# A Nonlinear Convolutional Neural Network-Based Equalizer for Holographic Data Storage Systems
## 1 Introduction  
In the current era of extensive data collection across various domains and devices, the need for substantial storage solutions has become apparent. According to the prediction of the International Data Corporation (IDC), the global datasphere will achieve 163 ZB (1 ZB = 10\({}^{9}\) TB) by 2025 and 2142 ZB by 2035 [1]. To address this increasing demand, several technologies have been proposed such as floating-gate memory, bit-patterned media recording (BPMR), heat-assisted magnetic recording (HAMR), deoxyribonucleic acid (DNA)-based storage systems, and holographic data storage (HDS) systems. Unlike semiconductor memories and magnetic hard disk drives, HDS systems can read out 2D data page bits at the same time, HDS can achieve a high data transfer rate. For BPMR, the data is stored on magnetic islands. When writing or reading the signal from BPMR, we need a physical mechanical system. Therefore, the data transfer rate is slow because of the limitation of motor movement speed. HAMR is similar to the BPMR but differs in the writing process. The disk material is heated during writing. This leads to being more receptive to magnetic effects and allows writing to much smaller regions (and much higher levels of data on a disk). Finally, a DNA storage system has been proposed to extend the capacity of storage systems. However, to access data in DNA, we need to implement chemical reactions to synthesize or analyze DNA. Therefore, the data transfer rate in DNA is very slow and inconvenient in commercialization. From the above disadvantages, we can see that HDS became a promising contender owing to its potential to achieve both higher data density and rapid access rates [2]. In HDS systems, to store digital data, two coherent laser beams are intersected to create optical interference patterns that present the information of digital data stored in the cubic media [3]. Figure 1 shows the structure ofan HDS system. User data are modulated into a spatial light modulator (SLM), similar to two-dimensional (2D) data pages. The object beam is projected through the SLM. This creates images of the ON and OFF pixels in the storage media. The reference beam is then interfered with the images of the object beam in the cubic media. The materials used in storage media are photorefractive polymers and crystals. Therefore, these interferences are retained in the cubic media as physical phenomena. This is the writing process of HDS systems. To retrieve the data, the reference beam is used to project onto the storage material. The interference patterns in the cubic media are illuminated to create a reconstructed beam as the object beam that provides user data information. A charge-coupled device (CCD) sensor is used to capture the images of the reconstructed beam. With the images on the CCD, HDS systems face the major challenge of 2D intersymbol interference (ISI) that includes horizontal interference (HI) and vertical interference (VI). Furthermore, with multiplexing modulation methods, many data pages can be simultaneously stored in the storage media. This leads to inter-page interference (IPI). To reduce IPI, in [4], guided scrambling (GS) is proposed to balance the number of \"1\"s and \"0\"s in a 2D array. In addition, the images on the detector array can be deviated from the sensor; this is called a misalignment. Beam blurring also reduces the bit error rate (BER) performance of HDS systems [5]. To mitigate these factors and improve the BER performance of HDS systems, we can use optimized structures of HDS systems, as in [5; 6; 7]. Modulation methods are also introduced in [8; 9; 10; 11] to reduce the crosstalk in HDS systems. In addition, error-correcting modulation codes in [12] are created to avoid isolated patterns in HDS systems, correct the error bits, and improve the BER performance with a high code rate. Then, using the theory of partial response maximum likelihood (PRML) detection, as specified in [13], a 2D equalizer and soft output Viterbi algorithm (SOVA) is proposed in [14] to reduce the 2D ISI in HDS systems.