# Simplified Two-Dimensional Generalized Partial Response Target of Holographic Data Storage Channel
## 1 Introduction  
Due to the demand for storage increasing at a high rate, devices with high capacity and fast transfer are a matter of common interest. At present, semiconductor memories [1] and magnetic hard disk drives [2] are widely used in many devices. However, unlike semiconductor memories and magnetic hard disk drives, holographic data storage systems can read out 2D data page bits at the same time [3]. Therefore, holographic data storage achieves a high data transfer rate. In addition, many researchers have proposed methods to multiplex multiple pages of data by changing the angle [4], wavelength [5, 6], or phase code [7, 8] of the reference beam. This helps to improve the capacity of the HDS and meet the requirements of greater capacity and fast transfer [3, 9].  
Therefore, the holographic data storage (HDS) system is a promising candidate for mass-storage devices. In HDS systems, the data are converted into the beam and stored on the holographic medium. Then, to read back the data, we use the reference beam to reconstruct the beam from the holographic medium. The image of the data is captured by a charge-coupled device (CCD). The data page suffers from blurring effects; therefore, the read-back data always face two serious problems. One is inter-page interference (IPI) between the pages, and another is two-dimensional (2D) inter-symbol interference (ISI) that appears on the data page of the HDS systems. To avoid IPI, the numbers of one and zero pixels must be almost equal on each page [10]. To implement this, we can use balanced coding, which ensures the intensity level of each page is the same [11]. Among these factors, 2D ISI is regarded as the main causative reason. To combat ISI, based on the one-dimensional (1D) partial response maximum likelihood (PRML) detection scheme in [12], [PERSON] and [PERSON] proposed the 2D soft-output Viterbi algorithm (SOVA) as the 2D detection for the HDS systems [13]. Then, the 2D SOVA is improved and applied to the bit-patterned media recording (BPMR) channel [14, 15]. In 2D SOVA, the authors use two parallel 1D PRML to remove the 1D interference from the horizontal and vertical directions. In addition, [PERSON] and [PERSON] [16] propose a general partial response (GPR) target, which achieves better performance than PRML. Then, the GPR target is developed and utilizedin [17; 18; 19; 20; 21; 22]. However, the authors only estimate 1D interference (i.e., designing a 1D GPR target) to avoid the 2D detection in [16]. In [22], to handle 2D interference, the authors introduce the estimator interference with a parallel structure to convert 2D interference into 1D interference. Although achieving high performance, the model in [22] has high complexity. In [23], the authors propose the decision feedback equalizer (DFE) to recover the original from the received signal, which is distorted by the 2D ISI. The DFE model is a simple method to solve 2D ISI, but the performance of the DFE model is unsatisfactory because of the simple detection scheme. Therefore, in this paper, we improve the GPR target for 2D interference. From the estimated 2D GPR target, we propose a simple method to decompose 2D ISI into two serial 1D vertical direction ISI and 1D horizontal direction ISI. From here, we can use the serial detection [21] to recover the original data from the HDS systems. In simulation, the result shows that our proposed model achieves a gain of 2.5 dB at the BER \(10^{-3}\) compared to the 1D GPR target in [16].  
In the remainder of this paper, we explain the 2D GPR target and serial detection in Section 2. In Section 3, we present the proposed model. Section 4 presents and discusses the simulations and results. Finally, in Section 5, the conclusions are drawn.