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Abstract
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.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The development of storage technology must meet the increasing demands of high data storage capacity and data life cycles [1]. Owing to their high theoretical storage density and long service life, holographic data storage (HDS) technologies are regarded as an appropriate choice for massive cold data storage in the era of big data [2–5]. HDS is a three-dimensional volume storage technology that records data using light [6]. Before saving data, user data, such as images, sounds, and documents, must be modulated into the phase or amplitude information of light. Compared with amplitude-modulated holographic data storage (AHDS) [7–11], phase-modulated holographic data storage (PHDS) [12–16] has higher code rates and can fully exploit the benefits of large storage capacity. Nevertheless, PHDS has an unavoidable flaw. An image detector, such as a complementary metal-oxide-semiconductor transistor (CMOS) camera, cannot directly receive phase information while reading data. To obtain phase information, phase reconstruction methods such as the iterative Fourier transform algorithm (IFA) [5,17–19] must be used. However, owing to the limitations of the phase reconstruction method and the influence of complex noise in the holographic storage channel, serious errors occur in the reconstructed phase data, severely impeding the practical application of PHDS.
Several efforts have been made to reduce the phase error of PHDS. Ke et al. proposed a phase pair coding method based on an unequal interval phase [20], which can ameliorate the phase ambiguity problem and thus reduce phase errors. The dynamic sampling iterative phase retrieval method selectively obtains the Fourier intensity distribution range and effectively eliminates high-frequency noise [21], thereby reducing phase errors. The interpixel crosstalk characteristics are used to aid phase data detection, improving the anti-noise capability and reducing phase errors [22]. Hao et al. investigated the effect of the amplitude weight of the reference beam on phase errors [23]. To reduce the phase error caused by the rotation or dislocation of a volume holographic storage disc during the reading process, the stored signal is preprocessed by the phase integral along the shearing direction [24]. These contributions reduce the phase error rate (PER) of PHDS to varying degrees. Nonetheless, the PER must be further reduced to meet the data availability requirements.
Note that these previous studies optimized various aspects of recording and reading in PHDS. However, an optimization scheme for the phase decision has not been studied. The accuracy of the phase decision determines the accuracy of reading data directly. Unfortunately, the traditional decision scheme does not fully consider the characteristics of the reconstructed phase data; thus, it is inaccurate. Therefore, it is necessary to design a more optimized and accurate decision scheme to reduce the PER and improve the data reliability of PHDS.
In this study, we propose a phase-distribution-aware adaptive (PDAA) decision scheme. We begin with a preliminary experiment to determine how phase decision thresholds affect the PER of a phase data page. The data page has a minimum PER on a specific decision threshold, which we refer to as the minimum PER decision threshold (MPDT). We discover that the MPDT of the data page is not the same as the threshold of the traditional decision scheme, indicating that the traditional decision is incorrect. We then check MPDTs from different data pages and discover that MPDTs from different data pages are also different. As a result, using a unified threshold to perform a phase decision is determined to be incorrect. We propose a PDAA decision scheme based on these two findings, which can determine a more accurate threshold via the phase distribution characteristics of the reconstructed data page. Different decision thresholds can be set for each data page. Consequently, the PDAA decision scheme can achieve an adaptive decision effect. This scheme is divided into four steps: obtaining the phase probability distribution, fitting the phase probability density function, calculating the phase decision thresholds, and performing adaptive decision operations. The experimental results show that the PDAA decision scheme can adaptively adjust the threshold based on the data characteristics of the reconstructed data pages, thereby reducing the phase error of each data page. Furthermore, the image read by the PDAA decision scheme was clearer than that read by the traditional decision scheme. Thus, the PDAA decision scheme can significantly improve the data reliability of a holographic storage system.
2. Background
2.1 Holographic data storage
HDS is a storage technology with a high theoretical storage density that generally records user data by modulating the amplitude or phase of light. In terms of high code rates, homogeneous recording, and anti-interference capability, PHDS outperforms AHDS. A typical PHDS reading and recording principle diagram, depicted in Fig. 1, includes a spatial light modulator (SLM), holographic medium, CMOS camera, and lenses. The SLM can produce a specific light field distribution related to each data pattern. The holographic medium is used to store the grating data that carries user information, and the lenses perform the optical operations. Finally, the CMOS camera captures the Fourier intensity information of each reconstructed beam.
