Dependence Balance Based Outer Bounds for Gaussian Networks With Cooperation and Feedback
Dependence Balance Based Outer Bounds for Gaussian Networks With Cooperation and Feedback
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DOI：
10.1109/tit.2011.2145150
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发表时间：
2008-12
影响因子：
2.5
通讯作者：
R. Tandon;S. Ulukus
中科院分区：
文献类型：
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作者：
R. Tandon;S. Ulukus
我们获得了具有广义反馈的两用户多址信道（MAC-GF）和具有广义反馈的两用户干扰信道（IC-GF）的容量区域的新外界。这些外部界限基于 Hekstra 和 Willems 提出的依赖平衡的思想。为了说明外界的有用性，我们研究了三种不同的通道模型。我们首先考虑带有噪声反馈的高斯 MAC (MAC-NF)，其中发射机 k, k = 1, 2 接收反馈 Y(Fk)，它是被加性高斯白噪声 Zk 破坏的通道输出 Y。对于该通道模型，割集外界对反馈噪声方差不敏感。我们证明了我们的外界改进了反馈噪声方差的所有非零值的割集界。此外，在 σ(Zk)2 → ∞, k = 1, 2 的极限下，我们的外界在没有反馈的情况下崩溃到高斯 MAC 的容量区域。其次，我们研究了具有用户协作的高斯 MAC (MAC-UC)，其中每个发射机接收另一个发射机的信道输入的加性高斯白噪声损坏版本。对于该通道模型，割集界对协作噪声敏感，但不够敏感。对于合作噪声方差的所有非零值，我们的外界严格改进了割集外界。此外，随着合作噪声变大，我们的外界会崩溃到没有合作的高斯 MAC 的容量区域。第三，我们研究了具有用户合作的高斯 IC (IC UC)。对于该信道模型，与 MAC-UC 信道模型的情况一样，割集界再次对协作噪声方差敏感，但不够敏感。我们证明，我们的外界严格改进了合作噪声方差的所有非零值的割集界。
We obtain new outer bounds on the capacity regions of the two-user multiple access channel with generalized feedback (MAC-GF) and the two-user interference channel with generalized feedback (IC-GF). These outer bounds are based on the idea of dependence balance which was proposed by Hekstra and Willems. To illustrate the usefulness of our outer bounds, we investigate three different channel models. We first consider a Gaussian MAC with noisy feedback (MAC-NF), where transmitter k, k = 1, 2, receives a feedback Y(Fk), which is the channel output Y corrupted with additive white Gaussian noise Zk. For this channel model, the cut-set outer bound is not sensitive to the feedback noise variances. We demonstrate that our outer bound improves upon the cut-set bound for all nonzero values of the feedback noise variances. Moreover, in the limit as σ(Zk)2 → ∞, k = 1, 2, our outer bound collapses to the capacity region of the Gaussian MAC without feedback. Secondly, we investigate a Gaussian MAC with user-cooperation (MAC-UC), where each transmitter receives an additive white Gaussian noise corrupted version of the channel input of the other transmitter. For this channel model, the cut-set bound is sensitive to the cooperation noises, but not sensitive enough. For all nonzero values of cooperation noise variances, our outer bound strictly improves upon the cut-set outer bound. Moreover, as the cooperation noises become large, our outer bound collapses to the capacity region of the Gaussian MAC without cooperation. Thirdly, we investigate a Gaussian IC with user-cooperation (IC UC). For this channel model, the cut-set bound is again sensitive to cooperation noise variances as in the case of MAC-UC channel model, but not sensitive enough. We demonstrate that our outer bound strictly improves upon the cut-set bound for all nonzero values of cooperation noise variances.