# Soft-Output Detector Using Multi-Layer Perceptron for Bit-Patterned Media Recording
## 4 Discussion  
To compare the BER performance depending on the detection schemes, we utilize a conventional detection technique based on PRML. A PRML detector employed in data storage systems consists of an equalizer and a channel decoder to mitigate ITI and ISI. In this simulation, we use a 2D equalizer and a 1D GPR target based on an MMSE criterion [5,6]. The size of the 2D equalizer is \(3\times 11\) and the length of the 1D GPR target is 3. After the readback signal is processed by the 2D MMSE equalizer, the equalizer output is fed to a four-state soft-output Viterbi algorithm (SOVA). In this simulation, we assume the regular BPMR channel model without media noise. The signal-to-noise ratio (SNR) is defined as \(10\text{log}_{10}(1/\sigma^{2})\). Figure 4 shows the BER performance comparison of the models at TMR of 0% and 30%. In Figure 4, each MLP detector is different only in the number of hidden layers and neurons per hidden layer, and random initialization by the He initialization, but has the same structure such as the activation functions, the locations of batch normalization, and so on. To compare the performance for the different number of hidden layers and neurons, two MLPs are designed. One has one hidden layer with sixteen neurons (blue solid line with triangle marker).The other has two hidden layers with 64 neurons per hidden layer (blue dotted line with triangle marker). Additionally, to investigate the performance of exploiting ensemble techniques, we apply the ensemble of five MLP detectors with 1 hidden layer and 16 neurons in each MLP detector (red solid line with circle marker) and the ensemble of 5 MLP detectors with 2 hidden layers and 64 neurons per hidden layer in each MLP detector (red dotted line with circle marker). Among various learning methods of the ensemble learning, the average is used in this simulation. Thus, the estimated values from five MLP detectors is shown in Figure 5 are averaged. Figure 3: Configuration of the MLP detector. As shown in Figure 4a, when SNR = 16 dB and TMR = 0%, the performances of the MLP (16) and (64, 64) detector alone (blue lines with triangle marker) are worse than that of the PRML detector. Furthermore, it shows unstable performance due to the overfitting problem. However, the ensemble schemes of MLP detectors (red lines with circle marker) show better BER performances compared to the PRML detector and provide stable BER performances compared to MLP alone. Additionally, the ensemble of MLP (64, 64) detectors performs better by approximately 0.3 dB compared to the ensemble of MLP (16) detectors at the BER of \(10^{-4}\). Thus, using the ensemble technique can provide more stable performance than using the MLP alone. As shown in Figure 4b, when TMR = 30%, the MLP detector (16) and (64, 64) alone show the inconsistent performance. However, the BER curves of the ensemble schemes of MLP (16) and (64, 64) detectors exhibit better performance than the MLP detector (16) and (64, 64) alone and the PRML detector. Again, the ensemble schemes of MLP detectors provide a consistent BER performance compared to the schemes of MLP detector alone. We investigate the probability density function of the output of the PRML detector, MLP (64, 64) detector alone, and an ensemble of the MLP (64, 64) detector at 3 Tb/in\({}^{2}\) and SNR = 14 dB, as shown in Figure 6. The ensemble of MLP detectors can reduce the overlapping area more than the PRML detector and MLP detector alone. Table 1 presents the mean and variance of the models. Compared with the PRML detector and MLP detector alone, the ensemble of MLP detectors provides a small variance. Thus, it is clear that the ensemble of MLP detectors provides more reliable information. Figure 4: BER performance comparison of the models: (**a**) TMR of 0%; (**b**) TMR of 30%. Figure 5: Block diagram of BPMR system with ensemble of MLP detectors. Figure 7 shows the BER performance comparisons according to the models using a 4/6 modulation coding scheme.