Information theoretic limits to the capacity of volume holographic optical memory

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.

Analog-to-digital conversion of information archived in display holograms: I. discussion

This discussion paper highlights the potential of display holograms in the storage of information about objects' shape. The images recorded and reconstructed from holograms have high visual appeal, and the holographic carrier has far higher information capacity than other storage media. One hindrance to the application of display holograms is the inadequate development of techniques for digitizing information from them, which is compounded by insufficient analysis and discussion of existing approaches. In this review, we provide a historical retrospective of the use of display holography to save comprehensive information on object morphology. We also discuss existing and emerging technologies for converting information into a digital format, addressing one of the most serious challenges to the widespread use of display holography. Potential applications of these technologies are also analyzed.

Dynamic sampling iterative phase retrieval for holographic data storage

A dynamic sampling iterative phase retrieval method, which dynamically samples the Fourier intensity distribution of the reconstruction beam captured by the detector, is proposed to shorten the iterative number and decrease the phase error rate of phase retrieval in the phase-modulated holographic data storage. By the dynamic sampling method, that keeping relatively low frequency component of Fourier intensity spectrum at the beginning of iteration and gradually releasing more high frequency component at the subsequent iterations, we shortened the iterative number by 2 times and decreased the phase error rate to some extent because our method provided a better convergent path to the phase retrieval. We also believe the thought of our method can be used in more image retrieval fields.

Fast non-interferometric iterative phase retrieval for holographic data storage

Fast non-interferometric phase retrieval is a very important technique for phase-encoded holographic data storage and other phase based applications due to its advantage of easy implementation, simple system setup, and robust noise tolerance. Here we present an iterative non-interferometric phase retrieval for 4-level phase encoded holographic data storage based on an iterative Fourier transform algorithm and known portion of the encoded data, which increases the storage code rate to two-times that of an amplitude based method. Only a single image at the Fourier plane of the beam is captured for the iterative reconstruction. Since beam intensity at the Fourier plane of the reconstructed beam is more concentrated than the reconstructed beam itself, the requirement of diffractive efficiency of the recording media is reduced, which will improve the dynamic range of recording media significantly. The phase retrieval only requires 10 iterations to achieve a less than 5% phase data error rate, which is successfully demonstrated by recording and reconstructing a test image data experimentally. We believe our method will further advance the holographic data storage technique in the era of big data.

Thousand-fold increase in optical storage density by polychromatic address multiplexing on self-assembled DNA nanostructures

A super-resolution optical storage technique enabled by DNA nanotechnology and the design of resonance energy transfer (RET) networks are demonstrated. The enhancement in storage density stems from non-linear interactions between excitons on the nanostructured RET circuits, which permit large-scale multiplexing with a small set of addressing wavelengths and a single output channel.

Improvement of bit error rate and page alignment in the holographic data storage system by using the structural similarity method

Although widely recognized as a promising candidate for the next generation of data storage devices, holographic data storage systems (HDSS) incur adverse effects such as noise, misalignment, and aberration. Therefore, based on the structural similarity (SSIM) concept, this work presents a more accurate locating approach than the gray level weighting method (GLWM). Three case studies demonstrate the effectiveness of the proposed approach. Case 1 focuses on achieving a high performance of a Fourier lens in HDSS, Cases 2 and 3 replace the Fourier lens with a normal lens to decrease the quality of the HDSS, and Case 3 demonstrates the feasibility of a defocus system in the worst-case scenario. Moreover, the bit error rate (BER) is evaluated in several average matrices extended from the located position. Experimental results demonstrate that the proposed SSIM method renders a more accurate centering and a lower BER, lower BER of 2 dB than those of the GLWM in Cases 1 and 2, and BER of 1.5 dB in Case 3.

Irregular repeat-accumulate codes for volume holographic memory systems

We investigate the application of irregular repeat-accumulate (IRA) codes in volume holographic memory (VHM) systems. We introduce methodologies to design efficient IRA codes. We show that a judiciously designed IRA code for a typical VHM can be as good as the optimized irregular low-density-parity-check codes while having the additional advantage of lower encoding complexity. Moreover, we present a method to reduce the error-floor effect of the IRA codes in the VHM systems. This method explores the structure of the noise pattern in holographic memories. Finally, we explain why IRA codes are good candidates for the VHM systems.

Experimental demonstration of gray-scale sparse modulation codes in volume holographic storage

We discuss experimental results of a versatile nonbinary modulation and channel code appropriatefor two-dimentional page-oriented holographic memories. An enumerative permutation code is used to provide a modulation code that permits a simple maximum-likelihood detection scheme. Experimental results from the IBM Demon testbed are used to characterize the performance and feasibility of the proposed modulation and channel codes. A reverse coding technique is introduced to combat the effects of error propagation on the modulation-code performance. We find experimentally that level-3 pixels achieve the beet practical result, offering an 11-35% improvement in capacity and a 12% increase in readout rate as compared with local binary thresholding techniques.

