We introduce a trainable coded modulation scheme that enables joint
optimization of the bit-wise mutual information (BMI) through probabilistic
shaping, geometric shaping, bit labeling, and demapping for a specific channel
model and for a wide range of signal-to-noise ratios (SNRs). Compared to
probabilistic amplitude shaping (PAS), the proposed approach is not restricted
to symmetric probability distributions, can be optimized for any channel model,
and works with any code rate $k/m$, $m$ being the number of bits per channel
use and $k$ an integer within the range from $1$ to $m-1$. The proposed scheme
enables learning of a continuum of constellation geometries and probability
distributions determined by the SNR. Additionally, the PAS architecture with
Maxwell-Boltzmann (MB) as shaping distribution was extended with a neural
network (NN) that controls the MB shaping of a quadrature amplitude modulation
(QAM) constellation according to the SNR, enabling learning of a continuum of
MB distributions for QAM. Simulations were performed to benchmark the
performance of the proposed joint probabilistic and geometric shaping scheme on
additive white Gaussian noise (AWGN) and mismatched Rayleigh block fading (RBF)
channels.

本文介绍了一种可训练的编码调制方案，通过概率调制、几何调制、比特标签和解调，结合特定信道模型和一定范围内的信噪比，实现比特间互信息（BMI）的联合优化。相比于概率幅度调制，该方法不仅适用于对称概率分布，而且可以优化任何信道模型下的输出，适用于任何码率 $k/m$，$m$ 为每个信道使用的比特数，$k$ 为 $1$ 到 $m-1$ 范围内的整数。该方法允许学习由信噪比确定的连续星座几何形状和概率分布，并扩展了 Maxwell-Boltzmann（MB）分布的 PAS 体系结构，使其能够根据信噪比控制 QAM 调制的 MB 分布学习连续的 MB 分布。通过模拟性能可以测量该方法在加性高斯白噪声（AWGN）和失配雷利衰落（RBF）信道上的性能表现。

编码调制系统概率与几何建模的联合学习

Joint Learning of Probabilistic and Geometric Shaping for Coded  Modulation Systems

Autoencoder-based geometric shaping is proposed that includes optimizing bit
mappings. Up to 0.2 bits/QAM symbol gain in GMI is achieved for a variety of
data rates and in the presence of transceiver impairments. The gains can be
harvested with standard binary FEC at no cost w.r.t. conventional BICM.

该论文提出一种基于自编码器的几何塑形方法，其中包括优化比特映射，即使面对发送接收设备失真，在各种数据速率下亦可获得高达 0.2 比特 / QAM 符号增益，同时可以通过标准二进制前向纠错码实现，且无需额外花费。

面向 GMI 优化几何星座形状的端到端学习

End-to-end Learning for GMI Optimized Geometric Constellation Shape

A new geometric shaping method is proposed, leveraging unsupervised machine
learning to optimize the constellation design. The learned constellation
mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a
simplified fiber channel model.

本论文提出了一种新的几何成形方法，利用无监督机器学习优化星座设计，当使用简化的光纤信道模型进行训练时，所学习的星座可以减轻非线性影响，最高可获得 0.13 比特 / 4D 的增益。