With the development of 5G technology, programs are gradually moving to cloud services. This leads to an increasing demand for storage. In the field of high-density data storage, bit-pattern media recording (BPMR) is considered a promising approach, as it can expand the data density to 4 Tb/in2. However, in high-density BPMR, bits or magnetic islands are very close to each other, leading to significant intertrack interference (ITI) from the cross-track direction and intersymbol interference (ISI) from the down-track direction. To minimize two-dimensional interference, including ITI and ISI, the serial detector method has been highly effective. However, in this method, the signal at the output of the first decoder is still a hard output. Therefore, we suggest methods to convert the output of the first detector into a soft output. Additionally, we have developed a new form of generalized partial response target to overcome the track mis-registration. The results show that our proposed methods apparently improve bit error rate performance.