## 4 Results and Discussions  
In this study, we simulated the proposed model in Figure 3. A sequence of bits representing user data, \(u[k]\), of size 1,440,000, is generated randomly. In this sequence, the probabilities of 0 and 1 bits are the same. To obtain a page of data, \(u[k]\) is transformed into \(a[j,k]\), which has a size of \(1200\times 1200\). This transformation resembles the data format used in HDS system media. A data page is then fed into the channel to generate \(y[j,k]\). To estimate the coefficients of F and G, \(a[j,k]\) and \(y[j,k]\) are supplied to Equations (15)-(17). To evaluate the BER performance of the proposed model, 10 data pages were used to go through the system. The output signal from HDS channel \(y[j,k]\) was fed to equalizer F to obtain \(z[j,k]\). With the previous estimated coefficients, the forms of \(z[j,k]\) and \(d[j,k]\) were among the same. Thus, \(z[j,k]\) could be handled by detection with parameters from target G. In detection, we used horizontal and vertical MAP. This is serial MAP detection with extrinsic information to create the iterative algorithm. The output of horizontal MAP is \(b[j,k]\). This signal included the probabilities of the symbols when the original is only affected by VI. Simultaneously, to improve the performance for horizontal MAP detection, we also used \(z[j,k]\) as the input to the VI/HI estimator to extract extrinsic information. The output of detection is compared with 0.5 as a threshold to detect bits 0 and 1 and obtained \(\hat{a}[j,k]\). Finally, we used demodulation to restore the original signal \(\hat{u}[k]\). \(\hat{u}[k]\) is compared with \(u[k]\) to calculate BER. In the first experiment, we varied the values of \(\alpha\) from 0 to 1 with the step of 0.1 to choose the optimized value of \(\alpha\). The results were shown in Figure 4. We can see that when \(\alpha=0.3\), the system achieves the best performance. Thus, we choose \(\alpha=0.3\) for our proposed model. In the second experiment, we focused on evaluating the two-dimensional (2D) interference reduction capability of the proposed model. To achieve this, we configured the system with 0% misalignment and a blur factor of 1.85. In HDS systems, as the blur level increased, a greater portion of the light energy was scattered in various directions, reducing the concentration of energy at the intended pixels. The blur level in the system was a key variable associated with the HDS channel, directly affecting the distribution of light energy on the projection screen. Additionally, the simultaneous scattering of light caused 2D ISI, where the signal from one symbol interfered with adjacent symbols, further complicating the decoding process and reducing signal clarity. Figure 3: Diagram of the proposed model. In Figure 5, we can observe that the user data went through the systems according to the decision in the starting paragraph of Section 4. With \"MAP and estimator without iteration\", we removed the feedback path from vertical MAP to horizontal MAP. With \"MAP and estimator with iteration\", we simulated the model in Figure 3. We can see that the proposed model without iteration can achieve gains of \(\sim\)0.6 dB and \(\sim\)0.5 dB at a BER of \(10^{-5}\) compared to a parallel ITI/ISI estimator [11] and serial MAP detection [22], respectively. If we added the iteration to the proposed model, the system could obtain gains of \(\sim\)1.5 dB and \(\sim\)5.5 dB at a BER of \(10^{-5}\) compared to a parallel ITI/ISI estimator [11] and serial MAP detection [22], respectively. Figure 4: BER performance according to \(\alpha\). Figure 5: BER performance of the proposed model. In the following simulation, we introduce a 10% misalignment into the HDS channel while maintaining a blur value of 1.85. Misalignment in holographic data storage (HDS) refers to any deviation in the precise alignment of the key components involved in reading and writing data.