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Latent Capacity Region: A Case Study on Symmetric Broadcast With Common Messages

机译:潜在容量区域:带有公共消息的对称广播的案例研究

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摘要

We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{cal A}$, i.e., the rate of the message intended for all the receivers in the set ${cal A}$, is the same for all the set ${cal A}$ of the same cardinality. Instead of attempting to characterize the capacity region of general broadcast channels, we only consider the structure of the capacity region that any broadcast channel should bear. The concept of latent capacity region is useful in capturing these underlying constraints, and we provide a complete characterization of the latent capacity region for the symmetric broadcast problem. The converse proof of this tight characterization relies on a deterministic broadcast channel model. The achievability proof generalizes the familiar rate transfer argument to include more involved erasure correction coding among messages, thus revealing an inherent connection between broadcast with common message and erasure correction codes.
机译:我们考虑了用公共消息广播的问题,并着眼于公共消息速率$ R_ {cal A} $,即打算发送给集合$ {cal A} $中的所有接收者的消息速率的情况,对于相同基数的所有集合$ {cal A} $都相同。与其试图表征一般广播频道的容量区域,不如考虑任何广播频道应承受的容量区域的结构。潜在容量区域的概念对于捕获这些基本约束很有用,并且我们为对称广播问题提供了潜在容量区域的完整表征。这种严格表征的相反证明依赖于确定性广播信道模型。可实现性证明将熟悉的速率传递参数推广为在消息之间包括更多涉及的纠删编码,从而揭示了具有公共消息的广播和纠删码之间的固有联系。

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