V-Shaped Viterbi Symbol Detection for Multilevel 2D Optical Storage

In this paper, use of recurrent neural network equalizer (RNNE) in place of linear equalizer (LE) to combat both linear and nonlinear distortions corrupting the Magneto-optical (MO) readback signal is discussed. It is shown that RNNE can outperform LE without introducing significant complexity. RNNE is used to equalize the MO recording readback signal corrupted by transition jitter, intersymbol interference (ISI) and additive white Gaussian Noise (AWGN) at a density of 50 kbpi. The MO signal is equalized to a partial response (PR) (1 + D) using either the RNNE or the LE and the equalizer's mean- squared-error (MSE) performance is compared. Then, the equalized signal is passed through a detector and it is shown that a signal equalized to a PR (1 + D) shape can be detected using either a bit-by-bit type of detector (BD) or a sequence detector implemented via Viterbi Algorithm (VA). The bit-error-rate (BER) performance of BD is compared to that of the Viterbi detector and it is shown that PR equalization of MO readback signals using RNNE improves MSE performance over linear equalizer, allowing use of BD rather than LE + Viterbi Algorithm with comparable BERs.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The increasing demand for high-density and high-speed digital optical recording systems has made the development of advanced coding and signal processing techniques for fast and reliable data recovery increasingly important. In recent years, the parity-check (PC)-code-based reception technique has been widely studied for magnetic recording systems, and it is projected to be highly promising for high-density optical recording. The PC code is an inner error correction code (ECC), which can detect dominant short error events of the system, using only a few parity bits. This reduces the loss in error correction capability of the outer ECC due to random short errors and results in a simple and efficient solution to improve the overall performance. This thesis is dedicated to the design and analysis of PCcode- based recording systems to achieve higher recording capacity with low implementation complexity, for high-density blue laser disc systems. In particular, most of the key components of the PC-code-based optical recording system have been designed and optimized for different recording densities, and different proportions of white noise and media noise. During the development of advanced coding and detection techniques, it becomes necessary to investigate the system’s performance with different coding schemes and recording densities. In Chapter 2 of the thesis, we propose a generalized Braat-Hopkins model for optical recording channels, which provides a fair basis for the performance comparison of detection schemes over different coding schemes and recording densities, for channels with additive, white Gaussian noise (AWGN) and media noise. Various basic issues associated with the PC-code-based systems are investigated in Chapter 3. These include bounds for bit error rates and error event probabilities, the dominant error events at channel detector output, different PC codes, simple and efficient post-processors, the impact of error events that are split across data block boundaries and the corresponding remedy, as well as the effects of code rates and recording densities. Simulation results show that a 4-bit PC code achieves the best performance. The corresponding bit error rates (BERs) are very close to the performance bounds, at both nominal and high densities. Constrained codes, which serve as a key component in the read-write channel of data storage systems, are desired to have a high code rate with low-complexity encoder/decoder. In Chapter 4, we investigate the design of certain capacity-approaching constrained codes for optical recording systems. In particular, we derive analytically the relationship between the number of encoder states and the maximum size of these codes. We identify the minimum number of encoder states that maximizes the code rate, for any desired codeword length. The design of constrained PC codes is key to the development of PCcode- based systems, and the systematic design of efficient constrained PC codes remains a challenging problem. In Chapter 5, we propose a general and systematic code design technique for constructing capacity-approaching constrained PC codes, which can detect any type of error events of the system, with the minimum code rate loss. Compared to the rate 2/3 code without parity, the newly designed constrained 4-bit PC code achieves a performance gain of 2 dB at nominal density, and 1.5 dB at high density, at BER = 10-5. As the dominant noise for high-density optical recording systems, media noise severely degrades the performance of channel detectors and postprocessors that are designed for AWGN. In Chapter 6, we propose two novel modifications to the bit detector to combat media noise. We further develop a data-dependent post-processing scheme for error correction. Compared to the system designed without considering media noise and without PC codes, the overall performance gain of the developed scheme can be more than 11 dB at high media noise levels. In data storage systems, the ECC failure rate (EFR) serves as the ultimate measure of the data recovery performance. In Chapter 7, we develop semi-analytical approaches for estimating the EFR, and analyze EFRs for the developed PC-code-based systems, for the cases without and with interleaving. Our analysis shows that with the optimum interleaving degrees, compared to the rate 9/13 code without parity, the 2-bit PC code achieves a gain of around 0.5 dB, and the 4-bit PC code gains 0.6 dB, at high record ing density and EFR = 10-16. The thesis concludes in Chapter 8 with some suggestions for further work.