During the recording process, data such as photographs, audio, videos, and documents are first transformed into user data in the form of a bit stream, and then the bit stream is modulated into signal data in the form of phase data. Signal and known-phase reference data are used to generate a signal beam (or information beam) and a reference beam using the SLM. After the signal and reference beams are polymerized by a lens, they interfere with each other in the holographic medium to form a stable grating. This grating is also called the interference fringe. The signal beam information is carried by the interference fringe, allowing user data to be recorded.
During the reading process, the same reference data used in the recording process are uploaded to the SLM to generate the same reference beam. The reference beam then irradiates the grating in the holographic medium and diffracts under the coupling of interference fringes to produce a diffracted beam. The light field distributions of the diffracted beam and the signal beam are the same. The diffracted beam is also known as the reconstructed beam. After the reconstructed beam passes through the optical Fourier transform of the lens, it is captured by the CMOS camera in the form of Fourier intensity spectrum information. The captured Fourier intensity data are used for phase demodulation, and user data can be recovered.
2.2 Phase decision
Multilevel modulation can be used to increase the capacity of HDS [20,25,26]. To balance storage capacity and data reliability, PHDS typically employs four-level phase modulation. In four-level phase modulation, user data are modulated into four phase values distributed at equal intervals, such as 0.5$\pi$, $\pi$, 1.5$\pi$, and 2$\pi$. The modulated phase data are organized in an orderly fashion into a phase data page, which is then uploaded to the SLM to complete the recording operation. A recorded phase data page is uploaded to the SLM, as shown in Fig. 2(a), where ${P_{ij}}$ represents the phase of the i-th row and j-th column cell in the phase data page. The IFA can be used to reconstruct the phase data from the Fourier intensity information captured by the CMOS camera during data reading. Owing to the effect of noise and the limitations of phase reconstruction methods, the reconstructed phase data are a series of values ranging from 0 to 2$\pi$ rather than the four phase values of 0.5$\pi$, $\pi$, 1.5$\pi$, and 2$\pi$. Figure 2(b) shows a reconstructed phase data page. A phase decision process is required to recover the recorded phase format from the reconstructed phase data page.
The traditional phase decision method uses the average value of the two adjacent modulation phases as a threshold. Figure 3 shows four decision thresholds Th1, Th2, Th3, and Th4 for four-level phase modulation with phases of $0.5\pi$, $\pi$, $1.5\pi$, and $2\pi$ are $1.25\pi$, $1.75\pi$, $0.25\pi$, and $0.75\pi$, respectively. If a phase is in the [Th1, Th2) range, it is set to $1.5\pi$. If a phase is in the [Th2, Th3) range, it is set to $2\pi$. If a phase falls within the [Th3, Th4) range, it is set to $0.5\pi$. Finally, if a phase falls within the [Th4, Th1) range, it is assigned a phase of $\pi$. Note that the phase is $2\pi$ periodic, with a phase value of ${P_{ij}} = {P_{ij}} + 2\pi$. For example, a phase value of $0$ corresponds to a phase value of 2$\pi$ and a phase value of $-0.5\pi$ corresponds to a phase value of $1.5\pi$.
3. Evaluation of traditional decision thresholds
The correctness of the reading data is determined by the accuracy of the decision thresholds, which influences the data reliability of PHDS. Based on our observations, we found that the typical decision threshold is incorrect. To confirm this finding, we conducted a series of experiments. The experimental setup was the same as that described in Section 5. Figure 4 depicts the phase distribution of a reconstructed phase data page acquired during the experiment. The phase distributions of the four modulation phases, which are spread to the left and right, exhibit four peaks. It should be noted that the phase distribution of the modulation phase $\pi$ includes the phase ranges [$0.75\pi$, $\pi$] and [$-\pi$, $-0.75\pi$]. The phase distributions of the two adjacent modulation phases overlap. It is easy to make errors in the overlapping area of the phase distribution when making a phase decision, causing errors in the read data. Using an accurate decision threshold can help reduce phase data errors.
