安全组播：超熵结构与线性可行性
Secure Groupcast: Extra-Entropic Structure and Linear Feasibility
摘要：
在安全组播问题中，发射机希望通过以最小带宽广播来以最大速率向$K$接收机中的第一个$N$安全地组播消息，其中每个$K$接收机配备有来自已知联合分发的密钥变量。通过实例证明了具有相同熵结构的不同安全组播实例，对于密钥变量的所有子集的相同熵可以具有不同的最大组播速率和不同的最小广播带宽。因此，超熵结构对于安全组播很重要。接下来，当关键变量是独立关键符号的基本集合的一般线性组合时，即，密钥位于通用子空间中。当每个密钥子空间的维数或小或大时，即，极端的政权。对于中间制度，各种干扰对齐计划起源于无线干扰网络，如基于特征向量和渐近计划，被证明是有用的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
