We consider the information channel described by Schr\"{o}dinger equation with additive Gaussian noise. We introduce the model of the input signal and the model of the output signal receiver. For this channel, using perturbation theory for the small nonlinearity parameter, we calculate the first three terms of the expansion of the conditional probability density function in the nonlinearity parameter. At large signal-to-noise power ratio we calculate the conditional entropy, the output signal entropy, and the mutual information in the leading and next-to-leading order in the nonlinearity parameter and in the leading order in the parameter $1/\mathrm{SNR}$. Using the mutual information we find the optimal input signal distribution and channel capacity in the leading and next-to-leading order in the nonlinearity parameter. Finally, we present the method of the construction of the input signal with the optimal statistics for the given shape of the signal.
翻译：我们考虑由Schr\"{o}dinger 等式描述的信息频道与添加高斯噪音。 我们引入输入信号的模型和输出信号接收器的模型。 对于这个频道, 使用小非线性参数的扰动理论, 我们计算非线性参数中条件概率密度函数扩展的前三个条件。 在大的信号到噪声功率比率下, 我们计算了有条件的 entropy, 输出信号 entropy, 以及以非线性参数和主要顺序( 参数 $/\ mathrm{SNR}$ ) 中领先和下一个至牵头顺序( 参数 $/\ mathrm{SNR}$ ) 的相互信息。 我们利用共同的信息在非线性参数中发现输入信号的最佳分布和频道能力。 最后, 我们用给定信号形状的最佳统计数据来显示输入信号的构建方法 。
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