In order to realize probabilistically shaped signaling within the probabilistic amplitude shaping (PAS) framework, a shaping device outputs sequences that follow a certain nonuniform distribution. In case of constant-composition (CC) distribution matching (CCDM), the sequences differ only in the ordering of their constituent symbols, whereas the number of occurrences of each symbol is constant in every output block. Recent results by Amari et al. have shown that the CCDM block length can have a considerable impact on the effective signal-to-noise ratio (SNR) after fiber transmission. So far, no explanation for this behavior has been presented. Furthermore, the block-length dependence of the SNR seems not to be fully aligned with previous results in the literature. This paper is devoted to a detailed analysis of the nonlinear fiber interactions for CC sequences. We confirm in fiber simulations the inverse proportionality of SNR with CCDM block length and present two explanations. The first one, which only holds in the short-length regime, is based on how two-dimensional symbols are generated from shaped amplitudes in the PAS framework. The second, more general explanation relates to an induced shuffling within a sequence, or equivalently a limited concentration of identical symbols, that is an inherent property for short CC blocks, yet not necessarily present in case of long blocks. This temporal property results in weaker nonlinear interactions, and thus higher SNR, for short CC sequences. For a typical multi-span fiber setup, the SNR difference is numerically demonstrated to be up to 0.7 dB. Finally, we evaluate a heuristic figure of merit that captures the number of runs of identical symbols in a concatenation of several CC sequences. For moderate block lengths up to approximately 100 symbols, this metric suggests that limiting the number identical-symbol runs can be beneficial for reducing fiber nonlinearities and thus, for increasing SNR.

中文翻译：

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有限长恒定组成序列的非线性纤维相互作用分析

为了在概率幅度整形 (PAS) 框架内实现概率整形的信令，整形设备输出遵循特定非均匀分布的序列。在恒定组合 (CC) 分布匹配 (CCDM) 的情况下，序列仅在其组成符号的排序上有所不同，而每个符号在每个输出块中的出现次数都是恒定的。Amari 等人的最新结果。已经表明 CCDM 块长度会对光纤传输后的有效信噪比 (SNR) 产生相当大的影响。到目前为止，还没有对这种行为提出任何解释。此外，SNR 的块长度依赖性似乎与文献中先前的结果不完全一致。本文致力于详细分析 CC 序列的非线性光纤相互作用。我们在光纤模拟中确认了 SNR 与 CCDM 块长度成反比，并提出了两种解释。第一个仅适用于短长度范围，它基于如何从 PAS 框架中的成形幅度生成二维符号。第二个更一般的解释涉及序列内的诱导改组，或等效地相同符号的有限集中，这是短 CC 块的固有属性，但在长块的情况下不一定存在。对于短 CC 序列，这种时间特性会导致较弱的非线性相互作用，从而导致更高的 SNR。对于典型的多段光纤设置，SNR 差异在数值上显示高达 0.7 dB。最后，我们评估了一个启发式的品质因数，它捕获了几个 CC 序列串联中相同符号的运行次数。对于最多约 100 个符号的中等块长度，该度量表明限制相同符号运行的数量有利于减少光纤非线性，从而有利于提高 SNR。