End-to-end learning has become a popular method to optimize a constellation shape of a communication system. When the channel model is differentiable, end-to-end learning can be applied with conventional backpropagation algorithm for optimization of the shape. A variety of optimization algorithms have also been developed for end-to-end learning over a non-differentiable channel model. In this paper, we compare gradient-free optimization method based on the cubature Kalman filter, model-free optimization and backpropagation for end-to-end learning on a fiber-optic channel modeled by the split-step Fourier method. The results indicate that the gradient-free optimization algorithms provide a decent replacement to backpropagation in terms of performance at the expense of computational complexity. Furthermore, the quantization problem of finite bit resolution of the digital-to-analog and analog-to-digital converters is addressed and its impact on geometrically shaped constellations is analysed. Here, the results show that when optimizing a constellation with respect to mutual information, a minimum number of quantization levels is required to achieve shaping gain. For generalized mutual information, the gain is maintained throughout all of the considered quantization levels. Also, the results implied that the autoencoder can adapt the constellation size to the given channel conditions.
翻译:端到端学习已成为优化通信系统星座形状的流行方法。 当频道模型是不同的时, 端到端学习可以使用常规的回映算法来优化形状。 还开发了各种优化算法, 用于在无差异的频道模型下端到端学习。 在本文中, 我们比较了基于幼稚卡尔曼过滤器的无梯度优化方法、 无模型优化和后向转换法, 用于在以分步 Fourier 方法为模型的光纤频道上进行端到端学习。 结果表明, 以计算复杂度为代价, 无梯度优化算法为业绩的反向调整提供了一种体面的替代。 此外, 数字到对等和模拟到数字转换器的有限比分解问题得到了解决, 并分析了其对几何形状的星座的影响。 在此, 结果显示, 在优化一个以相互信息为模型的星座时, 最小的四分位化水平需要达到最小的四分位化水平, 才能实现增益。 对于普遍化的正态, 共享的星座空间的增益度也得到了考虑。