## 4 Simulation and Results  
In this work, 100 pages with a page size of 900 \(\times\) 900 islands per page were simulated. The 1D PR target for the 2D equalizer was (0.1, 1.0, 0.1). The 1D SOVA was used for channel detection. The channel signal-to-noise ratio (SNR) was defined as 10 log\({}_{10}\)(1/\(\sigma^{2}\)), where \(\sigma^{2}\) is additive white Gaussian noise. Table 2 shows the read head and pulse response parameters [14]. Figure 5 displays the BER performance of the PRML and the proposed 7/10 modulation code at the same AD. At BER = 10\({}^{-6}\), when the AD was 2.0 Tb/in\({}^{2}\), the performance of the proposed code was 2 dB better than that of the PRML. In addition, when the AD was 3.0 Tb/in\({}^{2}\), the BER curve of the proposed code exhibited better performance than that of PRML detection. Since the proposed 7/10 modulation code eliminated ITI error patterns and provided enough distance among the nonidentical codewords, the performance of the proposed codes showed a better performance. To verify the performance in accordance with the modulation coding scheme, the PRML (uncoded system) and the 4/6 [15], 8/10 [16], and the proposed 7/10 modulation codes were compared. For a fair comparison, the user density (UD), which is defined by UD = AD \(\times\) code rate, should be considered. The code rate of the PRML was 1 because of the uncoded system. The code rates of the 4/6, 8/10, and 7/10 modulation codes were 0.66, 0.8, and 0.7, respectively. Figure 6 shows the BER comparison with respect to the modulation coding scheme at UD = 1.4 Tb/in\({}^{2}\). The AD of the PRML and the 4/6, 8/10, and 7/10 modulation codes were 1.4, 2.1, 1.75, and 2.0 Tb/in\({}^{2}\), respectively. The track pitch \(T_{z}\) and bit period \(T_{x}\) for each AD are shown in Table 3. For example, when the UD was 1.4 Tb/in\({}^{2}\) and 7/10 modulation code was used, the AD was 2.0 Tb/in\({}^{2}\). To achieve an AD of 2.0 Tb/in\({}^{2}\), \(T_{z}\) and \(T_{x}\) were 18 nm. In this simulation, the 8/10 modulation code had the worst performance. At a BER of 10\({}^{-6}\), the proposed 7/10 modulation code provided performance gains of approximately 0.4 and 1.6 dB over the 4/6 modulation code and the PRML detector, respectively. The proposed scheme has a higher code rate and better performance than the 4/6 modulation code, because the patterns that generate ITI are effectively removed. The 4/6 modulation code has the advantage of providing enough distance among the nonidentical codewords, and the 8/10 modulation code has the advantage of removing the ITI pattern. The proposed code showed good performance, because it combines these two advantages. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & \\ \hline Square island with length & 11 nm \\ Square island with thickness & 10 nm \\ Read head element thickness & 4 nm \\ Read head element width & 15 nm \\ Read head gap distance & 6 nm \\ Read head fly height & 10 nm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Read head and pulse response parameters. Figure 7 illustrates the BER performance according to the modulation coding scheme at UD = 2.1 Tb/in\({}^{2}\). For a fair comparison, the suitable \(T_{z}\) and \(T_{x}\) for each AD are as presented in Table 2. At a BER of 10\({}^{-3}\), the proposed modulation code performed approximately 0.8 and 2.3 dB better than the 8/10 and 4/6 modulation codes, respectively. In this simulation, the performance of the 4/6 modulation code was the poorest. The reason is that the 4/6 modulation code proposed for holographic data storage is not suitable for BPMR. Most importantly, however, the PRML detector provided the best performance in all cases because the ITI effect dramatically increased, because of the fair comparison. Therefore, the proposed modulation code is not suitable for BPMR. Figure 5: The bit error rate (BER) performance of the partial response maximum likelihood (PRML) and the proposed 7/10 modulation code at the same areal densities (AD).