Gaussian Channel With Noisy Feedback and Peak Energy Constraint
Gaussian Channel With Noisy Feedback and Peak Energy Constraint
复制标题
具有噪声反馈和峰值能量约束的高斯通道
DOI：
10.1109/tit.2013.2254233
复制
发表时间：
2011
影响因子：
2.5
通讯作者：
Young
中科院分区：
文献类型：
--
作者：
Yu Xiang;Young
研究了当正交加性高斯白噪声信道上存在噪声反馈时，峰值能量约束下加性高斯白噪声信道上的最优编码。正如 Pinsker 所示，在峰值能量约束下，具有无噪声反馈的 M 进制消息 M ≥ 3 的最佳误差指数严格大于无反馈的误差指数。本文扩展了 Pinsker 的结果，并表明如果反馈链路中的噪声功率足够小，则传输 M 元消息的最佳误差指数可以严格大于没有反馈的误差指数。该证明涉及两种反馈编码方案。一种是由 Burnashev 和 Yamamoto 用于二进制对称信道的两级噪声反馈编码方案激发的，而另一种是线性噪声反馈编码方案，扩展了 Pinsker 的无噪声反馈编码方案。当反馈噪声功率α足够小时，线性编码方案优于两级（非线性）编码方案，并且随着α趋于零而渐近最优。相比之下，当α相对较大时，两级编码方案表现更好。
Optimal coding over the additive white Gaussian noise channel under the peak energy constraint is studied when there is noisy feedback over an orthogonal additive white Gaussian noise channel. As shown by Pinsker, under the peak energy constraint, the best error exponent for communicating an M-ary message, M ≥ 3, with noise-free feedback is strictly larger than the one without feedback. This paper extends Pinsker's result and shows that if the noise power in the feedback link is sufficiently small, the best error exponent for communicating an M-ary message can be strictly larger than the one without feedback. The proof involves two feedback coding schemes. One is motivated by a two-stage noisy feedback coding scheme of Burnashev and Yamamoto for binary symmetric channels, while the other is a linear noisy feedback coding scheme that extends Pinsker's noise-free feedback coding scheme. When the feedback noise power α is sufficiently small, the linear coding scheme outperforms the two-stage (nonlinear) coding scheme, and is asymptotically optimal as α tends to zero. By contrast, when α is relatively larger, the two-stage coding scheme performs better.