Upper Bounds of Error Probabilities for Stationary Gaussian Channels With Feedback
Upper Bounds of Error Probabilities for Stationary Gaussian Channels With Feedback
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带反馈的稳态高斯通道的误差概率上界
DOI：
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发表时间：
2012
影响因子：
2.5
通讯作者：
S. Ihara
中科院分区：
文献类型：
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作者：
S. Ihara
在本文中，我们讨论了带反馈的加性高斯噪声信道上信息传输的编码方案和错误概率，其中高斯噪声过程是平稳的但不一定是白的。在白高斯通道的情况下，已知在平均功率约束下，最小错误概率比任何阶的指数下降得更快。最近 Gallager 和 Nakiboğlu (2010) 提出了一种白高斯信道的编码方案，并成功地展示了低于容量的所有速率的错误概率的多指数衰减。本文旨在证明，在对平稳高斯信道的噪声没有任何特殊假设的情况下，最小错误概率会快速呈多指数下降。一般来说，静态高斯信道的容量没有明确的公式。在本文中，我们在容量 C 上引入了下界 C*。然后我们证明，对于低于 C* 的所有速率，最小错误概率会以多指数方式快速下降，但并非对于低于 C 的所有速率。在证明过程中，Gallager 和 Nakiboğlu 提出的方案证明自己非常有用，即使高斯通道不是白色的。
In this paper, we discuss the coding schemes and error probabilities in information transmission over additive Gaussian noise channels with feedback, where the Gaussian noise processes are stationary but not necessarily white. In the case of the white Gaussian channel it is known that the minimum error probability, under the average power constraint, decreases faster than the exponential of any order. Recently Gallager and Nakiboğlu (2010) proposed a coding scheme for the white Gaussian channel and successfully showed the multiple-exponential decay of the error probability for all rates below capacity. This paper aims to prove that, without any special assumptions on the noise of the stationary Gaussian channel, the minimum error probability decreases multiple-exponentially fast. In general, no explicit formulas are known for the capacity of the stationary Gaussian channel. In this paper, we introduce a lower bound C* on the capacity C. Then we prove that the minimum error probability decreases multiple-exponentially fast for all rates below C*, but not for all rates below C. In the process of proving, the scheme proposed by Gallager and Nakiboğlu proves itself to be quite useful, even though the Gaussian channel is not white.