Network embedding operations preserving the insufficiency of linear network codes
Network embedding operations preserving the insufficiency of linear network codes
复制标题
网络嵌入操作保留了线性网络代码的不足
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. Walsh
中科院分区：
文献类型：
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作者：
Congduan Li;S. Weber;J. Walsh
提出了将较小网络扩展/嵌入到较大网络中的操作，该操作保留了线性网络码类的不足。有限域上的线性网络码对网络是充分的当且仅当对于网络码率区域中的每一点，都存在一个有限域上的码来实现它.定义了三种运算，并证明了它们分别对标量线性网络码和向量线性网络码都具有所需的继承性.多级分集编码系统（MDCS），具有特殊结构的多源多汇网络的更广泛的家庭的一个子类的速率区域的实验结果，演示。这些结果表明，这些嵌入操作的概念，使人们能够调查的存在少量的禁止网络子充分的线性网络代码在一个给定的字段。
Operations for extending/embedding a smaller network into a larger network that preserve the insufficiency of classes of linear network codes are presented. Linear network codes over some finite field are said to be sufficient for a network if and only if for every point in the network coding rate region, there exists a code over that finite field to achieve it. Three operations are defined, and it is proven that they have the desired inheritance property, both for scalar linear network codes and for vector linear network codes, separately. Experimental results on the rate regions of multilevel diversity coding systems (MDCS), a sub-class of the broader family of multi-source multi-sink networks with special structure, are presented for demonstration. These results demonstrate that these notions of embedding operations enable one to investigate the existences of small numbers of forbidden network minors for sufficiency of linear network codes over a given field.