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On the Per-Sample Capacity of Nondispersive Optical Fibers

机译：非色散光纤的单样本容量

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摘要

The capacity of the channel defined by the stochastic nonlinear Schrödinger equation, which includes the effects of the Kerr nonlinearity and amplified spontaneous emission noise, is considered in the case of zero dispersion. In the absence of dispersion, this channel behaves as a collection of parallel per-sample channels. The conditional probability density function of the nonlinear per-sample channels is derived using both a sum-product and a Fokker–Planck differential equation approach. It is shown that, for a fixed noise power, the per-sample capacity grows unboundedly with input signal. The channel can be partitioned into amplitude and phase subchannels, and it is shown that the contribution to the total capacity of the phase channel declines for large input powers. It is found that a 2-D distribution with a half-Gaussian profile on the amplitude and uniform phase provides a lower bound for the zero-dispersion optical fiber channel, which is simple and asymptotically capacity-achieving at high signal-to-noise ratios (SNRs). A lower bound on the capacity is also derived in the medium-SNR region. The exact capacity subject to peak and average power constraints is numerically quantified using dense multiple ring modulation formats. The differential model underlying the zero-dispersion channel is reduced to an algebraic model, which is more tractable for digital communication studies, and, in particular, it provides a relation between the zero-dispersion optical channel and a 2 $,times,$2 multiple-input multiple-output Rician fading channel. It appears that the structure of the capacity-achieving input distribution resembles that of the Rician fading channel, i.e., it is discrete in amplitude with a finite number of mass points, while continuous and uniform in phase.
机译：在零色散的情况下，考虑了由随机非线性Schrödinger方程定义的信道容量，其中包括Kerr非线性和放大的自发发射噪声的影响。在没有分散的情况下，此通道的行为就像是并行的每个样本通道的集合。使用求和积和Fokker-Planck微分方程方法，可以得出非线性每个样本通道的条件概率密度函数。结果表明，对于固定的噪声功率，每个样本的容量随输入信号的增加而无限制地增长。可以将通道分为幅度和相位子通道，这表明对于大输入功率，对相位通道总容量的贡献会下降。发现在振幅和均匀相位上具有半高斯分布的二维分布为零色散光纤通道提供了下限，这是简单的并且在高信噪比下渐近实现容量（SNR）。在中等SNR区域中也可以得出容量的下限。使用密集多环调制格式在数值上量化受峰值和平均功率约束的确切容量。零色散通道下面的微分模型被简化为代数模型，对于数字通信研究而言，该模型更易于处理，尤其是它提供了零色散光通道和2 $，times，$ 2倍之间的关系。输入多输出Rician衰落通道。看来，实现容量的输入分布的结构类似于里斯衰落信道的结构，即，它的振幅是离散的，具有有限数量的质点，而相位是连续且均匀的。

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