Frequency expanded non-interferometric phase retrieval for holographic data storage

Phase retrieval based on deep learning with bandpass filtering in holographic data storage

A phase retrieval method based on deep learning with bandpass filtering in holographic data storage is proposed. The relationship between the known encoded data pages and their near-field diffraction intensity patterns is established by an end-to-end convolutional neural network, which is used to predict the unknown phase data page. We found the training efficiency of phase retrieval by deep learning is mainly determined by the edge details of the adjacent phase codes, which are the high-frequency components of the phase code. Therefore, we can attenuate the low-frequency components to reduce material consumption. Besides, we also filter out the high-order frequency over twice Nyquist size, which is redundant information with poor anti-noise performance. Compared with full-frequency recording, the consumption of storage media is reduced by 2.94 times, thus improving the storage density.

Phase retrieval in holographic data storage by expanded spectrum combined with dynamic sampling method

Phase retrieval in holographic data storage by expanded spectrum combined with dynamic sampling method is proposed, which serves to both reduce media consumption and to shorten the iterative number of phase code retrieval. Generally, high-fidelity phase retrieval requires twice Nyquist frequency in phase-modulated holographic data storage. To increase storage density, we only recorded and captured the signal with Nyquist size and used the frequency expanded method to realize high-fidelity phase retrieval. In the decoding process, the iterative Fourier transform algorithm is used to retrieve the phase information of the reconstructed beam. The expanded spectrum is dynamically sampled, which can provide a faster convergence path for the phase retrieval. We aimed to demonstrate the possibility of integrating various methods on the Fourier domain and providing a potential way to improve the performance of holographic data storage systems. The simulation and experimental results proved the combination of processing methods in frequency spectrum was benefit.

Exploiting data compression to improve reliability of phase-modulated holographic data storage

Due to the interference of complex noise in holographic channels and the limitation of phase retrieve algorithms, the reliability of phase-modulated holographic data storage (PHDS) is seriously threatened, especially for multi-level phase modulation. A method for improving data reliability of PHDS is proposed by applying lossless data compression and low-density parity-check (LDPC) codes, which can eliminate data redundancy and correct errors effectively. We allocate the space saved by compression to store more LDPC parity bits and develop a method to determine the LDPC code rate and a method to manage the free space. Our method does not require the characteristics of the reconstructed phase distribution, which simplifies the statistical analysis and calculation. Simulation and experimental results demonstrate that our method greatly decreases the bit error rate (BER) and decoding iterations, and boosts the decoding success probability. For instance, when the phase error rate is 0.029 and the compression rate is 0.6, our method reduces the BER by 87.8%, the decoding iterations by 84.3%, and improves the decoding success probability by 93%. Our method enhances both data reliability and storage efficiency in PHDS.

Fast phase error correction with reference beam-assisted LDPC coding for collinear holographic data storage

Low-density parity-check (LDPC) coding is a significant technique for ensuring data reliability in phase-modulated holographic data storage. To accelerate LDPC decoding, we design reference beam-assisted LDPC coding for 4-level phase-modulated holography. The reliability of a reference bit is higher than that of an information bit during decoding because reference data are known during recording and reading processes. By considering the reference data as prior information, the weight of the initial decoding information (i.e., log-likelihood ratio (LLR) information) of the reference bit is increased during LDPC decoding. The performance of the proposed method is evaluated through simulations and experiments. In the simulation, compared with the conventional LDPC code with a phase error rate (PER) of 0.019, the proposed method can reduce bit error rate (BER) by 38.8%, uncorrectable bit error rate (UBER) by 24.9%, decoding iteration time by 29.9%, the number of decoding iterations by 14.8%, and improve decoding success probability by 38.4% approximately. Experimental results demonstrate the superiority of the proposed reference beam-assisted LDPC coding. The developed method can significantly decrease the PER, BER, the number of decoding iterations, and decoding time by using the real captured images.

Decision-free downsampling method assisted via channel-transfer information to improve the reliability of holographic data storage systems

A decision-free downsampling method (DFDS) assisted by channel-transfer information for phase-modulated holographic data storage is proposed. DFDS is used to address the issue of the accumulation of decision errors induced by traditional downsampling. The issue degrades the downsampling accuracy. DFDS comprises two functional segments: acquiring the channel-transfer information offline and performing decision-free downsampling online. With the assistance of the channel-transfer information, DFDS uses Bayesian posterior probabilities instead of traditional decision results to avoid the accumulation of decision errors and achieve more accurate downsampling. The simulation and experimental results show that DFDS reduces the phase error rate, thereby improving the reliability of the holographic data storage system.