To test the accuracy of the traditional threshold, we kept Th1, Th2, and Th4 constant and changed Th3 to determine the phase of the data page corresponding to Fig. 5. When the Th3 values were ($0.25\pi + \alpha$) and $\alpha$ was in the range of [-0.6, 0.2], we recorded the PERs for each Th3 value. As illustrated in Fig. 5, different decision thresholds correspond to different PERs. The PER first decreased and then increased as Th3 gradually increased. More importantly, the Th3 value corresponding to the minimum PER was not the Th3 used in the traditional decision scheme. The PER associated with the traditional threshold is higher, at 1.8 times the minimum PER. As a result, the traditional decision threshold is shown to be incorrect for this phase data page.
In fact, when a large number of phase data pages employ the same decision threshold, the traditional threshold is statistically the best. We maintained Th1, Th2, and Th4 while changing Th3 to execute conventional decision operations on 1024 reconstructed phase data pages. When the Th3 values were ($0.25\pi + \beta$) and $\beta$ was between [-0.4, 0.4], we calculated the average PERs of these 1024 phase data pages. When all phase data pages are analyzed using the same decision threshold, as shown in Fig. 6, the traditional decision is actually the best. However, using the same decision threshold for all phase data pages is not appropriate. This is because the reconstructed phase data pages are subjected to complex noise as well as crosstalk that includes inter-page and inter-symbol crosstalk. The degree of crosstalk in a phase data page depends on the data pattern of the phase data page and the data pattern of the phase data pages that surround it. Each phase data page contains unique data patterns, resulting in varying degrees of crosstalk and an effect on their best decision threshold. The traditional decision scheme applies a consistent threshold to all phase data pages and ignores their unique characteristics, raising the decision error rate.
To verify the above facts, we observed the threshold differences between different data pages. We chose 1024 reconstructed phase data pages to make optimal decisions by changing Th3 to ($0.25\pi + \alpha$), and $\alpha$ was in the range of [-0.6, 0.2]. As shown in Fig. 7, the thresholds corresponding to the minimum PER of each data page differ. Some are higher than the traditional threshold, whereas others are lower than or the same as the traditional threshold. As a result, using a uniform threshold in the traditional decision scheme to determine the phase value for each data page is really not appropriate.
Using the same method, we examined the PERs of Th1, Th2, and Th4 at various values and reached the same conclusion as that for Th3. In other words, the thresholds of the traditional decision scheme are incorrect. This is due to the fact that the traditional decision scheme determines the threshold solely based on the modulation phase, without taking into account the data characteristics of the reconstructed phase data page affected by the holographic storage channel. The occurrence of phase errors is exacerbated by incorrect decision thresholds. It is necessary to use more accurate decision thresholds and a more appropriate decision scheme to improve the accuracy of the read data and the reliability of holographic storage systems.
4. Method
Holographic storage channels are subjected to many types of complex noise, including electric, optical, medium, and interference noise. This noise causes the phase distribution of each modulation phase to shift side to side and widen, causing the phase distributions of adjacent modulation phases to overlap. The phase of the overlapping region is prone to errors when making phase decisions. Thus, choosing appropriate decision thresholds is critical in the phase decision process. Traditional decision thresholds, as discussed in Section 3, are inaccurate, resulting in a higher PER, which affects the data reliability of holographic storage systems. We propose an optimal PDAA decision scheme that improves data reliability by leveraging the phase distribution characteristics of each reconstructed data page, as shown in Fig. 8. The phase distribution of data pages directly influences the accuracy of the phase decision. If the phase distribution characteristics are used to determine the decision thresholds, then decision errors can be reduced. The PDAA decision scheme comprises four steps: obtaining the phase probability distribution, fitting the phase probability density function, calculating the phase decision threshold, and performing adaptive decision operations. These steps are detailed below.
