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Capacity Theorems for Broadcast Channels With Two Channel State Components Known at the Receivers

机译：接收器已知两个信道状态分量的广播信道的容量定理

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摘要

We establish the capacity region of several classes of broadcast channels with random state in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. When the channel components are deterministic, we show that the capacity region is achieved via Marton coding. This channel model does not belong to any class of broadcast channels for which the capacity region was previously known and is useful in studying wireless communication channels when the fading state is known only at the receivers. We then establish the capacity region when the channel components are ordered, e.g., degraded. In particular, we show that the capacity region for the broadcast channel with degraded Gaussian vector channel components is attained via Gaussian input distribution. Finally, we extend the results on ordered channels to two broadcast channel examples with more than two channel components, but show that these extensions do not hold in general.
机译：我们建立具有随机状态的几类广播信道的容量区域，其中从两个可能的信道状态分量中选择到每个用户的信道，并且仅在接收器处知道该状态。当通道分量是确定性的时，我们表明容量区域是通过Marton编码实现的。该信道模型不属于先前已知容量区域的任何广播信道类别，当仅在接收器处知道衰落状态时，可用于研究无线通信信道。然后，当订购信道组件（例如降级）时，我们建立容量区域。特别是，我们表明，通过高斯输入分布可以获得具有降低的高斯矢量信道分量的广播信道的容量区域。最后，我们将有序频道上的结果扩展到具有两个以上频道成分的两个广播频道示例，但表明这些扩展通常不成立。

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