Signal processing for multitrack digital data storage

Using a multitrack format in both optical and magnetic data storage applications yields important improvements in system performance, including higher data density and higher data transfer rates. However, the full advantage in data density can be achieved only through the use of joint equalization and joint detection. This paper addresses the complexity of implementing these functions and proposes a transform domain equalization architecture and a reduced-complexity detection method based on a breadth first search of a one-dimensional time-varying representation of a two-dimensional target response. With this method, the complexity of joint equalization and joint detection is not unreasonably greater than that of existing single-track systems and should be feasible for implementation with emerging integrated circuit technologies.     

Detector target response optimization for multitrack digital data storage

Data from digital data storage media employing a multitrack storage format can be efficiently detected with reduced complexity by using a breadth-first search algorithm on a one-dimensional time-varying trellis representation of the multitrack channel response. In this letter, we analyze the resulting performance. We propose a two-dimensional minimum phase detector target response and verify its performance through bit-error-rate simulations.     

Optimal code rates for the Lorentzian channel: Shannon codes and LDPC codes

We take an information-theoretic approach to obtaining optimal code rates for error-control codes on a magnetic storage channel approximated by the Lorentzian channel. Code rate optimality is in the sense of maximizing the information-theoretic user density along a track. To arrive at such results, we compute the achievable information rates for the Lorentzian channel as a function of signal-to-noise ratio and channel density, and then use these information rate calculations to obtain optimal code rates and maximal linear user densities. We call such (hypothetical) optimal codes "Shannon codes." We then examine optimal code rates on a Lorentzian channel assuming low-density parity-check (LDPC) codes instead of Shannon codes. We employ as our tool extrinsic information transfer (EXIT) charts, which provide a simple way of determining the capacity limit (or decoding threshold) for an LDPC code. We demonstrate that the optimal rates for LDPC codes coincide with those of Shannon codes and, more important, that LDPC codes are essentially capacity-achieving codes on the Lorentzian channel. Finally, we use the above results to estimate the optimal bit-aspect ratio, where optimality is in the sense of maximizing areal density.     

Power spectra of channel codes for digital magnetic recording

The power spectral density (PSD) is the average power per unit frequency of encoded random data transmitted over a perfect channel. The one-sided PSDs of a number of channel codes of recent interest in digital magnetic recording are calculated from codeword dictionaries and state diagrams. Given here are:     

A new signal processing technique for d=1 channel codes

This paper presents a strategy for reducing nonlinearities at high-recording densities; new additional encoding scheme for DC-free d=1 channel codes, and, a partial response (1+D) system with 2-bit decoding. This encoding scheme, which to DC-free codes, reduces by one bit transition interval of d=1 codes, and ensures a wide margin of timing offset. In order to use erasures for the error correction code, the 2-bit decoding scheme is employed in-parallel to detect errors in the decoding procedure. An improvement in the error rate by using parallel decoding is shown     

Pairwise error probability of space?time codes for a keyhole channel

A closed-form upper bound is presented for the average pairwise error probabilities (PEP) of space-time codes for a keyhole channel. It is derived from the exact conditional PEP for given fading channel coefficients using a moment generating function-based approach. Simulation results are included for varying numbers of antennas that affirm that the proposed PEP serves as a tight bound for codes in a keyhole channel     

Encrypted optical storage with wavelength-key and random phase codes

An encrypted optical memory system that uses a wavelength code as well as input and Fourier-plane random phase codes is proposed. Original data are illuminated by a coherent light source with a specified wavelength and are then encrypted with two random phase codes before being stored holographically in a photorefractive material. Successful decryption requires the use of a readout beam with the same wavelength as that used in the recording, in addition to the correct phase key in the Fourier plane. The wavelength selectivity of the proposed system is evaluated numerically. We show that the number of available wavelength keys depends on the correlation length of the phase key in the Fourier plane. Preliminary experiments of encryption and decryption of optical memory in a LiNbO(3):Fe photorefractive crystal are demonstrated.     

