility to achieve the network coding capacity by small alphabet,or its possibility to deal with other networks. There is no schema of nonlinear code in our literature. In this paper, a novel characterization of nonlinear code is proposed. We reveal that a kind of nonlinear code can be induced from linear code,and it has the same coding ability as linear code. We also show the existence of another kind of polynomial code.