4.1 Obtaining the phase probability distribution
After the Fourier intensity information of the reconstructed beam is captured by the CMOS camera, the IFA uses it to perform phase reconstruction. The phase values on the reconstructed data page are no longer the four modulation phase values used while recording the data, but a series of continuous phase distributions in the range of [0, $2\pi$], as indicated in Fig. 4. We divide the phase values of each reconstructed phase data page into $k$ intervals. Each interval is indicated by ${\delta _i}(i = 1,2,3, \cdots k)$, where ${\delta _i}$ falls within the range of $\left [{\begin {array}{*{20}{c}} {\frac {{2\pi (i - 1)}}{k},} & {\frac {{2\pi i}}{k}} \end {array}} \right )$. Then, for each ${\delta _i}$, we count the number ${N_i}$ of phase data and calculate the sum $S$ of all ${N_i}$, where $S = {N_1} + {N_2} + {N_3} + \cdots {N_k}$. We use $\delta = \left ( {\begin {array}{*{20}{c}} {{\delta _1},} & {{\delta _2},} & {{\delta _3},} & \cdots & {{\delta _k}} \end {array}} \right )$ as the abscissa and $N = \left ( {\begin {array}{*{20}{c}} {\frac {{{N_1}}}{S},} & {\frac {{{N_2}}}{S},} & {\frac {{{N_3}}}{S},} & \cdots & {\frac {{{N_k}}}{S}} \end {array}} \right )$ as the ordinate to obtain the phase probability distribution, as shown in Fig. 8. To simplify the description, Fig. 8 are drawn in the range of [$-\pi$, $\pi$]. The phase in the range of [$-\pi$, $\pi$] is similar to the phase in the range of [0, $2\pi$] because the phase has a period of $2\pi$. In addition, it is important to note that the phase data distributions in Fig. 8 consist of the values of each pixel. This is because each pixel participates in the original distribution of reconstructed phase data.
4.2 Fitting the phase probability density function
The phase probability distribution derived in Section 4.1 aggregates the phase distributions of the four modulation phases. The modulation phase, $\pi$, is distributed throughout the green and purple boxes on the left and right, respectively. Because the phase is distributed periodically with $2\pi$, we regularly extend the above phase distributions. The phase distribution in the range of [$-\pi$, $-0.75\pi$] is copied to [$\pi$, $1.25\pi$], whereas the phase distribution in the range of [$0.75\pi$, $\pi$] is copied to [$-1.25\pi$, $-\pi$]. Then, in the extended phase distribution, all phase values can be divided into five segments. Segments 1, 2, 3, 4, and 5 represent the intervals [$-1.25\pi$, $-0.75\pi$), [$-0.75\pi$, $-0.25\pi$), [$- 0.25\pi$, $0.25\pi$), [$0.25\pi$, $0.75\pi$), and [$0.75\pi$, $1.25\pi$]. Segments 1 and 5 have the same phase distributions. The distribution of each segment is approximately Gaussian. To obtain the probability density function for each segment, the curve was fitted. Although the phase distributions of the adjacent modulation phases have some offset and overlap, division according to the above interval can still ensure that the majority of the phase in each interval belongs to the corresponding modulation phase.
4.3 Calculating the phase decision threshold
The five probability density functions described in Section 4.2 are denoted by $f1$, $f2$, $f3$, $f4$, and $f5$. We assign $f1$, $f2$, $f3$, $f4$, and $f5$ to the probability density functions of segments 1, 2, 3, 4, and 5, respectively. These five probability density functions can be used to compute the decision thresholds of a phase data page. The PDAA decision scheme uses the intersection of two adjacent probability density functions as the decision thresholds, ensuring the lowest possible decision error rate. The decision thresholds with the lowest decision error rates are considered optimal. The decision threshold Th1 is the abscissa of the intersection of $f1$ and $f2$, the decision threshold Th2 is the abscissa of the intersection of $f2$ and $f3$, the decision threshold Th3 is the abscissa of the intersection of $f3$ and $f4$, and the decision threshold Th4 is the abscissa of the intersection of $f4$ and $f5$.
4.4 Performing the adaptive decision operation
After obtaining the four phase decision thresholds, we can perform decision operations on a phase data page. The decision method for a data page is the same as that used in the traditional decision scheme. A phase value in the range [Th1, Th2), for example, is determined as the modulation phase of $-0.5\pi$ ($1.5\pi$). However, to achieve the goal of adaptive decision, the PDAA decision scheme determines the decision threshold of each data page based on the phase distribution of each phase data page. This is because the data pattern and noise suffered by each data page are different, and thus the broadening and offset degree of the phase distribution are also different. The decision threshold changes depending on the phase distribution. Thus, the accuracy of the phase decision can be improved by implementing the corresponding decision threshold based on the unique phase distribution of each data page instead of using the unified threshold of the traditional decision scheme.
