In ultra-high areal density magnetic recording systems such as bit patterned media recording (BPMR) system, the width of a reader is expected to be relatively wider than the track pitch, thus, it will detect the magnetic field from the main track as well as those from the adjacent track which in turn resulting severe inter-track interference (ITI) effect on the readback signal. In the literature, multi-track joint detection techniques using array reader (AR) have been proposed to tackle ITI problem in future high areal density (AD) system [1]-[4] because it can provide a significant performance gain by processing multiple readback signals concurrently at the expense of high complexity. Most of researches focus on the data recovering from the single track or the number of tracks less than or equal to the number of readers while ITI effect from the sidetracks is alleviated. Considering the readback signal contains the significant contributions from the adjacent tracks, the system can generate the estimated data sequences not only from the main tracks but also from their adjacent tracks by employing the multi-track joint detection technique and AR. Therefore, in this paper, we propose a multitrack joint equalization and detection technique for a high AD magnetic recording system to recover the recorded data on four consecutive tracks (two tracks directly under the readers and two immediate sidetracks) by processing two readback signals from an array of two-reader. Given that each readback signal contains the substantial contributions from the sidetracks, we expect to achieve the estimated data from the sidetracks with the acceptable reliabilities for further decoding process. To reduce the detector's complexity, we also propose to use a multi-track Viterbi detector using a simplified trellis with parallel branches to recover data on the sidetracks. In the simulation model, we consider a discrete high areal density BPMR system with multi-track multi-head as shown in Fig. 1. The system is a two-head four-track system (2H4T) in which the data from four consecutive tracks, i.e., $a_{{1,} {k}}, a_{{2,} {k}}, a_{{3,} {k}}$ and $a_{{4,} {k}}$ are recovered by processing the readback signals, i.e., $r_{{2,} {k}}$ and $r_{{3,} {k}}$ from the array reader assuming that the centers of two head are aligned those of $2 ^{nd}$ and $3 ^{rd}$ track. To generate each readback signal, we use a two-dimensional (2-D) BPMR channel matrix with size of 5x3 and its coefficients are computed by a 2-D Gaussian pulse response using the parameters of areal density 4 Tb/in $^{2}$ from [4]. In the model, the readback signal, $r_{{2,} {k}}$ has the contributions mainly from the data on the $2 ^{nd}$ track, $a_{{2,} {k}}$ as well as partially from the data on the $1 ^{st}$ and $3 ^{rd}$ tracks, $a_{1,k}$ and $a_{3,}($ insignificantly from the 0 and $4 ^{th}$ track). Similarly, the readback signal, $r_{{3,} {k}}$ contains the contributions from the data on the $2 ^{nd}, 3 ^{rd}$ and $4 ^{th}$ track, $a_{{2,} {k}}, a_{{3,} {k}}, a_{{4,} {k}}$. In the equalization system, we employ two (2-D) equalizers, I and II, with size of 3x5 and two special (2-D) generalized partial response (GPR) targets, I and II, with size of 3x3, $G_{1} =[0, g_{1,2}$, 0; $g_{2,1}, g_{2,2}, g_{2,3}; g_{3,1}, g_{3,2}, g_{3,3}]$ and $G_{2} = [ g_{1,1}, g_{1,2}, g_{1,3}; g_{2,1}, g_{2,2}, g_{2,3}$; 0, $g_{3,2}$, 0] and they are designed using the minimum mean squared error (MMSE) method. Notice that some coefficients of target are set into zero aiming at reducing the trellis's complexity. The two readback siganls are sent to the system. Assuming that the system is well synchronized and no frequency offset, the signal sequence is the difference between two readback signals, i.e., $r_{{2,} {k}}$ and $r_{{3,} {k}}$. Assuming the sequence ${ r_{{2,} {k}} - r_{{3,} {k}}}$ contains the contributions of the data on all four tracks, it is also fed to both equalizers as shown in Fig.1(a). Finally, the equalized signals $d_{{2,} {k}}$ and $d_{{3,} {k}}$ are processed in the multi-track joint Viterbi detector to generate the estimated data from four tracks. For the detector, the states and input symbols in trellis are considered with only the data, $a_{{2} {,k}}, a_{{3,} {k}}$, thereby resulting only 16 states and 4 outgoing branches at each state. To recover the sidetracks' data, $a_{{1,} {k}}, a_{{4,} {k}}$ are considered as parallel branches between each state transition as shown in Fig. 2(a) [5]. In Viterbi algorithm, the branch with the minimum metric value among all parallel branches is selected as the survival path. To compare the proposed (2H4T) system, we consider a multi-track system employing a four-reader array (4H4T) in Fig.1(b). In this system, we consider a multi-track joint Viterbi detector employing a trellis with 256 states and 16 branches as a full-fledged system. The performance comparison of proposed 2H4T multi-track system and 4H4T multi-track system is shown in Fig.2(b). When we study the BER performance of both systems for recovering the on the center $2 ^{nd}$ and $3 ^{rd}$ tracks, $a_{{2,} {k}}, a_{{3,} {k}}($ solid lines), the proposed method is significantly inferior to the 4H4T system as we expected. However, the proposed method is outperformance over the latter for the performance recovering the data on the outer $1 ^{st}$ and $4 ^{th}$ tracks, $a_{{1,} {k}}, a_{{4,} {k}}($ dotted lines). Notice that the BER performances of the center and outer tracks are very similar in the proposed method. The performance of proposed method is not as good as the full-fledged system, but it can generate the estimated data sequence from the sidetracks with the acceptable reliabilities and then they can be improved by using a robust channel coding system.
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