###### Abstract  
In the big data era, data are created in huge volume. This leads to the development of storage devices. Many technologies are proposed for the next generation of storage fields. However, among them, holographic data storage (HDS) has attracted much attention and has been introduced as the promising candidate to meet the increasing demand for capacity and speed. For signal processing, HDS faces two major challenges: inter-page interference (IPI) and two-dimensional (2D) interference. To access the IPI problem, we can use balanced coding, which converts user data into an intensity level with uniformly distributed values for each page. For 2D interference, we can use the equalizer and detection to mitigate the 2D interference. However, the often-used equalizer and detection are methods in wireless communication and only handle the one-dimensional (1D) signal. Thus, we can combine the equalizer, detection, and estimator to reduce 2D interference into 1D interference. In this paper, we proposed a combined model using serial maximum a posteriori (MAP) detection and estimator to improve the detection of HDS systems. In our proposed model, instead of using an estimator with the Viterbi algorithm to predict the upper-lower interference (UPI) or left-right interference (LRI) and converting the received signal into 1D ISI, we used the estimator to predict the extrinsic information for serial MAP detection. This preserves the 2D information in the received signal in serial MAP detection and improves the detection of serial MAP detection by extrinsic information. The simulation results demonstrate that our proposed model significantly improves the bit-error rate (BER) performance compared to previous studies. 30 August 202417 December 202425 December 202425 December 202425 December 20  
optical field, as a refractive index variation inside the storage media [8]. Because of storing information as holographs, when the signal is retrieved from HDS, it is disturbed by inter-page interference (IPI) and two-dimensional (2D) interference [9]. To reduce IPI, we can use a balanced code to ensure an equal number of 0 and 1 bits [10]. In 2D interference, the desired signal is affected by horizontal interference (HI) according to the horizontal direction and vertical interference (VI) according to the vertical direction [11]. To solve the 2D interference in HDS systems, a modulation code with non-isolated patterns of codewords or detection techniques can be used. For modulation code, in [12], [PERSON] and [PERSON] introduced 6/8 modulation code in HDS systems. To improve the code rate and reduce the isolated patterns for the codewords, in [13], [PERSON], [PERSON], and [PERSON] proposed a 2D modulation code for HDS systems. In addition, because the interference in bit-patterned magnetic recording (BPMR) is similar to the interference of HDS, we can apply the modulation code in BPMR systems to HDS systems. In [14], [PERSON] and [PERSON] presented 9/12 modulation code to mitigate 2D interference. [PERSON], [PERSON], and [PERSON] proposed 5/6 modulation code to eliminate the patterns that lead to severe ITI [15]. Finally, recently, with development of AI and ML, the combination of modulation code and ML algorithms has also been proposed. In [16], a \(K\)-mean algorithm was used to decode 4/6 modulation code for a BPMR channel. [PERSON] and [PERSON] proposed non-isolated modulation code with a minimum Hamming distance of 3 for BPMR to reduce interference and improve the error correction of BPMR systems. For detection, we used the Viterbi [17] and maximum a posteriori (MAP) [18] algorithms to detect the received signal. However, with the Viterbi and MAP algorithms, we only handle one-dimensional (1D) interference because these algorithms are designed for the 1D signal in wireless communication. Thus, to apply the Viterbi and MAP algorithms to HDS, we need to modify these algorithms to handle 2D signals.