Improving the data reliability of phase modulated holographic storage using a reliable bit aware low-density parity-check code

Phase modulated holographic storage offers superior storage capacity and a longer life span compared with other storage technologies. However, its application is limited by its high raw bit error rate. We aimed to introduce low-density parity-check (LDPC) codes for data protection in phase modulated holographic storage systems. However, traditional LDPC codes can not fully exploit data error characteristics, causing inaccurate initial log-likelihood ratio (LLR) information, which degrades decoding performance, thus limiting the improvement degree of data reliability in phase modulated holographic storage. Therefore, we propose a reliable bit aware LDPC optimization method (RaLDPC) that analyzes and employs phase demodulation characteristics to obtain reliable bits. More accurate initial LLR weights are assigned to these reliable bits. Hence, the optimized initial LLR can reflect the reliability of the demodulated data more accurately. Experimental results show that RaLDPC can reduce the bit error rate by an average of 38.89% compared with the traditional LDPC code, improving the data reliability of phase modulated holographic storage.

Improving reliability using phase distribution aware LDPC code for holographic data storage

The iterative Fourier transform (IFT) algorithm is an effective solution for phase retrieval in phase-type holographic data storage systems, but introduces a higher phase error rate. As a result, data reliability becomes a significant issue. In this paper, to improve reliability and decrease decoding latency, we propose a phase distribution aware low-density parity-check (LDPC) code [called point data abstraction library (PDAL)] with outstanding error correcting capability. After experiencing IFT, we first investigate the phase distribution characteristics and find that the adjacent phase distribution is more likely to cross, resulting in higher phase shift percentages. Then, using phase distribution, PDAL optimizes LDPC codes with higher precision decoding information by dynamically applying the phase threshold based on the phase error rate. When the phase error rate is 0.04, the bit error rate, decoding iteration times, and decoding failure rate are all reduced by 51.5%, 26.9%, and 51.8% on average, respectively, compared with traditional LDPC code without exploiting phase distribution. PDAL, which is an efficient and practical error correction approach for phase-modulated holographic data storage, can improve data reliability by boosting error correction performance.

Double-frequency grating shearing interferometer with built-in phase-shifting function for robust multi-level phase retrieval

In this paper, we propose and demonstrate a novel interferometer and signal process to retrieve two-dimensional signals with multilevel phases. The interferometer is based on a shearing interferometry with double-frequency grating, and phase-shifting interferometry is derived as a built-in function of the lateral displacement of the grating. The interferometer not only retrieves the multilevel phase signals but also eliminates slow-varying phase errors wherever they occur. Owing to the common path algorithm, the new interferometer is more robust in dynamic circumstances for optical testing and data processing. We propose a pre-integral signal process for two-dimensional (2D) data processing to prevent post-phase-integral due to shearing interferometry. The simulation and experiment showed that the proposed interferometer with a pre-integral process has various advantages in signal processing for multilevel phase retrieval, and will be useful for higher data rates in optical data storage and free-space communication.

Phase-distribution-aware adaptive decision scheme to improve the reliability of holographic data storage

Owing to their high storage density and long storage life, holographic data storage (HDS) technologies are viable options for mass cold data storage in the era of big data. Phase-modulated holographic data storage (PHDS) is a promising implementation of HDS. However, because of complex noise in the storage channel, many errors remain after phase demodulation. This study investigates the phase decision in the data-reading stage of PHDS. We propose a phase-distribution-aware adaptive (PDAA) decision scheme to address the inaccurate thresholds in traditional phase decision schemes. The PDAA decision scheme can determine more accurate decision thresholds based on the phase distribution characteristics of each reconstructed phase data page and adaptively match different decision thresholds to each phase data page. The experimental results show that when compared to the traditional decision scheme, the PDAA decision scheme can significantly reduce the phase error of data pages, improving the data reliability of holographic storage.

Common-path angular-multiplexing holographic data storage based on computer-generated holography

An unconventional angular-multiplexed recording technique is proposed for holographic data storage based on a computer-generated hologram (CGH) technique. While general angular-multiplexed recording techniques require a Mach-Zehnder interferometer to record data pages as volume holograms, the proposed method records ones with a common-path configuration with the help of a CGH technique, which prevents the optical setup from being bulky. In the proposed method, the CGH reconstructs signal and reference beams simultaneously, and these beams interfere in a recording medium. By changing the diffraction angle of the reference beam from the CGH, angular multiplexing is accomplished with a common-path optical setup without additional optical elements. Multiplexed recording of four data pages is demonstrated in a proof-of-principle experiment, which indicates the feasibility of the proposed method.