###### Abstract
Numerous solutions have been proposed in the literature to tackle 2D interference and media noise during signal processing in BPMR systems. For instance, a joint detection and decoding technique has been proposed that combines the maximum a posteriori (MAP) detection algorithm with low-density parity-check (LDPC) decoding [12]. The MAP detector enhances detection by utilizing extrinsic information derived from LDPC decoding. Additionally, graph neural networks have replaced the traditional sum-product algorithm in LDPC decoding, offering improved performance compared to conventional methods. Furthermore, the extrinsic information predicted by the estimator is employed in serial MAP detection for holographic data storage systems [13], which is an effective approach for addressing 2D interference. Changing the medium configuration is one such technique. Notably, research in [14, 15, 16] suggested that utilizing staggered island arrays, instead of rectangular island arrays, can enhance the bit-error rate (BER) performance at the same AD. Staggered island arrays have been proven to be effective in mitigating the impact of ITI caused by the presence of adjacent tracks. Moreover, an array-reader magnetic recording (ARMR) is a signal processing technique that has been implemented in BPMR systems [17, 18, 19]. ARMR involves the simultaneous processing of signals from multiple readers, which allows for robust information recovery in ultrahigh AD BPMR systems when compared with a single-reader system [20]. The multiple readers yield multiple readback signals that correlate with the interference, thus improving the detection process. Furthermore, dual-reader ARMR has been utilized to evaluate the skew-induced variation in cross-track separation for increasing the recording performance [21]. The one-dimensional (1D) partial-response maximum-likelihood (PRML) technique is an essential and comprehensive approach that characterizes the signal's partial response,adapts to changing signal conditions through adaptive equalization, utilizes the soft-output Viterbi algorithm (SOVA) for efficient detection, and can incorporate error correction coding to enhance data reliability. It is an essential technique that plays a vital role in ensuring accurate and reliable data retrieval in magnetic recording. In addition, improving the soft information or log-likelihood ratio (LLR) generated from the SOVA detector is also proposed to enhance the overall system performance. For instance, the encoding criteria of a modulation encoder are utilized to improve the LLRs before sending them to the decoders [22; 23]. Specifically, the encoding condition is used as the criterion for flipping the obtained LLRs: as a result, the LLRs can be significantly enhanced, improving system performance. Moreover, recent advances in deep neural networks (DNNs) have also revolutionized the approach to signal processing in magnetic recording. The proposed DNN-based detectors in [24; 25; 26] can accurately produce soft-output information, which significantly simplifies turbo decoding. The combination of the DNN-based predictor with conventional detection reveals that it can improve detection accuracy, as suggested in [27; 28]. Furthermore, in [29], DNNs, such as long-short-term memory (LSTM) networks, and supervised learning were also utilized to improve LLR reliability, resulting in better BER performance. Hence, the use of DNNs significantly improves LLR reliability and is a suitable solution for signal processing in ultra-high-density BPMR systems. Additionally, the multilayer perceptron (MLP) is a strong candidate due to its high potential for signal processing in magnetic recording systems. For example, the MLP is used in conjunction with the traditional Viterbi algorithm for iterative signal detection in order to enhance the performance of a BPMR system [30]. In this context, the MLP generates a priori information that aids the equalization process, resulting in improved extrinsic information. This extrinsic information can help mitigate the effects of \(\Pi\Pi\).