# Soft-Output Detector Using Multi-Layer Perceptron for Bit-Patterned Media Recording
## 1 Introduction  
To match data growth, the capacity of hard disk drives (HDDs) is required to increase. However, shrinking the magnetic grains further and cramming them closer to increase the capacity of the HDD results in the superparamagnetic effects [1]. To overcome these problems and increase areal density (AD) beyond one terabit per square inch (Tb/in\({}^{2}\)), bit-patterned media recording (BPMR) is considered as one of the promising future magnetic storage technologies [2]. Each data bit is recorded on a nano-sized grain or island that is arranged separately. Thus, BPMR can offer advantages such as extending AD to 4 Tb/in\({}^{2}\), simplified tracking, and reduced track-edge noise, transition noise, and nonlinear bit shift [3].  
To achieve a high AD in BPMR, the bit period and track pitch in the down and cross-track direction, respectively, must be reduced. However, the decrease in distances between the islands encourages both intersymbol interference (ISI) and intertrack interference (TII), which disturb signal detection and degrade the BPMR system performance [4]. To alleviate the effects of ISI and ITI, a two-dimensional (2D) equalizer with a one-dimensional (1D) generalized partial response (GPR) target based on a minimum mean square error (MMSE) criterion for a BPMR system has been introduced [5, 6]. Additionally, as ITI is generally more severe than ISI in a BPMR system, modulation coding schemes have been proposed to prevent the occurrence of cross-track patterns such as [\(-\)1, \(+\)1, \(-\)1]\({}^{\text{T}}\) and [\(+\)1, \(-\)1, \(+\)1]\({}^{\text{T}}\)[7, 8].  
In recent years, neural networks (NNs) have been used for equalization, signal detection, and modulation coding for data storage systems. [PERSON] et al. proposed a turbo decoder scheme for a 1D HDD, which consists of a Bahl-Cocke-Jelinek-Raviv (BCJR) detector and a deep neural network (DNN) media noise predictor [9]. The proposed BCJR-DNNturbo detector exhibited better performance than a pattern-dependent noise prediction detector. In [10], a detection scheme with a track misregistration (TMR) estimator based on multi-layer perceptrons (MLPs) was proposed for BPMR systems. Because the estimated TMR by the MLP-based TMR estimator helps the MLP-based data detector to detect the received signal, the proposed scheme exhibits a better bit error ratio (BER) performance than a conventional partial response maximum likelihood (PRML) detector. For a shingled magnetic recording system, a log-likelihood ratio (LLR) modulator based on an NN was developed to improve the reliability of the decoder output and recalculate the LLR value [11]. The LLR modulator, which was designed to be used in conjunction with a low-density parity check code, improves iterative decoding performance. In [12], a convolutional NN (CNN) modulation decoding scheme was investigated for holographic data storage systems. It was shown that the CNN-based demodulator decreases the number of demodulation errors compared to a hard decision method.  
Herein, we introduce a soft-output detector using multi-layer perceptron for a BPMR system to predict reliable information. For the design of the MLP detector, an identity (linear) function and binary cross-entropy are used as an activation function in the output layer and a loss function, respectively, to predict information reliability similar to the soft decision value. This study investigates the received probability distributions out of the detectors and compares the performance of various versions against a conventional detector.  
The rest of the paper is organized as follows. In Section 2, we introduce the BPMR channel model. Section 3 explains the design of a soft output MLP detector. Section 4 presents and discuss the simulation results. Finally, Section 5 concludes the paper.