Iterative optimization for joint design of source and channel codes using genetic algorithms

Abstract

This paper presents a novel algorithm for the joint design of source and channel codes. In the algorithm, channel‐optimized vector quantization (COVQ) and rate‐punctured convolutional coding (RCPC) are used for design of the source code and the channel code, respectively. We employ the genetic algorithm (GA) to prevent the design of COVQ from falling into a poor local optimum. We also adopt the GA to reduce the computational time needed for realizing the unequal error protection scheme best matched to the COVQ. Both the GA‐based source coding and channel coding scheme are then iteratively combined to achieve a near global optimal solution for the joint design. Numerical results show that the algorithm can be an effective alternative for applications where high rate‐distortion performance and low computational complexity are desired.     

Optimal code rates for concatenated codes on a PR4-equalizedmagnetic recording channel

At some nominal recording density, the read signal in digital magnetic recording resembles a Class IV partial response (PR4) signal and, hence, may be equalized to the PR4 shape with relatively little noise enhancement. When coding is added, for a fixed user density, the recording density must increase as a result of coding overhead, and the read signal will resemble PR4 to a lesser extent. Equalization to PR4 in this case will produce excessive noise enhancement. Thus, coding overhead (or rate) must be selected for optimum tradeoff between code strength and noise enhancement. Toward this end, we provide results for high-rate concatenated codes, assuming a Lorentzian recording channel model. In addition to examining optimal code rates, we compare parallel and serial concatenated code performance on the PR4 channel     

Efficient secure channel coding based on quasi-cyclic low-density parity-check codes

A secure channel coding (joint encryption-channel coding) scheme provides both data security and reliability in one combined process to achieve faster processing and/or more efficient implementation. The issue of using quasi-cyclic low-density parity-check (QC-LDPC) codes in a symmetric-key secure channel coding scheme is addressed. A set of this class of LDPC codes has recently been recommended by the NASA Goddard Space Flight Center for near-earth and deep-space communications. The proposed scheme provides an efficient error performance, an acceptable level of security and a low-complexity practicable implementation. The results indicate that the proposed scheme can efficiently employ large QC-LDPC codes to achieve a relatively smaller secret-key size to be exchanged by the sender and the receiver, and higher information rates in comparison with the previous symmetric-key McEliece-like schemes. Simulation results indicate that there is no trade-off between the error performance and the security level of the proposed scheme unlike that of the previous ones. These characteristics make the proposed scheme suitable for high-speed communications, such as satellite communication 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.     

Power optimised channel coding in wireless sensor networks using low-density parity-check codes

Energy consumption of low-density parity-check (LDPC) codes in different implementations is evaluated. Decoder's complexity is reduced by finite precision representation of messages, that is, quantised LDPC decoder, and replacement of function blocks with look-up tables. It is shown that the decoder's energy consumption increases exponentially with the number of quantisation bits. For the sake of low-power consumption, 3-bit magnitude and 1-sign bit representation for messages are used in the decoder. It is concluded that high-rate Gallager codes are as energy efficient as the Reed-Solomon codes, which till now have been the first choice for wireless sensor networks (WSNs). Finally, it is shown that using LDPC codes in WSNs can be justified even more by applying the idea of trading the transmitter power with the decoder energy consumption. By exploiting the trade-off inherent in iterative decoding, the network lifetime is increased up to four times with the 3-6 regular LDPC code. Hence, it is inferred that the LDPC codes are more efficient than the block and the convolutional codes.     

An investigation of the effects of media characteristics on read channel performance for patterned media storage

Many view data storage on patterned magnetic media as one way of attaining storage densities in excess of 1 Tb/in/sup 2/ and thus overcoming the problems associated with recording at ultrahigh densities on conventional continuous media. In this paper we investigate, through the use of a replay simulation developed to take into account the three-dimensional nature of the patterned media, the effects that the shape-constrained media have on the bit-error-rate performance of the read channel in 1-Tb/in/sup 2/ perpendicular recording. In particular, we analyze how media configurations with varying island shape, size, and distribution affect the channel performance.     

