## 1 Introduction  
Unlike traditional storage methods that rely on binary encoding and magnetic or optical media, holographic data storage (HDS) leverages holography, a three-dimensional imaging technique, to store vast amounts of data in a compact and efficient manner. In HDS, cubic media, including photorefractive crystals and polymers, can store many data pages. Thereafter, when reading the data from the cubic media, a charge-coupled device (CCD) sensor is used to capture the data pages as an image [1]. Thus, two-dimensional (2D) intersymbol interference (ISI), misalignment, blur, and noise are the factors that cause errors in the reading process of HDS systems [2]. To solve these problems, architectures for HDS systems, modulations, detections, and error-correcting codes have been proposed. To modify the structure of HDS, the aperture is optimized according to size [3]. Subsequently, [PERSON] et al. proposed medium defocusing and aperture methods [4]. In [5], [PERSON] et al. proposed a pixel-matching method. For the modulation technique, the authors changed the angle to multiplex multiple pages of data [6]. In [7; 8], the wavelength was used for the modulation. In addition to these studies, the phase code of a reference beam was presented in [9; 10]. To design the detections, a one-dimensional (1D) partial response maximum likelihood (PRML) model was used in [11]. PRML includes two parts: partial response (PR), which is used to estimate the channel, and maximum likelihood (ML), which is used to recover the original signal. In PR,the minimum mean square error (MMSE) algorithm is applied to determine the parameters of the equalizer and target. In ML, algorithms based on trellises are used to find a branch that is similar to the original signal. In [12], as PRML is designed for 1D data, the authors modified the soft output Viterbi algorithm (SOVA) to create a PRML model with 2D SOVA for HDS systems. In 2D SOVA detection, which was first developed by [PERSON] and [PERSON] [13; 14], two 1D SOVAs were combined in a parallel structure. Subsequently, PR was also improved into generalized PR (GPR) by [PERSON] and [PERSON] in [15]. However, in the original scheme, the authors only proposed GPR for 1D data. Therefore, [PERSON] and [PERSON] developed GPR suitable for 2D data in [16]. Because 2D interference consists of intertrack interference (ITI), vertical interference (VI), intersymbol interference (ISI), and horizontal interference (HI), there are two main methods for designing GPR for 2D data. First, we can estimate the 2D GPR and apply 2D detection with high complexity, as described in [16]. Second, ITI or ISI can be removed from the 2D GPR to apply 1D detection, as in [17]. For error-correcting codes, researchers proposed the 8/10 modulation codes in [18]. These codes can avoid the isolated patterns causing the detection errors in HDS systems. Recently, machine learning (ML) and deep learning (DL) have been widely used in several fields. Similar to object detection [19; 20] and image processing [21; 22], ML and DL have been applied to storage systems. In addition, a convolutional neural network (CNN) was utilized to predict noise as the extrinsic information, which was supplied to the Bahl-Cocke-Jelinek-Raviv (BCJR) detector [23]. With the advantages of ML and DL, a recurrent neural network (RNN) is applied to many scientific fields as in [24; 25; 26]. Therefore, in this paper, we proposed a detection model using an RNN to improve the ISI and ITI estimators. These estimators were designed according to a parallel structure. In the proposed model, we used the 2D GPR target in [16] to estimate the channel coefficients. The simulation results showed that the proposed model could improve the bit error rate (BER) performance compared to those of the previous studies. This study has the following contributions:  
* A RNN was applied to HDS systems. * The RNN was designed to achieve the optimized structure of ISI or ITI estimators. * Analysis of the RNN equalizer to estimate ISI and ITI is presented.