5. Experiment
5.1 Experimental setup
In this section, we test the proposed PDAA decision scheme on a real-world experimental coaxial HDS system, as shown in Fig. 9. The system aperture was a device with two identical rectangular windows. The left window handled the signal light, whereas the right window handled the reference light. To ensure that the corresponding light field distribution of the data patterns on the SLM was correctly transmitted, the aperture and SLM were placed on the same plane using a 4f system. During the recording process, the signal and reference data were combined to form a phase data page, which was then uploaded to the SLM. Both rectangular apertures were open, and light from the laser irradiated the SLM, producing a signal beam and a reference beam. In the holographic medium of the PQ/PMMA, the signal beam interfered with the reference beam to generate gratings. The holographic medium records gratings that carry signal information. During the reading process, the right window of the aperture was open, and the gratings in the holographic medium were exposed to the same reference beam to diffract a reconstructed beam containing signal information. Because the CMOS camera cannot directly receive phase data, we placed a lens behind the reconstructed beam. The reconstructed beam was transformed into Fourier information by using this lens. The Fourier intensity information of the reconstructed beam was captured using the CMOS camera. The phase reconstruction was then processed using IFAs.
The parameters of each device in the experimental system were as follows. The SLM was a pure-phase version of X10468-04 from Hamamatsu. This SLM had a $792\times 600$ resolution and a pixel pitch of 20 $\mathrm{\mu}$m. The holographic medium, 784-doped PQ/PMMA photopolymer [27], was 1.5 mm thick. The CMOS camera was a DCC3260M produced by Thorlabs. This CMOS camera had a resolution of $1936\times 1216$ and a pixel pitch of 5.86 $\mathrm{\mu}$m. The focal length of the lenses, such as lenses 1, 2, 3, and 4, was 150 mm. Lens 5 had a focal length of 300 mm and was used to transform the reconstructed beam into Fourier information. Furthermore, we employed four-level phase modulation with phases of 0, $0.5\pi$, $\pi$, and $1.5\pi$. The phase data page was $32\times 32$ in size, with $32\times 16$ on the left for the signal data and $32\times 16$ on the right for the reference data.
We used the above experimental system to record and read gray images to validate the effectiveness of the proposed PDAA decision scheme. As shown in Fig. 10, we used a gray image with $128\times 128$ gray values to demonstrate the experimental method. When recording the image, we first converted the gray values of the image into a bit stream according to the mapping table between the gray values and bits. The bit stream was then modulated into phase data according to the mapping table between the bit and phase data. Each gray value corresponds to an 8-bit value. The $128\times 128$ grayscale image was first transformed into a 131072-bit ($128\times 128\times 8$) stream. Every two-bit unit in the bit stream formed a group for phase modulation to obtain 65536 phase data. Specifically, bit units 00, 01, 10, and 11 are modulated into phase 0, 0.5$\pi$, $\pi$, and 1.5$\pi$, respectively (i.e., 131072/2=65536). Those 65536 pieces of phase data were organized into 128 signal data pages, each with a size $32\times 16$. A reference data page with a size of $32\times 16$ and each signal data page are combined to form 128 phase data pages with a size of $32\times 32$. These phase data pages are then uploaded to the SLM for recording. Each phase of data is represented by $4\times 4$ pixels. When reading an image, we first utilize the CMOS camera to capture the Fourier intensity information of the reconstructed beam. Then, IFAs were used to reconstruct the phase data and obtain the phase data pages. The maximum number of iterations in the IFA was set at 50. Subsequently, we used the traditional and PDAA decision schemes to perform phase decision operations on the reconstructed phase data pages and obtain the corresponding modulated phase data pages. Finally, the gray image was restored from the modulated phase data pages using the inverse process shown in Fig. 10.
