Outer Bounds for Multiple-Access Channels With Feedback Using Dependence Balance
Outer Bounds for Multiple-Access Channels With Feedback Using Dependence Balance
复制标题
使用依赖平衡的带有反馈的多路访问信道的外界
DOI：
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复制
发表时间：
2008
影响因子：
2.5
通讯作者：
S. Ulukus
中科院分区：
文献类型：
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作者：
R. Tandon;S. Ulukus
利用依赖平衡的思想，得到了具有无噪声反馈的离散无记忆多址信道（MAC-FB）容量区域的新外界。我们考虑一个反馈容量未知的二元加性噪声MAC-FB。本文所考虑的二元加性噪声MAC可以看作是高斯MAC- fb的离散对应物。Ozarow建立了双用户高斯MAC-FB的容量区域由切集界给出。我们的结果表明，对于Ozarow考虑的离散版本的通道，情况并非如此。直接评估我们的外部边界是棘手的，因为涉及一个辅助随机变量，其大基数禁止穷举搜索。我们通过使用复合函数及其性质来显式地计算外边界来克服这个困难。在反馈增加容量的容量区域的所有点上，我们的外界严格小于切集界。此外，我们明确地评估了二元加性噪声MAC-FB的Cover-Leung可达速率区域。此外，利用我们开发的评估外界的工具，我们还明确地表征了二进制擦除MAC的反馈容量区域的边界，其中Cover-Leung可实现速率区域已知是紧的。最后的结果证实了Kramer为二元擦除MAC开发的反馈策略是容量实现的。
We use the idea of dependence balance to obtain a new outer bound for the capacity region of the discrete memoryless multiple-access channel with noiseless feedback (MAC-FB). We consider a binary additive noisy MAC-FB whose feedback capacity is not known. The binary additive noisy MAC considered in this paper can be viewed as the discrete counterpart of the Gaussian MAC-FB. Ozarow established that the capacity region of the two-user Gaussian MAC-FB is given by the cut-set bound. Our result shows that for the discrete version of the channel considered by Ozarow, this is not the case. Direct evaluation of our outer bound is intractable due to an involved auxiliary random variable whose large cardinality prohibits an exhaustive search. We overcome this difficulty by using a composite function and its properties to explicitly evaluate our outer bound. Our outer bound is strictly less than the cut-set bound at all points on the capacity region where feedback increases capacity. In addition, we explicitly evaluate the Cover-Leung achievable rate region for the binary additive noisy MAC-FB in consideration. Furthermore, using the tools developed for the evaluation of our outer bound, we also explicitly characterize the boundary of the feedback capacity region of the binary erasure MAC, for which the Cover-Leung achievable rate region is known to be tight. This last result confirms that the feedback strategies developed by Kramer for the binary erasure MAC are capacity achieving.