Multi-Gb/s high-speed links face significant challenges in keeping up with the increase in desired data rates. In the evaluation of achievable data rates, it is necessary to include both link-specific noise sources and implementation driven constraints. We construct models of these noise sources and constraints in order to estimate the theoretical limits of typical high-speed link channels. In order to estimate the data rates of practical baseband architectures, we solve the power constrained optimal linear precoding problem and formulate a bit-error rate (BER) driven optimization, including all link-specific noise sources. The problem is shown to be quasiconcave, hence, a globally optimal solution is guaranteed. Using this optimization framework, we show that practical data rates are mainly limited by inter-symbol interference (ISI) due to complexity constraints on the number of precoder and equalizer taps. After these constraints are removed, we further show that slicer resolution and sampling jitter are limiting the higher bandwidth utilization provided by multi-level modulations. Better circuits are needed to improve the bandwidth utilization to more than 2bits/dimension in baseband.

In this work, we base on multi-layered perceptron neural networks with backpropagation algorithm (MLP/BP) to construct multi-input multi-output (MIMO) decision feedback equalizers (DFEs). The proposal is used to recover distorted quadrature phase-shift keying (QPSK) signal. From the simulations, we note that the proposed scheme can recover severe distorted signals as well as suppress intersymbol interference (ISI), adjacent channel interference (ACI) and background additive white Gaussian noise (AWGN). The better bit-error-rate (BER) and packet-error-rate (PER) performance as compared to a set of least-mean-square (LMS) DFEs is achieved. The presented MLP/BP-based MIMO DFE under the severe ISI channels with ACI and AWGN can improve over 1.5dB at PER=10-1 and BER=10-3.

Multistage decoding of multilevel block multilevel phase-shift keying (M-PSK) modulation codes for the additive white Gaussian noise (AWGN) channel is investigated. Several types of multistage decoding, including a suboptimum soft-decision decoding scheme, are devised and analyzed. Upper bounds on the probability of an incorrect decoding of a code are derived for the proposed multistage decoding schemes. Error probabilities of some specific multilevel block 8-PSK modulation codes are evaluated and simulated. The computation and simulation results for these codes show that with multistage decoding, significant coding gains can be achieved with large reduction in decoding complexity. In one example, it is shown that the difference in performance between the proposed suboptimum multistage soft-decision decoding and the single-stage optimum decoding is small, only a fraction of a dB loss in SNR at the block error probability of 10/sup -6/. >

A differentially coherent receiver which uses the Viterbi algorithm is presented. This receiver compensates for intersymbol interference (ISI) and avoids noise enhancement. A phase estimate which takes into account the presence of inherent ISI in the signal is derived. This phase estimate is then used in the decision metric of a coherent receiver. The resulting decision rule can be implemented using the Viterbi algorithm. The complexity of the resulting receiver increases with the duration of observation used by the implicit phases estimator. A simple four-state Viterbi receiver with good performance is obtained when the phase estimate is based on one observable. Simulation results are given. >

Discrete multitone modulation allows for a simple receiver structure if the impulse response of the communication channel is shorter than the cyclic prefix. In ADSL, a time-domain equalizer (TEQ) is used to fulfil this requirement. Without a TEQ, unwanted intercarrier interference (ICI) and intersymbol interference (ISI) occur. In this paper, quadratic forms are developed to calculate the contributions of ICI and ISI to the desired signal. Based on these expressions, a new method for calculating the TEQ coefficients, which minimizes the effects of ICI, ISI, and additive noise, is derived. Simulations in the context of ADSL compare the performance of this new algorithm with one that is state of the art.

