## 1 Introduction  
For most conventional magnetic storage systems, the superparamagnetic limit is a significant obstacle to increasing the areal density (AD). To overcome the problem and extend the AD to more than 1 terabit per square inch (Tb/in\({}^{2}\)), bit-patterned media recording (BPMR) has become a candidate for the next generation of magnetic storage systems [1]. In addition, BPMR has such advantages as improved thermal stability, a decreased nonlinear transition shift, and reduced transition noise [2]. Because of these advantages, BPMR can satisfy the demand for storing a tremendous quantity of data in the information age. However, as the distances of down-track bit period \(T_{x}\) and cross-track pitch \(T_{z}\) for achieving high AD become closer, two-dimensional (2D) interference, which comprises intersymbol interference (ISI) and intertrack interference (ITI), is increased [3, 4]. In addition, BPMR has unavoidable problems, such as track misregistration (TMR) and media noise caused by imperfect fabrication. According to the lithography method adopted, bit-patterned media (BPM) structures can be placed in a regular or staggered array BPM layout, as shown in Figure 1. When the islands are placed hexagonally in the staggered array, the bit error rate (BER) performance when the staggered array is used is better than when the regular array is used, because of reduced ITI [5, 6].  
To eliminate the 2D interference that degrades system performance, various schemes have been proposed for BPMR, such as signal detection methods, error control codes, and modulation codes. To address the 2D interference problem and help detect the input data, the partial response maximum likelihood (PRML) method has been employed [7]. This is applied to data storage systems where the channel response is equalized to a partial response (PR) pulse shape and a maximum likelihood (ML) sequence detector. For 2D data storage systems, a 2D equalizer and detection schemes have been proposed [6, 8]. To ensure the reliability of data storage systems, error control codes, such as the low-density parity check (LDPC) code, are required. They considerably improve system performance [9, 10]. In a previous study [10], a proposed product code that consists of inner and outer code using a LDPC exhibited better BER performance than the LDPC code alone. To prevent error patterns that cause 2D interference, such modulation codes as 5/6 and 9/12 modulation have been proposed for BPMR [11; 12]. Because data storage systems cannot retransmit data, unlike typical communication systems with such retransmission schemes as automatic repeat requests, strict requirements for a low probability of decoding failure and a high code rate should be met [9].  
In this work, a 7/10 modulation code for staggered BPMR is proposed. To reduce ITI effectively, the proposed code focuses on the ITI problem rather than the ISI problem, because the effect of ITI is greater than that of ISI in the BPMR [13]. Moreover, because the Hamming distance among codewords is at least 2 or more, the decoding capability is improved.  
The remainder of this paper is organized as follows. In Section 2, the staggered BPMR channel model and PRML detection for staggered BPMR are explained. In Section 3, the proposed 7/10 modulation code is introduced. The simulation and results are discussed in Section 4. Section 5 provides conclusions.