论文标题
安全的集体广播：外部结构和线性可行性
Secure Groupcast: Extra-Entropic Structure and Linear Feasibility
论文作者
论文摘要
在安全的集体广播问题中，发射器希望通过与最小带宽的广播，将最大汇率的最大汇率分组为最大$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。提供了示例以证明具有相同熵结构的安全组播放的不同实例，即关键变量的所有子集的相同熵，可以具有不同的最大组播放速率和不同的最小广播带宽。因此，对安全组播放的全面结构至关重要。接下来，当关键变量是一组独立关键符号的基础线性组合时，探索最大集体速率，即，键位于通用子空间中。当每个密钥子空间的尺寸较小或大，即极端机制时，最大的组播种速率是特征的。对于中间状态，各种干扰一致性方案源自无线干扰网络，例如基于特征向量的和渐近方案，被证明是有用的。
In the secure groupcast problem, a transmitter wants to securely groupcast a message with the maximum rate to the first $N$ of $K$ receivers by broadcasting with the minimum bandwidth, where the $K$ receivers are each equipped with a key variable from a known joint distribution. Examples are provided to prove that different instances of secure groupcast that have the same entropic structure, i.e., the same entropy for all subsets of the key variables, can have different maximum groupcast rates and different minimum broadcast bandwidth. Thus, extra-entropic structure matters for secure groupcast. Next, the maximum groupcast rate is explored when the key variables are generic linear combinations of a basis set of independent key symbols, i.e., the keys lie in generic subspaces. The maximum groupcast rate is characterized when the dimension of each key subspace is either small or large, i.e., the extreme regimes. For the intermediate regime, various interference alignment schemes originated from wireless interference networks, such as eigenvector based and asymptotic schemes, are shown to be useful.