5.2 Results and discussion
Using the experimental method described in Section 5.1, we compared traditional and PDAA decision schemes. We use a total of eight grayscale images with $128\times 128$ gray values in the experiments, and 1024 phase data pages are generated from these grayscale images. Figure 11 depicts the related results of the first phase data page. Figure 11(a) shows the recorded phase data page uploaded onto the SLM. The Fourier intensity information captured by the CMOS camera is shown in Fig. 11(b). The reconstructed phase data page obtained using the IFA is shown in Fig. 11(c), which shows that the signal part of the reconstructed phase data page became severely distorted because of holographic storage channel noise. To recover the modulated phase data, we made a phase decision on the distorted signal part of the reconstructed phase data page. Table 1 lists the four thresholds of the traditional and PDAA decision schemes. The four thresholds obtained by the phase distribution characteristics are not the same as the four traditional thresholds because the phase distributions of the four modulation phases have a certain offset after the holographic storage channel and because the offsets of the four phase distributions may be different. The modulated phase data pages obtained using the traditional and PDAA decision schemes are presented in Fig. 11(d) and 11(f), respectively. Figure 11(e) and 11(g) show phase error distributions under traditional and PDAA decision schemes, respectively. Because the thresholds of the PDAA decision scheme obtained through the phase distribution characteristics of the reconstructed data page are more accurate, phase errors obtained using the PDAA decision scheme are less severe than those obtained using the traditional decision scheme.
Fig. 11. Related results of the first phase data page. (a) Recorded phase data page uploaded on the SLM; (b) Fourier intensity information captured by the CMOS camera; (c) reconstructed phase data page obtained by the IFA; (d) phase data page obtained by the traditional decision on (c); (e) phase error distributions of (d); (f) phase data page obtained by the PDAA decision on (c); (g) phase error distributions of (f).
Table 1. Traditional thresholds and PDAA thresholds of the first phase data page
Furthermore, we obtained the thresholds using the PDAA decision scheme on all 1024 phase data pages, as shown in Fig. 12. The decision threshold is clearly different for each phase data page. Compared to the traditional decision scheme, the PDAA decision scheme can adaptively match the optimal phase decision thresholds. As a result, under the PDAA decision scheme, more accurate decision thresholds can be applied to every phase data page.
Figure 13 depicts the PERs of 1024 phase data pages on two different decision schemes. The PER of each phase data page is different. For the majority of phase data pages, the PERs of the PDAA decision scheme are lower than those of the traditional scheme. On the 60th phase data page, in particular, the PER of the PDAA decision scheme is less than 42% of that of the traditional decision scheme. The average PER of 1024 reconstructed phase data pages in the traditional scheme is 0.0188, while the average PER of 1024 reconstructed phase data pages in the PDAA decision scheme is 0.0150. The PDAA decision scheme reduces the PER by an average of 20.21% compared with that of the traditional decision scheme. Therefore, the proposed PDAA decision scheme can identify more precise thresholds for phase data pages, lowering the PERs of phase data pages and thus improving the data reliability of phase modulated holographic data storage.
6. Conclusion
This study examines the phase distribution characteristics of a reconstructed data page and the effect of phase decision thresholds on the PER in PHDS. We discovered that the traditional decision thresholds are inaccurate and exacerbate phase errors. To address this inaccuracy, a PDAA decision scheme that is optimized based on phase distribution characteristics is proposed. The PDAA decision scheme includes two optimizations: using the phase distribution characteristics of the reconstructed data pages to determine the decision threshold and applying adaptive decisions to each reconstructed data page. We implemented and evaluated the PDAA decision scheme on a real platform. Our experimental results show that the PDAA decision scheme outperforms the traditional decision scheme in terms of the PER. This result shows that the PDAA decision scheme has the potential to significantly improve the data reliability of holographic data storage systems. In addition, while the PDAA decision scheme greatly improves data reliability over the traditional decision method, there is still a significant gap between the data error rate and the data availability requirements. In the future, we will investigate the cooperative optimization scheme of combining phase decision with other technologies, such as error correction codes, to improve data reliability and promote the practical process of holographic data storage.
Funding
National Key Research and Development Program of China (2018YFA0701800); Project of Fujian Province Major Science and Technology (2020HZ01012).
Acknowledgments
This work is supported by Key Laboratory of Information Storage System, Ministry of Education of China, and the Engineering Research Center of Data Storage Systems and Technology.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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