Convolutional code is a coding scheme used in communication systems including deep space communications and wireless communications.It provides an alternative approach to block codes for transmission over a noisy channel.The block codes can be applied only for the block of data.The Convolutional coding has an advantage over the block codes in that it can be applied to a continuous data stream as well as to blocks of data.Viterbi decoder employed in digital wireless communication plays a rife role in the overall power consumption of trellis coded modulation decoder.Power reduction in Viterbi decoder could be achieved by reducing the number of states.A pre-computation architecture with T-algorithm was implemented for this purpose, and when we compare this result with full Trellis Viterbi decoder, this approach significantly reduces power consumption without degrading decoding speed.Convolutional encoding with viterbi decoding is a powerful FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by Additive White Gaussian Noise (AWGN).It operates on data stream and has memory that uses previous bits to encode.The Viterbi Algorithm (VA) is proposed, used for decoding a bit stream that has been encoded using FEC code.The Convolutional encoder adds redundancy to a continuous stream of input data by using a linear shift register.A pre-computation architecture with Viterbi algorithm is implemented for this purpose, Viterbi (Convolutional) encoder and Viterbi decoder are designed and implemented using FPGA technology, which are the essential blocks in digital communication systems.It is particularly suited to a channel in which the transmitted signal is corrupted mainly by AWGN.The Viterbi decoder of Constraint length 7 and code rate ½ is considered.The design is implemented using verilog on Xilinx Spartan 3E and advanced Spartan 6 board and the results and Comparisons are presented.

A Novel Analytical OFDM Modulation Framework using Wavelet Transform with Window Function in the Hilbert space

Motivated by the capacity-approaching property of both binary polar codes (PCs) and the multi-level coding (MLC) scheme, we consider the design of modulated PC over additive white Gaussian noise (AWGN) channels. The capability of modulated PC essentially depends on the selection of information bits set from all the virtual bit channels formed by both modulation and channel polarization. To this end, we characterize the a priori distribution density as the sufficient statistic for the bit channel of individual modulation levels formed by an MLC scheme, in which the codeword of symbols is split into parallel bits streams. According to the factor graph generated by the binary PC, we apply the density evolution (DE) for each binary modulation level. Consequently, distribution densities of every bit within the modulated codeword can be obtained and we select the most reliable bits as information bits and set the complement as frozen bits. Comprehensive simulations demonstrate the validness of this approach compared to the benchmark scheme.

Fog is a highly dispersive medium at optical wavelengths, and the received pulse waveform may suffer significant distortion. Thus it is desirable to have the impulse response of the propagation channel to recover data transmitted through fog. The fog particle density and the particle size distribution both strongly influence the channel impulse response, yet it is difficult to estimate these parameters. We present a method using a dual-wavelength free-space optical system for estimating the average particle diameter and the particle number density and for approximating the particle distribution function. These parameters serve as inputs to estimate the atmospheric channel impulse response using simulation based on the modified vector radiative transfer theory. The estimated channel response is used to design a minimum mean-square-error equalization filter to improve the bit error rate by correcting distortion in the received signal waveform due to intersymbol interference and additive white Gaussian noise.

Coherent detection of asynchronous Code-Division MultipleAccess (CDMA) data transmissions over a Rician fading channel is considered in the context of a multipoint-to-point communication system, where a centralized receiver that is assumed to have knowledge of the signature signals of the system uaers, including the arrival times of the former, observes a superposition of the specular and faded signal components of each of the users in additive noise, The channel itself is assumed to be non-dispersive, and with no fading memory, i.e., the random attenuations and phase shifts experienced by the users’ transmissions over different bit intervals are assumed to be independent of each other, rendering them inestimable. It turns out that this channel is equivalent to a fictitious CDMA-AWGN (Additive White Gaussian Noise) channel from the point of view of optimal detection [I]; it may be shown that the optimum decision rules over the two channels as well as the statistical characterization of the sufficient statistics in each case parallel each other. Unlike the optimum AWGN multiuser detector however, the optimum faded detector is unimplementable using a Viterbi algorithm. This motivates the derivation of the polynomial- complexity faded decorrelator for this channel. Detector performance in a multiuser faded environment may be adversely affected by both the interferer specular (or known) and faded (or unestimatable) signal components. The performance limiting effect of the former on conventional detection as well as the ability of fading channel strategies to withstand such interference has been studied earlier [I]. The issue of the limitations on detector performance, if any, due to interfering fading is addressed here. To this end, we introduce the fading susceptance and fading resistance measures; the former as a measure of whether degradations in detector performance due to interfering fading are so great so as to prevent them from being compete tive with optimum detection strategies over single-user channels, and the latter as a measure that captures the ability of detectors to withstand such interference These asymptotic measures characterize detector performance in regions where the fading of the interfering users as opposed to their specular energies, is the dominant impediment to detection. An analysis of the conventional detector’s performance in the multiuser faded environment reveals that fading interference is capable of limiting detector performance in a manner similar to specular component interference bringing out the hitherto unrecognized performance limiting effect of fading interference in Rician fading CDMA channels. The AWGN niultiuser detectors (optimal and decorrelating), which are designed for the CDMAAWGN channel, while sub-optimally resistant to specular interference, pay a penalty for ignoring the presence of fading in that they are also found to be susceptible to fading interference. Thus we demonstrate that, even in environments where specular interference is marginal, both of the above detectors are incapable of competing with detectors of isolated transmissions, if the fading of an intefering user dominates the background noise. The faded detectors, both optimal and decorrelating, are however found to withstand such interference. In light of their previously demon46 strated resistance to specular interference, and the additional computational considerations, our results make the case for the use of the faded decorrelators for multiuser detection over asynchronous Rician faded CDMA channels. The plots of Figure 1 are an illustiation of the irnplications of our results for detector Bit-Error Rates (BERs) in realistic as opposed to asymptotic environments. We observe that, over a two-user channel, even with a weak interferer specular signal, the first user of the faded decorrelator alone exhibits an exponential decay in BER with increasing Signal-to-Noise Ratio (SNR) with both the conventional detector and the AWGN decorrelator forced by the non-zero, fixed interferer fading, to approach error floors

