Optimizing the input probability distribution of a discrete-time channel is a standard step in the information-theoretic analysis of digital communication systems. Nevertheless, many practical communication systems transmit uniformly and independently distributed symbols drawn from regular constellation sets. The introduction of the probabilistic amplitude shaping architecture has renewed interest in using optimized probability distributions, i.e., probabilistic shaping. Traditionally, probabilistic shaping has been employed to reduce the transmit power required for a given information rate over additive noise channels. While this translates into substantive performance gains for optical fiber communication systems, the interaction of shaping and fiber nonlinearity has posed intriguing questions. At first glance, probabilistic shaping seems to exacerbate nonlinear interference noise (NLIN) due to larger higher-order standardized moments. Therefore, the optimization of shaping distributions must differ from those used for linear channels. Secondly, finite-length effects related to the memory of the nonlinear fiber channel have been observed. This suggests that the marginal input-symbol distribution is not the only consideration. This paper provides a tutorial-style discussion of probabilistic shaping for optical fiber communication. Since the distinguishing property of the channel is the signal-dependent NLIN, we speak of probabilistic shaping for nonlinearity tolerance. Our analysis builds on the first-order time-domain perturbation approximation of the nonlinear fiber channel and revisits the notion of linear and nonlinear shaping gain. We largely focus on probabilistic amplitude shaping with popular shaping methods. The concept of shaping via sequence selection is given special consideration, as it inherently optimizes a multivariate distribution for shaped constellations.

翻译：优化离散时间信道的输入概率分布是数字通信系统信息论分析的标准步骤。然而，许多实际通信系统传输的是从规则星座图中抽取的均匀独立分布符号。概率幅度整形架构的提出重新激发了人们对使用优化概率分布（即概率整形）的兴趣。传统上，概率整形被用于降低加性噪声信道中给定信息速率所需的发射功率。虽然这为光纤通信系统带来了实质性的性能增益，但整形与光纤非线性的相互作用引发了引人深思的问题。乍看之下，由于高阶标准化矩更大，概率整形似乎会加剧非线性干扰噪声（NLIN）。因此，整形分布的优化必须不同于线性信道所用的方法。其次，已观察到与非线性光纤信道记忆性相关的有限长度效应。这表明边际输入符号分布并非唯一需要考虑的因素。本文以教程形式探讨光纤通信中的概率整形。由于该信道的显著特性是信号相关的NLIN，我们将其称为面向非线性容限的概率整形。我们的分析基于非线性光纤信道的一阶时域微扰近似，并重新审视了线性与非线性整形增益的概念。我们主要关注采用主流整形方法的概率幅度整形。序列选择整形这一概念受到特别关注，因为它本质上优化了整形星座的多变量分布。