On group network codes: Ingleton-bound violations and independent sources
On group network codes: Ingleton-bound violations and independent sources
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关于团体网络代码：Ingleton 约束违规和独立来源
DOI：
10.1109/isit.2010.5513749
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
B. Hassibi
中科院分区：
文献类型：
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作者：
W. Mao;Matthew Thill;B. Hassibi
从原理上讲，从非阿贝尔群导出的网络码可以用来获得有线无环网络容量区域中的每一点。然而，从一个特定的组，它的子组，是有用的，只有当它可以模拟独立的源，以及违反英格尔顿限制的能力范围内可获得的线性网络码。研究了素数ρ ≥ 5的群PGL（2，ρ）和GL（2，ρ）的子群的独立源和Ingleton-违背要求.对于这两个群，我们证明了可以满足要求，这表明PGL（2，ρ）和GL（2，ρ）是足够丰富的群，可以构造优于线性网络码的上级网络码。我们还构建了一个模型，独立的来源，使用上述群体的直接产品。
In principle, network codes derived from non-Abelian groups can be used to attain every point in the capacity region of wired acyclic networks. However, group codes derived from a particular group, and its subgroups, is useful only if it can model independent sources, as well as violate the Ingleton bound which restricts the capacity region obtainable by linear network codes. We study both the independent source and the Ingleton-violating requirement for subgroups of the groups PGL(2, ρ) and GL(2, ρ) with primes ρ ≥ 5. For both these groups we demonstrate that the requirements can be met, which suggests that PGL(2, ρ) and GL(2, ρ) are rich enough groups to construct network codes superior to linear ones. We also construct a model for independent sources using the direct product of the aforementioned groups.