摘要翻译：
我们得到了一类离散无记忆中继信道容量的一个新的上界。对于这类中继信道，中继观察到一个I.I.D。序列$t$，它独立于通道输入$x$。对于所有$(x,t,y)\in\mathcal{x}\times\mathcal{t}\times\mathcal{y}$,信道由一组概率转移函数$p(yx,t)$描述。此外，从中继到接收机存在有限容量$R_{0}$的无噪声链路。虽然这些信道的容量一般是未知的，但在文献[1]中得到了这些信道的一个子类的容量，即对于某些确定性函数$G$，当$t=G(X,Y)$时，它等于割集界。另一个获得容量的实例是在[2]中，其中通道输出$Y$可以写成$Y=X\oPlus z$，其中$\oPlus表示模-$m$加法，$z$独立于$X$，$\mathcal{X}=\mathcal{Y}=m$，$t$是$z$的某个随机函数。压缩转发(CAF)可实现性方案[3]在这两种情况下都被证明是可实现的。利用我们的上限，我们恢复了[1]和[2]的容量结果。我们还得到了一类信道的容量，它不属于文[1]和文[2]中所研究的任何一类。对于这类信道，CAF方案被证明是最优的，但容量严格小于某些值$R_{0}$的割集界。对于具有二进制乘性状态和二进制加性噪声的特定中继信道，我们还计算了我们的外界，对于该信道，我们给出了$y=tx+n$。我们证明，对于某些值$r_{0}$，我们的上界严格地优于割集上界，但它严格地高于CAF可实现性方案产生的速率。
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英文标题：
《A New Upper Bound on the Capacity of a Class of Primitive Relay Channels》
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作者：
Ravi Tandon, Sennur Ulukus
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最新提交年份：
2008
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
  We obtain a new upper bound on the capacity of a class of discrete memoryless relay channels. For this class of relay channels, the relay observes an i.i.d. sequence $T$, which is independent of the channel input $X$. The channel is described by a set of probability transition functions $p(y|x,t)$ for all $(x,t,y)\in \mathcal{X}\times \mathcal{T}\times \mathcal{Y}$. Furthermore, a noiseless link of finite capacity $R_{0}$ exists from the relay to the receiver. Although the capacity for these channels is not known in general, the capacity of a subclass of these channels, namely when $T=g(X,Y)$, for some deterministic function $g$, was obtained in [1] and it was shown to be equal to the cut-set bound. Another instance where the capacity was obtained was in [2], where the channel output $Y$ can be written as $Y=X\oplus Z$, where $\oplus$ denotes modulo-$m$ addition, $Z$ is independent of $X$, $|\mathcal{X}|=|\mathcal{Y}|=m$, and $T$ is some stochastic function of $Z$. The compress-and-forward (CAF) achievability scheme [3] was shown to be capacity achieving in both cases.   Using our upper bound we recover the capacity results of [1] and [2]. We also obtain the capacity of a class of channels which does not fall into either of the classes studied in [1] and [2]. For this class of channels, CAF scheme is shown to be optimal but capacity is strictly less than the cut-set bound for certain values of $R_{0}$. We also evaluate our outer bound for a particular relay channel with binary multiplicative states and binary additive noise for which the channel is given as $Y=TX+N$. We show that our upper bound is strictly better than the cut-set upper bound for certain values of $R_{0}$ but it lies strictly above the rates yielded by the CAF achievability scheme.
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PDF链接：
https://arxiv.org/pdf/0810.0747