The Gaussian Channel with Noisy Feedback
The Gaussian Channel with Noisy Feedback
复制标题
具有噪声反馈的高斯通道
DOI：
10.1109/isit.2007.4557421
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
T. Weissman
中科院分区：
文献类型：
--
作者：
Young;A. Lapidoth;T. Weissman
上限和下限是根据加性高斯白噪声通道的可靠性函数得出的，输出通过独立的加性高斯白噪声通道反馈到发射机。特别关注反馈噪声方差非常低的情况，结果表明可靠性函数与反馈噪声方差渐近成反比。该结果表明，反馈链路中的噪声无论多么小，都会导致带有噪声反馈的通信与完美反馈情况有根本不同。例如，事实证明，在有噪声反馈的情况下，线性编码方案无法实现任何正率。相反，基于三相检测/重传协议设计了渐近最优编码方案，对于小于容量的任何速率，该方案实现了与反馈噪声方差成反比的误差指数。
Upper and lower bounds are derived on the reliability function of the additive white Gaussian noise channel with output fed back to the transmitter over an independent additive white Gaussian noise channel. Special attention is paid to the regime of very low feedback noise variance and it is shown that the reliability function is asymptotically inversely proportional to the feedback noise variance. This result shows that the noise in the feedback link, however small, renders the communication with noisy feedback fundamentally different from the perfect feedback case. For example, it is demonstrated that with noisy feedback, linear coding schemes fail to achieve any positive rate. In contrast, an asymptotically optimal coding scheme is devised, based on a three-phase detection/retransmission protocol, which achieves an error exponent inversely proportional to the feedback noise variance for any rate less than capacity.