瑞利信道下高速LDPC码和OFDM在图像传输中的应用

本文研究了OFDM调制技术以及LDPC编码技术在图像传输中的应用,分别对OFDM和三种不同LDPC码对无线信道下图像传输质量的影响做了仿真研究.仿真结果表明,把高速LDPC编码和OFDM调制技术结合起来应用在图像传输当中可以实现图像的可靠和高质量传输,即说明LDPC码和OFDM调制技术可以解决由于图像数据量大带来的传输速率和效率的问题,实现高速的和高频谱利用率的图像传输.     

Experimental Designs for Constrained Regions

The familiar factorial, fractional factorial, and response surface designs are designs for regularly-shaped regions of interest, typically cuboidal regions and spherical regions. An irregularly shaped region of experimentation arises in situations where there are constraints on the factor level combinations that can be run or restrictions on portions of the region of exploration. Computer-generated designs based on some optimality criterion are a logical alternative for these problems. We give a brief tutorial on design optimality criteria and show how one of these, the D-optimality criteria, can lead to very reasonable designs for constrained regions of interest. We show through a simulation study that D-optimal designs perform very well with respect to the capability of selecting the correct model and accurately estimating the design factor levels that result in the optimal response.     

Discrete magnitude-squared channel modeling, equalization, and detection for volume holographic storage channels

As storage density increases, the performance of volume holographic storage channels is degraded, because intersymbol interference and noise also increase. Equalization and detection methods must be employed to mitigate the effects of intersignal interference and noise. However, the output detector array in a holographic storage system detects the intensity of the incident light's wave front, leading to loss of sign information. This sign loss precludes the applicability of conventional equalization and detection schemes. We first address channel modeling under quadratic nonlinearity and develop an efficient model named the discrete magnitude-squared channel model. We next introduce an advanced equalization method called the iterative magnitude-squared decision feedback equalization (IMSDFE), which takes the channel nonlinearity into account. The performance of IMSDFE is quantified for optical-noise-dominated channels as well as for electronic-noise-dominated channels. Results indicate that IMSDFE is a good candidate for a high-density, high-intersignal-interference volume holographic storage channel.     

Concatenated coded modulation techniques and orthogonal space-time block codes in the presence of fading channel estimation errors

Performance of coding and modulation systems in fading channels is usually analysed under the assumption that the receiver has perfect knowledge of channel condition. However, various shortcomings in practical channel estimation techniques lead to imperfections, resulting in channel estimation errors. The authors analyse a practical coding and modulation scheme for multiple-antenna systems considering channel estimation errors. The novelty of this study resides in providing error probability bounds for concatenated trellis coded modulation (TCM) or bit-interleaved coded modulation (BICM) schemes with orthogonal space--time block codes (OSTBC) under imperfect channel estimation assumption. Moreover, our analytical results quantify the performance degradation associated with various levels of channel estimation error variance. The authors also show that if channel estimation quality does not improve sufficiently with SNR, there would be error floor in performance, such that the coded system could get outperformed by a system with differential signalling that requires no channel estimation. Simulation results are presented, which confirm the validity of the analytical results.     

求解约束优化问题的退火遗传算法

针对基于罚函数遗传算法求解实际约束优化问题的困难与缺点,提出了求解约束优化问题的退火遗传算法。对种群中的个体定义了不可行度,并设计退火遗传选择操作。算法分三阶段进行,首先用退火算法搜索产生初始种群体,随后利用遗传算法使搜索逐渐收敛于可行的全局最优解或较优解,最后用退火优化算法对解进行局部优化。两个典型的仿真例子计算结果证明该算法能极大地提高计算稳定性和精度。