[论文解读] Feedback Can Double the Prelog of Some Memoryless Gaussian Networks

Michael Gastpar, Amos Lapidoth+2 more|arXiv (Cornell University)|Mar 31, 2010

Wireless Communication Security Techniques参考文献 28被引用 6

一句话总结

该论文表明，在特定噪声相关性条件下，反馈可使某些无记忆高斯网络的和容量渐近加倍——具体而言，是在两接收机广播信道和两用户干扰信道中。作者提出了一种新颖的反馈编码方案，通过利用接收机之间完美噪声相关性（正相关或负相关）来实现高信噪比（SNR）下的乘法容量增益，当噪声协方差矩阵为秩一时，增益随接收机数量而增长。

ABSTRACT

We exhibit two memoryless Gaussian networks where the capacity-gains afforded by feedback are unbounded in the signal-to-noise ratio (SNR). The networks are instances of the Gaussian broadcast channel and the two-user Gaussian interference channel. To demonstrate the capacity-gains we propose and analyze a novel feedback coding scheme. For the broadcast channel with two receivers it is shown that if the noise sequences at the two receivers are perfectly anticorrelated, then, at high SNR, feedback asymptotically doubles the sum-capacity. The same holds if the noise sequences are perfectly correlated provided that they are of unequal variances. This result extends to the multi-receiver broadcast channel: if the noise sequences are all different and have a rank-one covariance matrix, then, at high-SNR, feedback asymptotically multiplies the sum-capacity by the number of receivers. However, as we show, these multiplicative gains collapse when the feedback is noisy. For the two-receiver Gaussian broadcast channel with noisefree feedback we also derive the high-SNR asymptotic sumcapacity. The expansion is exact in the sense that, as the SNR tends to infinity, the difference between the sum-capacity and our asymptotic expression tends to zero. If the noise sequences are perfectly anticorrelated or if they are perfectly correlated and of unequal variances, then the asymptotic expansion is as if the transmitter communicated to the two receivers over two parallel Gaussian channels. Otherwise, the asymptotic expansion is the same as if the receivers could cooperate. For the two-user interference channel it is shown that if the noises experienced by the two receivers are perfectly correlated or perfectly anticorrelated, then for most channel-gains feedback doubles the high SNR sum-capacity.

研究动机与目标

• 研究在高信噪比下，反馈是否能为无记忆高斯网络提供无界的容量增益。
• 分析反馈在何种条件下可使高斯广播信道和干扰信道的和容量加倍或乘法增长。
• 提出一种新颖的反馈编码方案，利用接收机噪声相关性以实现高信噪比下的容量增益。
• 确定在各种噪声相关性模型下，无噪声反馈条件下两接收机高斯广播信道的渐近和容量。

提出的方法

• 提出一种新颖的反馈编码方案，利用接收机噪声序列之间的完美相关性或反相关性来提升容量。
• 在接收机噪声完全反相关或相关且方差不等的假设下，分析两接收机高斯广播信道。
• 推导出无噪声反馈下广播信道的高信噪比渐近和容量，证明其在 SNR → ∞ 时精确收敛。
• 将分析扩展至噪声协方差矩阵为秩一的多接收机广播信道，以证明反馈使和容量乘以接收机数量。
• 研究在完美噪声相关性或反相关性下，两用户高斯干扰信道的反馈影响，以确定其对高信噪比和容量的影响。
• 将反馈方案的渐近行为与接收机协作或并行高斯信道等效情形进行比较。

实验结果

研究问题

• RQ1 在何种条件下，反馈可在高信噪比下为无记忆高斯网络提供无界的容量增益？
• RQ2 反馈能否使两用户高斯广播信道的和容量加倍，若能，需满足何种噪声相关性假设？
• RQ3 噪声协方差矩阵的结构如何影响多接收机广播信道中反馈的增益？
• RQ4 无噪声反馈下，两接收机高斯广播信道的精确高信噪比渐近和容量是多少？
• RQ5 当接收机噪声完全相关或完全反相关时，反馈是否会使两用户高斯干扰信道的高信噪比和容量加倍？

主要发现

• 对于两接收机高斯广播信道，当接收机噪声序列完全反相关时，反馈可渐近使和容量加倍。
• 若噪声序列完全相关且方差不等，反馈在高信噪比下同样可渐近使和容量加倍。
• 在多接收机广播信道中，当噪声协方差矩阵为秩一且所有噪声序列互不相同时，反馈可渐近使和容量乘以接收机数量。
• 当噪声完全反相关或完全相关且方差不等时，无噪声反馈下两接收机广播信道的渐近和容量与两平行高斯信道的容量相匹配。
• 对于两用户干扰信道，当接收机噪声完全相关或完全反相关时，反馈可使高信噪比和容量加倍。
• 当反馈存在噪声时，反馈增益会消失，表明干净反馈是实现乘法容量增益的关键。