On the Gap Between Scalar and Vector Solutions of Generalized Combination Networks
On the Gap Between Scalar and Vector Solutions of Generalized Combination Networks
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DOI：
10.1109/tit.2021.3065364
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发表时间：
2021-08
影响因子：
2.5
通讯作者：
Hedongliang Liu;Hengjia Wei;S. Puchinger;A. Wachter-Zeh;Moshe Schwartz
中科院分区：
文献类型：
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作者：
Hedongliang Liu;Hengjia Wei;S. Puchinger;A. Wachter-Zeh;Moshe Schwartz
我们研究广义组合网络的标量线性和向量线性解。我们根据网络参数和字母表大小得出中间层最大节点数的新上限和下限。这些界限改进并扩展了已知界限的参数范围。使用这些新界限，我们提出了最佳标量线性和最佳向量线性网络编码解决方案之间字母表大小差距的下界和上限。对于固定的网络结构，当改变中间层节点的数量 $r$ 时，上下界的渐近行为表明差距在 $\Theta (\log (r))$ 中。
We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower bound and an upper bound on the gap in the alphabet size between optimal scalar-linear and optimal vector-linear network coding solutions. For a fixed network structure, while varying the number of middle-layer nodes $r$ , the asymptotic behavior of the upper and lower bounds shows that the gap is in $\Theta (\log (r))$ .