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arXiv 0812.1857cs.ITmath.IT
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基于依赖平衡的合作反馈高斯网络的外界

Dependence Balance Based Outer Bounds for Gaussian Networks with Cooperation and Feedback

Ravi Tandon, Sennur Ulukus

摘要:

获得了广义反馈两用户多址接入信道(MAC-GF)和广义反馈两用户干扰信道(IC-GF)容量区域的新外界。这些外边界是基于Hekstra和Willems [1]提出的依赖平衡的思想。为了说明我们的外部边界的有用性,我们调查三种不同的信道模型。我们首先考虑具有噪声反馈的高斯MAC(MAC-NF),其中发射机$k$、$k=1,2$接收反馈$Y_{F_{k}}$,其是被加性高斯白噪声$Z_{k}$破坏的信道输出$Y$。当反馈噪声方差变大时,人们会期望反馈变得无用,这并不反映在割集界限中。我们证明,我们的外边界改善后,割集界的反馈噪声方差的所有非零值。此外,在限制为$σ_{Z_{k}}^{2}\to \infty$,$k=1,2$,我们的外部边界崩溃的高斯MAC的容量区域没有反馈。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破坏版本[2]。对于这种信道模型,割集界对合作噪声敏感,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。第三,我们研究了一个具有用户协作的高斯IC(IC-UC)。对于该信道模型,割集界再次对合作噪声方差敏感,但不够敏感。我们证明了我们的外边界严格提高后,割集界的合作噪声方差的所有非零值。

英文摘要:

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 [1]. 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 $Y_{F_{k}}$, which is the channel output $Y$ corrupted with additive white Gaussian noise $Z_{k}$. As the feedback noise variances become large, one would expect the feedback to become useless, which is not reflected by the cut-set bound. We demonstrate that our outer bound improves upon the cut-set bound for all non-zero values of the feedback noise variances. Moreover, in the limit as $σ_{Z_{k}}^{2}\to \infty$, $k=1,2$, 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 [2]. For this channel model, the cut-set bound is sensitive to the cooperation noises, but not sensitive enough. For all non-zero values of cooperation noise variances, our outer bound strictly improves upon the cut-set outer bound. 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 but not sensitive enough. We demonstrate that our outer bound strictly improves upon the cut-set bound for all non-zero values of cooperation noise variances.

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