## 4 Results and Discussions
Since HDS relies on the interference patterns of laser beams to store information within a 3D medium, even minor misalignment can degrade data integrity, reduce storage capacity, or lead to read/write errors. The behavior of these systems was simulated in a manner similar to the models shown in Figure 5. The results, presented in Figure 6, demonstrate that our proposed model continues to deliver the best performance under the 10% misalignment condition of the HDS channel. In addition, comparing with 0% misalignment, the BER performance of our proposed model is changed less than that of serial MAP detection [22] and a parallel ITI/ISI estimator [11]. This shows that our proposed model can resist the misalignment effect in HDS systems. Next, we varied the blur from 1.8 to 3 while setting the SNR to 15 dB to evaluate the BER performance of the HDS channel under media noise conditions. The results, shown in Figure 7 for 0% misalignment and Figure 8 for 10% misalignment, indicate that our proposed model achieves optimal performance when the blur is less than 3. Consequently, our model can effectively resist blur levels up to 3. To estimate the complexity of the proposed model, we counted the number of operations per detected bit, from the equalizer to the detection stage, for each method. For the equalizer with a size of 5 \(\times\) 5, obtaining one element in the signal \(z\)[\(j\),\(k\)] requires 25 multiplications and 24 additions. In our proposed model, the signal \(z\)[\(j\),\(k\)] is supplied to the \"HI/VI estimator\" and \"Horizontal MAP\". For the \"HI/VI estimator\", the number of input data points corresponds to the number of state transitions in the trellis diagram. To determine the number of operations per bit, we estimate the operations required for a single state transition. The diagram consists of 36 states, each with 6 input/output branches, resulting in a total of 216 branches. Therefore, calculating the branch metrics involves 432 additions and 216 multiplications. Figure 6: BER performance of the proposed model with 10% misalignments. For the \"Horizontal MAP\" algorithm, which is based on the trellis diagram, we calculate the operations for a single state transition, similar to the HI/VI estimator. Unlike the Viterbi algorithm, the MAP detection uses Equation (37) to compute \(\gamma\) for the branch metrics, which involves addition, multiplication, and exponential operations. Additionally, Equation (36) is used to determine the probabilities for each symbol on each branch. Consequently, the total number of operations for the \"Horizontal MAP\" algorithm is 657 additions, 1107 multiplications, and 312 exponential operations. The \"Vertical MAP\" algorithm is similar to the \"Horizontal MAP\" algorithm; however, the number of states and branches is smaller. It consists of four states, with two input/output branches in each state, resulting in a total of eight branches. Consequently,  
Figure 8: BER performance of the proposed model according to blur with 10% misalignment. Figure 7: BER performance of the proposed model according to blur with 0% misalignment. the \"Vertical MAP\" algorithm requires 48 additions, 51 multiplications, and 21 exponential operations. Finally, to achieve feedback from the \"Vertical MAP\" to the \"Horizontal MAP\", the method in [22] was used. This process involves 4 additions, 18 multiplications, and 3 exponential operations. Table 3 presents the results for the number of operations in each method.