# Tabu Search Aided Multi-Track Detection Scheme for Bit-Patterned Media Recording
## 1 Introduction  
Bit-patterned media recording (BPMR) is one of the promising technologies that is considered to attain an areal density of up to 4 Tb/in\({}^{2}\)[1; 2]. In BPMR, high areal density is enabled by reducing the inter-symbol and inter-track distances. Therefore, inter-track interference (ITI) in the cross-track also occurs in addition to inter-symbol interference (ISI) in the along-track. As the recording density increases, the performance degradation caused by ITI becomes more severe. Therefore, robust signal processing techniques to mitigate ITI are essential [1].  
Various detection schemes were introduced for high density BPMR channels [3; 4; 5]. The single-track detection using a one-dimensional (1D) equalizer with a 1D generalized partial response (GPR) target was proposed in [3]. By using the 1D equalizer and 1D GPR target, the performance of the single-track detection operating on four states and eight branches is severely degraded. To employ a two-dimensional (2D) GPR target, the joint-track detection was proposed in [4] by applying the 1D equalizer with the 2D GPR target. For the complexity reduction in the detectors using the 2D GPR target, the joint-track detection used a reduced-state trellis diagram operating on four states and eight branches. Despite considering the 2D GPR target, the performance of the joint-track detection is also severely degraded due to the reduced-state trellis diagram [4] where ITI is strong. To overcome the performance degradation, the simplified multi-track detection was proposed in [5]. The simplified multi-track detection with the reduced-state trellis diagram achieves a substantial gain by using a priori information of the side-tracks from the single-track detection, since a priori information contributes to the reliability improvement of the branchmetric. However, as the recording density increases, the performance of the simplified multitrack detection is gradually degraded, since the reliability of a priori information from the single-track detection is seriously reduced. Therefore, an efficient detection scheme for improving the reliability of side-track information should be studied for high density BPMR systems.  
In this paper, we propose a tabu search (TS) aided multi-track detection scheme for BPMR systems to enhance the performance of the simplified multi-track detector by improving the reliability of side-track information. The proposed detection scheme using the 2D equalizer with the 2D GPR target adopts the simplified multi-track detector using the simplified detection algorithm in [4], uses a priori information as in [5], and employs a reliability test and a TS detector. That is, the proposed detection scheme additionally considers the reliability test and TS detector to the simplified multi-track detection in [5]. To improve the reliability of side-track information, the TS detector is conducted for bits with low reliability in the side-tracks in the proposed detection scheme, where bits with low reliability are selected by the reliability test. For minimizing the increase in complexity, the TS algorithm [6; 7], which is a low-complexity local search procedure, is considered for the additional detector, and the TS detector works for a very small number of bits with low reliability. This improved reliability of side-track information from the TS detector is employed as a priori information in the simplified multi-track detection in [5] for the main-track data. For the reliable bits, the a posteriori probabilities (APPs) computed by the single-track detection are delivered to the simplified multi-track detector. Then, the simplified multi-track detector detects the main track data by using a priori information from the outputs of the TS or single-track detectors for the side-tracks. By using a priori information with improved reliability, the proposed detection scheme with slightly additional complexity has the significantly enhanced performance for high density BPMR systems.