# Estimating Interference with a Two-Dimensional Viterbi Algorithm for Bit-Patterned Media Recording
###### Abstract  
Bit-patterned media recording (BPMR) is proposed as a candidate for future magnetic data storage to overcome superparamagnetism. The distance between magnetic islands in BPMR must be reduced to increase the areal density (AD). As magnetic islands become closer, two-dimensional (2D) interference is increased, including intersymbol interference (ISI) based on the down-track direction and intertrack interference (ITI) from the cross-track direction. We propose an estimator to predict interference from neighboring (upper and lower) tracks. This estimator exploits the 2D Viterbi algorithm (VA) with reduced states. We removed the interference from the neighboring track and applied a simple 1  
apply the Viterbi algorithm (VA) for 2D interference, [PERSON] et al. proposed a modified VA, which mitigates the effect of ITI [16]. GPR and MVA were used by [PERSON] and [PERSON] to design a hybrid 2D equalizer [17]. [PERSON] and [PERSON] developed a feedback scheme for MVA to improve ITI prediction [18]. To combat ITI with a low implementation cost, [PERSON] and [PERSON] proposed an effective detection technique in [19]. In addition, [PERSON] and [PERSON] [20] also proposed a multitrack detector with 2D pattern-dependent noise prediction, which significantly outperformed a conventional 2D Viterbi detector when the channel noise was pattern-dependent. [PERSON] and [PERSON] introduced an iterative 2D soft-output VA (SOVA) for BPMR systems [21]. This scheme was inspired by the 2D SOVA for holographic data storage systems and designed as a parallel structure of two 1D VA detectors along the horizontal and vertical directions, respectively [22]. [PERSON] and [PERSON] proposed a serial detection scheme for two 1D VA detectors along the horizontal and vertical directions [23]. In serial detection, the signal is detected by the horizontal detector, and then the output signal is detected by the vertical detector. Furthermore, a soft output between horizontal and vertical detection was introduced to improve the performance of serial detection [24].  
Because the VA is used to remove 1D interference, the above detection algorithms are modifications of the VA to handle 2D interference. Thus, we can use the estimator to convert 2D interference into 1D interference and apply the conventional VA. For ITI estimation, [PERSON] and [PERSON] used a GPR target to create feedback for a multitrack, multihead system to estimate ITI [25]. To remove the ITI effect from the desired track, an ITI cancellation model using the feedback of sidetrack information was proposed by [PERSON], [PERSON], and [PERSON] [26]. In [18], owing to the asymmetrical target, the authors were able to extract the ITI information. To improve detection on the center track, [PERSON] and [PERSON] designed a multitrack detection technique to estimate the interference from the sidetrack [27]. Recently, [PERSON] and [PERSON] proposed an ITI estimation scheme based on a neural network [28] to achieve interference with high accuracy.  
In this paper, we propose an ITI estimator that exploits 2D VA. First, we considered the sum of product between the signal and the interference as the symbols, which can be detected by 2D VA. After detecting these symbols, we summed the suitable symbols to estimate the interference from the sidetrack. Then, we removed these interferences from the received signal to convert 2D interference into 1D interference. The simulation results show that the ITI information improves the quality of the equalizer output signal and the performance of the BPMR systems.  
The remainder of this study is organized as follows. Section 2 explains the 2D VA for interference estimation. Section 3 presents the proposed detection model. Section 4 presents and discusses the simulations and results. Finally, Section 5 concludes the study.