Recent studies have introduced multi-level recording methods with amplitude 7) , phase 8) , and their combination 9) to record data in HDS. However, compared with the conventional binary modulation code, the multilevel modulation code handles larger quantities of minute signals and suffers from noise in the optical path. Therefore, the resulting low robustness must be taken into consideration. Hence, it is difficult to directly improve the signal-to-noise ratio (SNR) of the reproduced data, as

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... he system becomes more complex with the introduction of the multi-level modulation code and optical elements to handle both the phase and amplitude. As a demodulation method, we previously reported an image recognition method using convolutional neural network (CNN) for HDS 10) . The retrieved data from the HDS are accurately demodulated by the CNN, based on the trained network. Although the CNN demodulation method is effective for multi-level amplitude modulation and binary modulation codes 11) , however, bit errors after the demodulation must be completely removed. Thus, the error correction code is important. Various error correction codes are introduced in the HDS, such as the Reed-Solomon 12) , turbo code 13) , and low-density paritycheck (LDPC) code 14) . Among them, the spatially coupled LDPC (SC-LDPC) code 15) is one of the strongest error correction codes that approaches the Shannon limit, based on the LDPC code 16) . We confirmed that the capability of error correction of the SC-LDPC code outperforms that of the LDPC code in the HDS 17) . This study presents an effective data-decoding method by combining the CNN demodulation and SC-LDPC code to enable a more powerful error correction by using the likelihood information obtained as the output from the CNN. We evaluated the characteristics of the demodulation and error correction method using the reproduced data with numerically added noise. Abstract In this study, we propose an effective data-decoding method for holographic data storage (HDS) by combining convolutional neural network (CNN) and spatially coupled low-density parity-check (SC-LDPC) code. The trained CNN provides output class probabilities and accurately demodulates the reproduced data from HDS. We focus on these probabilities, wherein only the untrainable noise components such as white Gaussian noise remain. These are used for calculating the log likelihood ratio in the sum-product decoding for the SC-LDPC code. We demonstrate an improvement of approximately 10 dB in the required signal-to-noise ratio for an errorfree decoding in numerical simulations.