# A Nonlinear Convolutional Neural Network-Based Equalizer for Holographic Data Storage Systems
## 1 Introduction
Because PRML and SOVA are designed to handle one-dimensional (1D) ISI, the modified model in [14] is necessary to adapt to the 2D ISI of HDS systems. With an outstanding ability to reduce 2D ISI, PRML and 2D SOVA are also applied in BPMR systems. A nonlinear equalizer in [15] is proposed to improve the BER performance of BPMR systems. The equalizer is an important part of the development of PRML. In addition, in [16], the authors proposed a 2D SOVA for a 2D PR target using dual equalizers: one evaluates the corrected signal, and the other estimates the binary signal. In [17], to develop the 2D SOVA, the authors designed the iterative algorithm for 2D SOVA. Subsequently, based on the  
Figure 1: Structure of an HDS system. generalized PR (GPR) target, as specified in [18], [PERSON] and [PERSON] proposed serial detection and a maximum a posteriori (MAP) detection algorithm to improve BER performance [19]. For HDS systems, in [20], the authors proposed a modified 2D SOVA with 2D PR target to reduce 2D ISI. In [5], a variable reliability factor is supplied to 2D SOVA algorithm to improve the BER performance of HDS systems. Based on 2D SOVA, [PERSON] et al. introduced data page reconstruction method as the image processing method for HDS systems to mitigate 2D ISI and improve the performance of 2D SOVA detection [21]. In addition to using the Viterbi algorithm, many researchers proposed methods in image processing for the detection of HDS systems. In [22], [PERSON] et al. presented an image upscaling method to reduce bit errors caused by Nyquist apertures. To improve the BER in HDS systems, [PERSON] et al. applied an iterative method for an image filter to HDS systems [23]. In [24], [PERSON] et al. introduced an image filter based on primary frequency analysis to improve the BER in an HDS system. Finally, in [25], [PERSON] et al. presented low-complexity pixel detection for images to reduce misalignment and ISI in HDS systems. Recently, deep learning (DL) and machine learning (ML) have been applied in various fields, such as object detection [26; 27], image processing [28; 29], and speech processing [30; 31]. In the field of data storage systems, multilayer perceptrons (MLPs) are used to predict noise and decode modulation codes in BPMR systems [32]. In [33], 1D Viterbi detection is supplied with extrinsic information by the MLP to create an iteration algorithm and improve the BER performance of BPMR systems. In addition, in [34], to improve the Bahl-Cocke-Jelinek-Raviv (BCJR) detector, a convolutional neural network (CNN) is used to exploit noise as extrinsic information. To remove the noise in HDS systems, a CNN is proposed and applied to classify data pages for HDS systems [35]. In addition, with similarity to image data, an autoencoder-based tool is applied to HDS systems in [36]. In addition, DL and ML models were used to demodulate the received data in HDS systems. Firstly, in [37], the authors proposed a data demodulation method based on a CNN structure. Because modulation is like codeword classification, this work is suitable for the CNN structure, which achieves high accuracy in classification. Then, [PERSON] et al. developed CNN demodulation by using a complex amplitude as established in [38]. In [39], the authors used a CNN to recognize the pattern of multi-level data in HDS systems. Using the benefits of the GPR target, equalizer, and DL, in this study, we proposed a CNN-based equalizer to nonlinearly convert the received signal into the desired signal in HDS systems. The structure of the CNN was optimized to be suitable as an equalizer to make the received signal close to the desired target signal. For the structure of the CNN, we surveyed straight and branch structures with skip lines. These structures were applied to the current models (ResNet and GoogLeNet) to obtain a good performance. With skip lines, the CNN structure avoids a vanishing gradient. Therefore, in the training process, the CNN model can be close to the global optimized point and improve the BER performance of the equalizer.