论文标题
钻石消息集组播放：从DM广播频道的内部界限到组合网络的容量区域
Diamond Message Set Groupcasting: From an Inner Bound for the DM Broadcast Channel to the Capacity Region of the Combination Network
论文作者
论文摘要
研究了广播频道（BC）上的多个集体广播。特别是，对于$ k $ -Receiver离散的无内存（DM）BC的钻石消息集获得了内部界限，该钻石消息集由四个集体播放消息组成：所有接收器都需要一个，一个除两个接收器外，另一个是两个接收器，除了所有两个接收器外，所有收到的所有接收器都需要另外两个接收器。内部结合基于速率分解和叠加编码，在本文中以显式形式给出，作为四维多型的编码分布的结合。当专门针对所谓的组合网络时，该网络是一类三层（两人）广播网络，由$ 2^k-1 $参数的参数列出了有限的和无保证的能力，从第一层的源节点到第二层的源节点到第二层的节点，我们的第二层节点，我们的自上而下的方法，从DM BC识别一个单一的分发，将一个单一的分配量化为单一的分配。这种内部结合由不等式组成，然后被确定为在Salimi等人最近获得的广播网络最近获得的（实际上是无限的）广义切割式外边界（实际上是无限的）广义外部边界的类别中。因此，我们建立了用于钻石消息集的一般$ k $用户组合网络的容量区域，并以明确的形式进行。这样的结果意味着我们内部对DM BC的一定强度，因为它（a）专门针对组合网络时会产生迄今为止未知的能力区域，并且（b）可能捕获$ K $ -RECEIVER DM BC本身的容量区域的许多组合方面（用于钻石消息集）。此外，我们通过向其添加包裹并以明确的形式将内部绑定作为一个联合来扩展到内部界限，以此作为一个在消息速率中的四维多型的编码分布的结合。
Multiple groupcasting over the broadcast channel (BC) is studied. In particular, an inner bound is obtained for the $K$-receiver discrete memoryless (DM) BC for the diamond message set which consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional polytopes. When specialized to the so-called combination network, which is a class of three-layer (two-hop) broadcast networks parameterized by $2^K-1$ finite-and-arbitrary-capacity noiseless links from the source node in the first layer to as many nodes of the second layer, our top-down approach from the DM BC to the combination network yields an explicit inner bound as a single polytope via the identification of a single coding distribution. This inner bound consists of inequalities which are then identified to be within the class of a plethora of (indeed, infinitely many) generalized cut-set outer bounds recently obtained by Salimi et al for broadcast networks. We hence establish the capacity region of the general $K$-user combination network for the diamond message set, and do so in explicit form. Such a result implies a certain strength of our inner bound for the DM BC in that it (a) produces a hitherto unknown capacity region when specialized to the combination network and (b) may capture many combinatorial aspects of the capacity region of the $K$-receiver DM BC itself (for the diamond message set). Moreover, we further extend that inner bound by adding binning to it and providing that inner bound also in explicit form as a union over coding distributions of four-dimensional polytopes in the message rates.
