# Machine Learning Applications for Short Reach Optical Communication
## 3 Machine Learning for Short-Reach Optical Communication System Signal Processing
### Other Machine-Learning Based Signal Processing Applications for Short-Reach Communication Systems
#### 3.2.3 Soft Demapping  
The soft-decision forward error correction (FEC) and higher-order QAM data transmission have been considered as feasible technologies for achieving high-speed and high-spectral efficiency in optical communication systems. In a fading transmission channel such as the optical fiber channel, the bit interleaved code modulation (BICM) is a feasible approach for integrating channel coding and digital modulation, where the modulation constellation can be chosen irrespective of the coding rate. The BICM block's structure is made up of a series of forwards error correction (FEC) codes, bit interleavers, and constellation mappers [123]. The soft demapper, which evaluates the soft bit (\(L\) value), is an important part of the soft decision FEC-BICM system [110]. Due to the high complexity of the Volterra-based equalization, a soft neural network-based method for nonlinear equalization and soft-decision demapping has been presented as an alternative [76].  
In [76], the soft DNN (SDNN) architecture is investigated as a solution for nonlinear equalization and soft demapping. The soft DNN design consist of 17 input nodes (8 previous symbols + the current symbol + 8 future symbols) and two hidden layers with 26 and 25 nodes, respectively. The outcomes are then fed into 3 output nodes. The training process is shown in Figure 12. In the training process, symbols \(x(i)\), \(i=1\ldots n\) are transmitted through a coherent short-reach optical communication system. An observation value \(y(i)\) is presented to the SDNN-based demapper, which represents the output of several consecutive channels before and after the \(i\)th channel. The calculated soft bit \(\ell_{i}\) represents the hard decision for soft-decision FEC decoding. If \(\ell_{i}>0\), then the bit is decided to be 0, and if \(\ell_{i}<0\), then it is decided to be 1. The absolute value of \(\ell_{i}\) indicates the degree of confidence of the soft demapper in its decision. In this work, the bit-wise equivocation is used as the loss function [76]:  
\[\mathcal{L}(b,\ell_{i})=\log_{2}[1+exp(-(1-2b)\ell_{i})] \tag{20}\]  
where \(b\) is the transmitted bit and \(\ell_{i}\) is the output \(L\) value of the neural network. Experiments are conducted to assess the performance and complexity of the proposed SDNN. Back-to-back transmitted 92 GBaud/s data with dual-polarized 64-QAM is utilized. Under the 15% overhead FEC restriction, the proposed bit-wise SDNN equalizer is compared to the fifth-order Volterra equalizer. Results show that the computational complexity is lowered by 65% when the same performance is achieved. Under the same complexity, an OSNR gain of 0.35 dB is achieved using the proposed SDNN, and hence, the system performance is improved.  
A bi-directional RNN based soft demapper (BRNN-SD) has also been proposed in [122], which has shown better functionality than the ANN based soft demapper [76; 110] on modeling the nonlinear infinite impulse response due to its ability to exhibit temporal dynamic behavior of time sequences. The BRNN-SD model is trained with pre-processed digital signal (a repeated 4096 symbols constant amplitude zero auto-correlation based training sequence). The iterative training is based on gradient descent and the back-propagation method using the adaptive moment estimation (ADAM) optimizer. The loss function is also based on the bit-wise equivocation. The capability of the BRNN has been compared with the reference Volterra based DSP. In the back-to-back system with 92 GBaud/s dual-polarization 32-QAM signals, the proposed BRNN-SD matches the performance of the reference DSP with less complexity. When a 32 channels DWDM system is considered, where each channel has a data rate of 800 Gb/s (DP-32 QAM at 96 GBaud/s), the proposed BRNN-SD method outperforms the reference DSP on the signal recovery.