###### Abstract  
In bit-patterned media recording (BPMR) systems, two-dimensional (2D) interference, which includes intersymbol and intertrack interference from down- and across-track directions, respectively, increases when the distance between the islands is reduced with increasing areal density. In recent studies, a general partial response (GPR) target was often deployed with the equalizer to estimate and reduce interference. With this combination, the BPMR system becomes a promising candidate for high-density storage systems and achieves high bit error rate (BER) performance. Therefore, in this study, we investigate the detection capability while varying the form of the GPR target and implement a multilayered 2D GPR target and a detection method for improving the accuracy in estimating the interference. The simulation results demonstrate that the proposed model improves by a gain of \(\sim\)1 dB compared to the previous studies. bit-patterned media recording (BPMR); equalizer; general partial response; interference mitigation; Viterbi algorithm +
Footnote †: journal: Applied  
noise and track misregistration (TMR) [7; 8]. Currently, the AD value of BPMR has been developed up to 4 Tb/in\({}^{2}\)[8; 9]. To overcome these obstacles, signal-processing research has focused on two common approaches: symbol detection and error-control coding and/or modulation coding. In addition, there are collaborating methods in which the feedback line between the detection and error-control and/or modulation coding is designed to create an iterative algorithm. We used two approaches for modulation coding. First, the symbols must avoid patterns causing errors frequently, for instance, a bit encircled by opposite polarity bits. Second, if the minimum distance between codewords is >1, these symbols can achieve some error-correction capability. [PERSON] et al. [10] designed an 8/9 2D modulation code to eliminate the fatal interference patterns. With improvement, [PERSON] and [PERSON] [11] proposed a rate 9/12 2D modulation code that ensures a reasonable Hamming distance in the codeword set and avoids fatal interference as much as possible. By proposing a 3/4 2D modulation code that removes the ITI. [PERSON] and [PERSON] [12] reduced the ITI in BPMR systems using an array reader. To adapt to the staggered structure of BPMR, [PERSON] and [PERSON] [13] designed an error-correcting 5/6 modulation code that can correct the errors and reduce the isolated bit. In addition, [PERSON] and [PERSON] [14] proposed a multilayer perceptron decoding modulation code for BPMR systems. To mitigate 2D interference, we used an equalizer and partial-response maximum-likelihood detection. [PERSON] and [PERSON] [15] used a 2D equalizer combined with a general partial response (GPR) target to convert 2D interference into one-dimensional (1D) interference and applied 1D detection. The GPR target is presented as a matrix \(\mathbf{G}\), as shown in Figure 1. To avoid using 2D Viterbi detection, [PERSON] et al. [16] proposed a modified Viterbi algorithm (MVA) that supplies ITI information for the Viterbi algorithm (VA). [PERSON] and [PERSON] [17] proposed a hybrid 2D equalizer that was used to improve the MVA when the ITI type was known. [PERSON] and [PERSON] [18] proposed an effective detection technique to combat ITI at a low implementation cost. With the superiority of the soft-output Viterbi algorithm (SOVA), [PERSON] and [PERSON] [19] designed a 2D SOVA that exploits two 1D SOVAs in the horizontal and vertical directions. The original version of the 2D SOVA was introduced to handle the 2D interference in holographic data storage systems; it was later developed into an iterative 2D SOVA for BPMR [20]. However, in these studies, only the 1D form of the GPR target was used (or a 2-way GPR target according to the definition in [21], which is presented in Figure 1). [PERSON] and [PERSON] [21] designed feedback for the MVA to apply the 3-way GPR. This model achieves better BER performance than the 2-way GPR target.