Soft-decision array decoding for volume holographic memory systems.

We study the use of soft-decision array decoding in a volume holographic memory (VHM) system that is corrupted by interpixel interference (IPI) and detector noise. Soft-decision methods can unify equalization and error decoding. A highly parallel array decoder is presented in the context of two-dimensional low-pass channel mitigation and error correction. The new decoding algorithm is motivated by iterative turbo-decoding methods and is capable of incorporating a priori knowledge of the corrupting IPI channel during decoding. The resulting joint detection decoding algorithm is shown to offer VHM capacity and density performance superior to that of hard-decision n = 255 Reed-Solomon codes in concatenation with a Wiener filter.

Blockwise data detection for spectral hole-burning memories.

We consider the retrieval of data from a time-domain spectral hole-burning (SHB) memory system. A new iterative log-likelihood (ILL) algorithm is used to reliably detect corrupted retrieved data signals. It is a blockwise technique that takes advantage of the known SHB system characteristics to mitigate time-varying intersymbol interference and detector shot noise. We present bit-error-rate results obtained with the ILL algorithm and five other typical methods (i.e., precompensator, simple threshold, adaptive threshold, a simple Wiener filter, and an adaptive Wiener filter). Results show that the ILL algorithm outperforms all five techniques and hence offers improved SHB storage capacity. In a SHB system with typical material parameters, we find that ILL offers a storage capacity gain of 197% as compared with simple thresholding.

Image restoration with the Viterbi algorithm.

The Viterbi algorithm (VA) is known to given an optimal solution to the problem of estimating one-dimensional sequences of discrete-valued pixels corrupted by finite-support blur and memoryless noise. A row-by-row estimation along with decision feedback and vector quantization is used to reduce the computational complexity of the VA and allow the estimation of two-dimensional images. This reduced-complexity VA (RCVA) is shown to produce near-optimal estimation of random binary images. In addition, simulated restorations of gray-scale images show the RCVA estimates to be an improvement over the estimates obtained by the conventional Wiener filter (WF). Unlike the WF, the RCVA is capable of superresolution and is adaptable for use in restoring data from signal-dependent Poisson noise corruption. Experimental restorations of random binary data gathered from an optical imaging system support the simulations and show that the RCVA estimate has fewer than one third of the errors of the WF estimate.

Communication theoretic image restoration for binary-valued imagery.

We present a new image-restoration algorithm for binary-valued imagery. A trellis-based search method is described that exploits the finite alphabet of the target imagery. This algorithm seeks the maximum-likelihood solution to the image-restoration problem and is motivated by the Viterbi algorithm for traditional binary data detection in the presence of intersymbol interference and noise. We describe a blockwise method to restore two-dimensional imagery on a row-by-row basis and in which a priori knowledge of image pixel correlation structure can be included through a modification to the trellis transition probabilities. The performance of the new Viterbi-based algorithm is shown to be superior to Wiener filtering in terms of both bit error rate and visual quality. Algorithmic choices related to trellis state configuration, complexity reduction, and transition probability selection are investigated, and various trade-offs are discussed.

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.

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).

Gray-scale data pages for digital holographic data storage.

The prospects for gray-scale (or multilevel) digital holographic data storage are theoretically and experimentally investigated. A simple signal-to-noise ratio (SNR) partitioning argument shows that when SNR scales as 1 over the number of holograms squared, five gray levels (log(2) 5 bits/pixel) would be expected to result in a 15% capacity increase over binary data pages. However, the additional signal-dependent noise sources present in practical systems create a baseline SNR that reduces both the optimal number of gray levels and the resulting gain in capacity. To implement gray-scale recording experimentally, we adapt the predistortion technique previously developed for binary page-oriented memories [Opt. Lett. 23, 289 (1998)]. Several new block-based modulation codes for decoding gray-scale data pages are introduced. User capacity is evaluated by an experimental technique using LiNbO(3) :Fe in the 90 degrees geometry. Experimental results show that a balanced modulation code with three gray levels provides a 30% increase in capacity (as well as a 30% increase in readout rate) over local binary thresholding.

Information, resolution, and space-bandwidth product.

The information capacities of two-dimensional optical low-pass channels are discussed. Coherent and incoherent systems operating under finite optical power and area constraints are characterized in terms of two criteria:spacebandwidth product (SBP; the number of pixels required for achieving maximum information capacity) and resolution (G(min); the smallest spot size capable of supporting positive capacity gain). A coherent system operating with an initial signal-to-noise ratio (SNR) of 5 can achieve a 48% capacity gain by operating at an optimal SBP that is 3.4 times that of the nominal system. The same system has a resolution that is 0.31 times nominal. Incoherent systems experience additional SNR loss, and with an initial SNR of 5 they achieve capacity gains of 29% at the optimal SBP of 2.8 times nominal. The incoherent system resolution is found to be 0.4 times nominal.

