###### Abstract  
The ever-increasing demand for data in recent times has led to the emergence of big data and cloud data. The growth in these fields has necessitated that data be centrally stored in data centers. To meet the need for large-scale storage systems at data centers, innovative technology such as bit-pattern media recording (BPMR) has been developed. With BPMR technology, we are able to achieve significant improvements in high areal density (AD) of magnetic data storage systems. However, two-dimensional (2D) interference is a common issue faced with high AD. Intersymbol interference and intertrack interference occur when the distance between the islands is decreased in the down-track and cross-track, respectively. 2D interference adversely affects the performance of BPMR. In this paper, we propose an improved modified Viterbi algorithm (MVA) exploiting a feedback and a new 2D three-way form of a generalized partial response (GPR) target. The proposed MVA with feedback is superior to the previous MVA by eliminating intertrack interference (ITI) more effectively. With the three-way GPR target, the proposed algorithm achieves more stable performance compared to the previous detection algorithms for the track misregistration effect.  
information storage; bit-patterned media recording; intersymbol interference; hard disk drive; area density; partial response maximum likelihood +
Footnote †: journal: Applied Sciences  
BPMR is an extremely promising technology to overcome the AD limitations seen in existing magnetic storage. For BPMR-based systems, data bits are stored on magnetic islands. To increase the AD, the distance between the magnetic islands has to be reduced. This increases the intersymbol interference (ISI) and intertrack interference (ITI) in the down-track and cross-track direction, respectively. Owing to the increase in 2D interference, such as ISI and ITI, the BPMR channel performance in terms of bit error rate (BER) is negatively affected.  
Error correction codes and modulation code are two common methods to minimize 2D interference in signal processing. [PERSON] and [PERSON] [7] proposed the use of modulation code and multilayer perceptron decoding for BPMR to reduce and correct errors due to ITI, respectively. Error-correcting 5/6 modulation code was introduced [8] by [PERSON] and [PERSON] to reduce 2D interference and correct errors. [PERSON] proposed a combination of rate-3/4 modulation code and ITI subtraction in [9] to reduce ITI. In addition, we can use an equalizer and detector with a generalized partial response (GPR) target to minimize 2D interference. Additionally, [PERSON] proposed a 2D soft-output Viterbi algorithm (2D SOVA) [10] to reduce the effects of 2D interference. The 2D SOVA method was further developed as an iterative 2D SOVA for bit-patterned media [11]. In addition, the modified Viterbi algorithm (MVA) proposed by [PERSON], [PERSON], and [PERSON] in [12] is widely used [13; 14; 15; 16]. However, the MVA [12] was only used as part of the detector in their study. Therefore, in this paper, we propose a three-way GPR utilizing a three-way MVA [12] with feedback. This is a huge improvement over the original MVA [12] standalone implementation. Besides, there are detection schemes based on the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm [17; 18]. In [17], an iterative row-column soft decision feedback algorithm (IRCSDFA) is presented. Then, in [18], the IRCSDFA reduced the complexity by applying Gaussian approximation (IRCSDFA-GA). Although IRCSDFA-GA has low complexity compared to IRCSDFA, the main detection is still the BCJR algorithm, which is much more complex than the MVA.  
The rest of the paper is divided as follows. Section 2 discusses the N-way GPR target and N-way detection. Section 3 explains the proposed model and details of our algorithm. The simulation results and conclusions are discussed in Sections 4 and 5, respectively.