We simulate and experimentally demonstrate a feedback-based probabilistic constellation shaping (FB-PCS) of a 10 Gbaud 16-ary quadrature amplitude modulation (16-QAM) signal. Our approach is to adaptively modify the distribution of transmitted symbols based on errors at the receiver, and assumptions about the channel model are not required. Specifically, the error feedback enables solving an optimization problem to find the distribution that maximizes the mutual information between the input and output of the channel without knowledge of the channel itself. A known training sequence with uniform distribution is transmitted, and the errors at each constellation point are counted at the receiver. This information is relayed to the transmitter, which then updates the data constellation with a new probability distribution such that constellation points with more errors are used less frequently. We examine four different system scenarios in simulation and one scenario in experiment. In simulation, we find that FB-PCS (a) reduces the number of errors when compared to uniform shaping for the four scenarios, and (b) reduces symbol error rate (SER) by approximately an order of magnitude or has similar SER compared to conventional Maxwell–Boltzmann (M–B) shaping. Moreover, we demonstrate that FB-PCS can lead to an SER reduction of ${\sim}{{50}}\%$.

中文翻译：

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通过根据接收器的错误自适应地修改传输符号的分布，实现16-QAM概率星座图整形。

我们模拟并实验证明了基于反馈的10 Gbaud 16进制正交幅度调制（16-QAM）信号的星座图整形（FB-PCS）。我们的方法是根据接收器上的错误来自适应地修改传输符号的分布，并且不需要有关信道模型的假设。具体地，错误反馈使得能够解决优化问题，以找到使信道的输入和输出之间的互信息最大化的分布，而无需了解信道本身。发射具有均匀分布的已知训练序列，并在接收器处计算每个星座点的误差。该信息被中继到发送器，然后，它会使用新的概率分布更新数据星座图，从而减少了使用更多误差的星座图点的频率。我们在仿真中检查了四种不同的系统方案，在实验中检验了一种方案。在仿真中，我们发现FB-PCS（a）与四种情况下的统一整形相比减少了错误数量，并且（b）将符号错误率（SER）降低了大约一个数量级，或者与传统的麦克斯韦-玻尔兹曼成形法。此外，我们证明FB-PCS可以导致SER降低 （b）将符号错误率（SER）降低约一个数量级，或者与传统的Maxwell-Boltzmann（MB）成形相​​比具有相似的SER。此外，我们证明FB-PCS可以导致SER降低 （b）将符号错误率（SER）降低约一个数量级，或者与传统的Maxwell-Boltzmann（MB）成形相​​比具有相似的SER。此外，我们证明FB-PCS可以导致SER降低$ {\ sim} {{50}} \％$。