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.

Experimental evaluation of user capacity in holographic data-storage systems.

An experimental procedure for determining the relation between the number of stored holograms and the raw bit-error rate (BER) (the BER before error correction) of a holographic storage system is described. Compared with conventional recording schedules that equalize the diffraction efficiency, scheduling of recording exposures to achieve a uniform raw BER is shown to improve capacity. The experimentally obtained capacity versus the raw-BER scaling is used to study the effects of modulation and error-correction coding in holographic storage. The use of coding is shown to increase the number of holograms that can be stored; however, the redundancy associated with coding incurs a capacity cost per hologram. This trade-off is quantified, and an optimal working point for the overall system is identified. This procedure makes it possible to compare, under realistic conditions, system choices whose impact cannot be fully analyzed or simulated. Using LiNbO(3) in the 90 degrees geometry, we implement this capacity-estimation procedure and compare several block-based modulation codes and thresholding techniques on the basis of total user capacity.

SPICE-Based Optoelectronic System Simulation.

spiceis a widely used simulation tool for electrical circuits and systems. When optoelectronic elements, such as lasers, detectors, modulators, etc., and optical elements, such as lenses, gratings, beam splitters, etc., are incorporated into spice, optoelectronic system simulation can be combined with that of electronic systems, facilitating hybrid system design and analysis. We discuss an optoelectronic spice implementation that includes time-, power-, and wavelength-domain behaviors. Examples of optical component simulation and optical interconnect system simulation by use of spice are included and compared with the results from a conventional ray-tracing optical analysis tool.

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.

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.

Information theoretic limits to the capacity of volume holographic optical memory.

We derive the information theoretic limit to storage capacity in volume holographic optical memories for the limiting cases of dominant intensity noise (Gaussian noise) and dominant field noise (Rician noise). These capacity bounds are compared with the performance achievable using simple Reed-Solomon error-correcting codes.

Technique for controlling cross-talk noise in volume holography.

We study cross-talk noise in holographic memory and estimate storage limits. We examine the effects of reduced angular density and the use of an apodized reconstruction beam on capacity, cross-talk noise, and diffraction efficiency. Experimental Bragg-selectivity curves with and without an apodized reconstruction beam verify the expected reduction in cross talk.

Parallel data detection in page-oriented optical memory.

We discuss a novel two-dimensional parallel technique for reliable data detection in page-oriented optical memories. The method is motivated by decision feedback techniques and is fully parallel, offering convenient, locally connected electronic implementation. The algorithm is shown to offer significant improvements over simple threshold detection and in some cases can approach the maximum-likelihood bound of data reliability.

Optical design for page access to volume optical media.

4F lens designs are optimized for parallel access to volume holographic memories. Aberrations, diffraction, and component tolerancing are considered for their impact on parallelism, crystal information density, and overall system storage density. We find that a parallelism of ≥ 10(5) bits per page and a crystal information density of ≈2 Mbits/mm(3) are achievable with standard optical elements and that advanced designs offer significant improvements. Crystal surface tolerance measurements show that a diffraction-limited performance is achievable over apertures of 7.1 mm for LiNbO(3) and 1.5 mm for KNSBN(60). Lens-tolerancing simulations show that lens decenter degrades peak parallelism and peak crystal information density. Anew nonconfocal 4F system design with improved performance is presented.

Multiple-error-correcting codes for improving the performance of optical matrix-vector processors.

I examine the use of Reed-Solomon multiple-error-correcting codes for enhancing the performance of optical matrix-vector processors. An optimal code rate of 0.75 is found, and n = 127 block-length codes are seen to increase the optical matrix dimension achievable by a factor of 2.0 for a required system bit-error rate of 10(-15). The optimal codes required for various matrix dimensions are determined. I show that single code word implementations are more efficient than those utilizing multiple code words.

Improvements in the capacity of computer-generated holographic storage using the Lee method with sparse multivalued reconstructions.

The use of sparse multivalued data encodings for the purpose of increasing the capacity of parallel-access optical memories based on Fourier-transform computer-generated holography is discussed. Results based on the Lee method indicate that a sparse encoding of nonbinary data words can be used to increase the storage-area utilization efficiency from 35% to > 70%. It is also found that for signal-to-noise ratios greater than 200, five-level data encoding can be used to achieve bit error rates less than 10(-12) reliably with 60% area efficiency.