Improving on the Cut-Set Bound via a Geometric Analysis of Typical Sets
Improving on the Cut-Set Bound via a Geometric Analysis of Typical Sets
复制标题
通过典型集的几何分析改进割集界
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Ayfer Özgür
中科院分区：
文献类型：
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作者：
Xiugang Wu;Ayfer Özgür
-我们考虑离散无记忆对称基元中继信道，其中，源X想要在中继器Z的帮助下向目的地Y发送信息，并且中继器可以通过速率为R0的无差错数字链路与目的地通信，而Y和Z在给定X的情况下是条件独立且同分布的。我们开发了该通道容量的两个上限，这两个上限比现有的上限更紧，包括著名的割集上限。我们的方法明显不同于用于证明多用户信道容量上限的标准信息论方法fi。我们建立在Blow-up引理的基础上，分析了典型的n字母随机变量集之间的概率几何关系，这些随机变量集与用于在该信道上进行通信的可靠代码相关联。这些关系转化为所涉及的n字母随机变量之间的新的熵不等。
—We consider the discrete memoryless symmetric primitive relay channel, where, a source X wants to send information to a destination Y with the help of a relay Z and the relay can communicate to the destination via an error-free digital link of rate R 0 , while Y and Z are conditionally independent and identically distributed given X . We develop two upper bounds on the capacity of this channel that are tighter than existing bounds, including the celebrated cut-set bound. Our approach significantly differs from the standard information-theoretic approach for proving upper bounds on the capacity of multi-user channels. We build on the blowing-up lemma to analyze the probabilistic geometric relations between the typical sets of the n -letter random variables associated with a reliable code for communicating over this channel. These relations translate to new entropy inequalities between the n - letter random variables involved.