Neural network based equalizers can easily compensate channel impairments; such additive noise and inter symbol interference (ISI). The authors present a new approach to improve the training efficiency of the multilayer perceptron (MLP) based equalizer. Their improvement consists on modifying the back propagation (BP) algorithm, by adapting the activation function in addition to the other parameters of the MLP structure. The authors report on experiment results evaluating the performance of the proposed approach namely the back propagation with adaptive activation function (BPAAF) next to the BP algorithm. To further prove its effectiveness, the proposed approach is also compared beside a so known nonlinear equalizer explicitly the multilayer perceptron with decision feedback equalizer MLPDFE. The authors consider various performance measures specifically: signal resorted quality, lower steady state MSE reached and minimum bit error rate (BER) achieved, where nonlinear channel equalization problems are employed.

High Peak-to-Average Power Ratio (PAPR) of the transmitted OFDM signal is a well-known major drawback of the Orthogonal Frequency-Division Multiplexing (OFDM), so the High-Power Amplifier (HPA) is therefore necessary to operate in its linear region, i.e. with large back-off between the operating input power and its saturation region, so introducing not only in-band distortion, but also the adjacent channel interference. Specifically with the Long-Term Evolution (LTE) systems downlink, some sort of PAPR reduction, such as e.g. clipping, must be utilized. Considering that in many practical situations, determining PAPR demands complex test equipment, such as e.g. Vector Signal Analyzer (VSA), which might not be available, in this paper, we develop a simple Bit-Error-Rate (BER) based model for the (residual) PAPR estimation, by applying link abstraction, i.e. considering the easy measurable BER degradation due to HPA non-linearity, as if it were the consequence of the according level of additive white Gaussian noise (AWGN) abstracting the HPA distortion, while considering high Signal-to-Noise Ratio (SNR) and long enough cyclic prefix (CP), thus neglecting (real) additive noise and time dispersion (i.e. multipath fading and the consequent inter-symbol interference). The analytical model is verified by the appropriate Monte-Carlo simulations.

We report on optimum direct detection of digital data signals that are transmitted over optical fibers. Direct detection is provided by a photodetector whose output current is modeled as a noisy filtered Poisson stream of pulses. In this model, the time-varying pulse arrival rate is proportional to a linearly distorted version of the modulating signal. We show how the photodetector output is processed to derive the minimum probability-of-error receiver. Special attention is given to certain practical limiting cases. When the average energy in the response of the photodetector to an individual photon is small compared to the additive thermal noise, the optimum detector is shown to be linear except for the use of precomputed bias terms. At the other extreme are the photomultiplier and the avalanche photodiode where the average energy in the response of the photodetector to a single photon is large compared with the additive noise. In this situation, we show that the optimum detector estimates the photon arrival times and then uses these estimates in a weighted counter. In both limiting cases, the detectors are specialized to one-shot M-ary and synchronous multilevel pulse-amplitude modulated (pam) signals with intersymbol interference. For pam signaling, we demonstrate that finite system memory allows application of dynamic programming to provide a detector implementation whose computational complexity does not increase with time.