Low-density parity-check codes for volume holographic memory systems

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used for designing as well as decoding the LDPC codes. We show that these codes have a superior performance to that of Reed-Solomon (RS) codes and regular LDPC counterparts. Our simulation shows that we can increase the maximum storage capacity of holographic memories by more than 50 percent if we use irregular LDPC codes with soft-decision decoding instead of conventionally employed RS codes with hard-decision decoding. The performance of these LDPC codes is close to the information theoretic capacity.

Sparse modulation coding for increased capacity in volume holographic storage

In page-oriented memories, data pages commonly consist of comparable numbers of on and off pixels. Data-page sparsity is defined by reduction of the number of on pixels per page, leading to an increased diffracted power into each pixel. When page retrieval is dominated by a fixed noise floor, the number of pages in the memory is limited by the pixel diffraction efficiency. Sparsity increases the number of storable pages while reducing the amount of user information per page. A detailed analysis of sparsity in volume holographic memories shows that the total memory capacity can be increased by 15% by use of data pages that contain on average 25% on pixels. Sparsity also helps to reduce the effects of interpixel cross talk by strongly reducing the probability that worst-case pixel patterns (e.g., blocks of on pixels with a center off pixel) will occur in the data page. Enumeration block coding techniques provide construction of sparse-data pages with minimal overhead. In addition, enumeration coding offers maximum-likelihood detection with low encoding-decoding latency. We discuss the theoretical advantages of data-page sparsity. We also present experimental results that demonstrate the proposed capacity gain. The experiment verifies that it is practical to construct and use sparse-data pages that result in an overall user capacity gain of 16% subject to a page retrieval bit-error rate of 10(-4).

Information-based optical design for binary-valued imagery

Applications such as optical data storage, optical computing, and optical interconnects require optical systems that manipulate binary-valued images. Such an optical system can be viewed as a two-dimensional array of binary communication channels. This perspective is used to motivate the use of pagewise mutual information as a metric for optical system analysis and design. Fresnel propagation and coherent imaging both are analyzed in terms of mutual-information transmission. An information-based space-bandwidth product is used to analyze the trade-off between the numerical aperture and the number of image pixels in a coherent 4f system. We propose a new merit function to facilitate information-based optical system design. Information maximization and bit-error-rate minimization both are possible with the new radially weighted encircled-energy merit function. We demonstrate the use of this new merit function through a design example and show that the information throughput is increased by 8% and the bit-error rate is reduced by 36% when compared with systems designed with traditional criteria.

Interleaving and error correction in volume holographic memory systems

We study the use of error-correction coding (ECC) and two-dimensional interleaving for volume holographic memory (VHM) systems suffering from both random and systematic errors. The bit-error rate (BER) is used as the data-fidelity measure and as a design metric for optical 4f systems. The correlated error patterns arising from both lens aberrations and misalignment errors are analyzed, and we discuss the information theoretic storage capacity of VHM in the presence of such correlated error patterns. The performance of interleaving and ECC is analyzed from both BER and storage-capacity perspectives. Magnification, rotation, tilt, and defocus errors are also studied, and an experimental demonstration that combines ECC with two-dimensional interleaving is included.

Parallel detection algorithm for page-oriented optical memories

We present a parallel algorithm for the reliable detection of two-dimensional binary data in page-oriented memories. The development of the proposed pseudodecision-feedback equalization (PDFE) method is motivated by the classical decision-feedback equalization receiver. The technique takes advantage of the known or the estimated optical system characteristics to mitigate space-variant blur and additive thermal noise. We extend the method to correct for fixed-pattern errors including magnification, rotation, and transverse shift. Advantages of the PDFE algorithm include its parallel design, low computational complexity, and local connectivity. A system-capacity metric is used to compare the performance of the PDFE receiver with other conventional approaches, including the simple threshold, the 1:2 modulation code, and the Wiener filter. Results show the PDFE to outperform all the above techniques over a variety of channels for both incoherent and coherent systems. Implementation issues are discussed, and a MOSIS (Metal-Oxide Semiconductor Implementation Service) 2-mum design is presented.

Error correction for free-space optical interconnects: space-time resource optimization

We study the joint optimization of time and space resources withinfree-space optical interconnect (FSOI) systems. Both analyticaland simulation results are presented to support this optimization studyfor two different models of FSOI cross-talk noise: diffraction froma rectangular aperture and Gaussian propagation. Under realisticpower and signal-to-noise ratio constraints, optimum designs based onthe Gaussian propagation model achieve a capacity of 2.91 x10(15) bits s(-1) m(-2), while therectangular model offers a smaller capacity of 1.91 x10(13) bits s(-1) m(-2). We alsostudy the use of error-correction codes (ECC) within FSOIsystems. We present optimal Reed-Solomon codes of various length, and their use is shown to facilitate an increase in both spatialdensity and data rate, resulting in FSOI capacity gains in excess of8.2 for the rectangular model and 3.7 for the Gaussian case. Atolerancing study of FSOI systems shows that ECC can provide toleranceto implementational error sources. We find that optimally codedFSOI systems can fail when system errors become large, and we present acompromise solution that results in a balanced design in time, space, and error-correction resources.