Bit errors due to channel modulation of media jitter

Partial-response (PR) signaling is used to model communications channels with intersymbol interference (ISI) such as the magnetic recording channel and the copper-wire channel for digital subscriber lines. Coding for improving noise immunity in higher order partial-response channels, such as the extended class-4 channels denoted EPR4, E/sup 2/PR4, E/sup 3/PR4, has become an important subject as the linear densities in magnetic recording approach those at which these partial-response channels are the best models of real channels. In this paper, we consider partial-response channels for which ISI is so severe that the channels fail to achieve the matched-filter bound (MFB) for symbol error rate, assuming maximum-likelihood decoding. We show that their performance can be improved to the MFB by high-rate codes based on constrained systems, some of which may even simplify the Viterbi (1979) detectors relative to the uncoded channels. We present several examples of high-rate constrained codes for E/sup 2/PR4 and E/sup 3/PR4 channels and evaluate their performance by simulation.

A number of papers have recently been published on the concatenation of an outer code with a partial response (PR) channel, where the outer code is a turbo code, a convolutional code, or a low density parity check code. This paper deals with the second case assuming EPR4 and modified extended EPR4 (MEEPR4) partial response targets. The goal in this work is the joint optimization of interleaver and precoder for a fixed outer convolutional code and PR target. We introduce mathematical and algorithmic tools for accomplishing this goal and present simulation results which support our approach. Among the positive results is the ability to lower the well-known error rate floor of these concatenated schemes for arbitrary partial response channels.

We present a systematic way to construct multilevel concatenated codes for partial response (PR) channels using: (1) a structured set partition (SSP) of multiple channel output sets and (2) a set of conventional block codes with different error correcting capabilities. A lower bound on the minimum squared Euclidean distance of the constructed codes is given. This bound is based on the interset minimal Euclidean distances of the SSP and the minimum Hamming distances of the used block codes. An example of SSP for the extended class 4 partial response channel (EPR4) is presented. Iterative suboptimal decoding, which combines Viterbi detection on the trellis of the PR channel with algebraic error detection/correction, can be applied to the constructed concatenated codes. Truncated versions of the iterative decoding scheme are simulated and compared with each other.

Towards the goal of achieving better error correction performance in data storage systems, iterative soft decoding of low density parity check (LDPC) codes and soft-decision decoding of Reed-Solomon (RS) codes have started receiving increasing research attention. However, even with increased computing power, complexities of soft-decision decoding algorithms are still too high for real products which require high throughput and small hardware area. Another problem is that the performance gains of those approaches are smaller for magnetic recording channels than they are for memoryless additive white Gaussian noise (AWGN) channels. We propose a new soft-decision decoding algorithm (based on the Chase algorithm), which takes advantage of pattern reliability instead of symbol reliability or bit reliability. We also present a modified Viterbi algorithm that provides probable error patterns with corresponding reliabilities. Simulation results of the proposed algorithms over the partial response (PR) channel show attractive performance gains. The proposed algorithm dramatically reduces the number of iterations compared to the conventional Chase2 algorithm over the PR channel.

Combination of turbo codes with partial response (PR) channels was comprehensively studied in magnetic recording systems. In this paper, we investigate a decoding scheme called 'iterative tri-stage decoding' for the turbo code as the outer code and the precoded PR channel as the inner code. This decoding scheme reduces the computational complexities by reducing the number of iterations without degrading the coding gain.

The dependence of MSE and marginalized BER on amplitude asymmetry for two partial response channels is reported. To eliminate the impact of variations in other head parameters, we varied the bias point of a given head using an external magnetic field. We find that the MSE degrades continuously as the magnitude of the amplitude asymmetry is increased; the marginalized BER is at most weakly dependant on amplitude asymmetry for magnitudes less than 15%. At larger magnitudes the channel performance is more severely impacted, Finally, we were able to simulate these results using a simplified model of the read channel.

This paper is concerned with the applications of majority-logic decodable nonbinary low-density parity-check (LDPC) codes to partial response (PR) channels. We propose a joint detection/decoding algorithm that works in an iterative manner by exchanging messages between the Viterbi detector and a generalized majority logic decoder (GMLGD). The Viterbi detector is implemented over a sectionalized trellis. The hard-decisions made by the Viterbi detector are then passed to the decoder. The decoder delivers as output estimates of each coded symbols, which will be utilized in next iteration to update the branch metrics of the trellis. Since the proposed algorithm requires only integer operations and finite field operations, it can be implemented with simple combinational logic circuits. Simulation results and complexity analysis show that, when compared with the conventional turbo equalizer implemented with the BCJR algorithm and the Q-ary sum-product algorithm (BCJR-QSPA), the proposed algorithm has a much lower complexity but suffers from a little performance degradation. So the proposed algorithm provides a good candidate for trade-offs between performance and complexity.

Summary form only given. Following the work done by Ryan (Proc. ICC Int. Conf. on Communications, 1998), considerable research has been reported on the application of concatenated codes to partial response (PR) channels. Both parallel concatenated codes (PCC) and serial concatenated codes (SCC) have been studied. In all of those works, a linear model for the channel was assumed, which is a valid assumption for low recording densities. However, as the recording density increases, the channel becomes nonlinear where nonlinearity arises from closely spaced recorded transitions. In this paper, we combine concatenated coding and nonlinear equalization for PR channels that suffer from nonlinear distortion (or intersymbol interference) according to the setup shown in Fig 1. We extend the RAM-search/Viterbi-detector concept to the a posteriori probability (APP) and soft-output Viterbi algorithm (SOVA) detectors that are used with turbo-coded partial response channels. The modified APP and SOVA are called RS-APP and RS-SOVA, respectively.

Transmitter and receiver filter design plays a key role in communication systems with partial response channels. For a partial response system, a nonmaximally decimated multirate filter bank can be used as a precoder. Based on the MMSE criterion, a closed-form solution to the joint transmitter-receiver optimization problem for noisy partial response channels is presented in this paper. It is found that the redundancy introduced by the nonmaximally decimated filter bank precoder can compensate for spectral nulls in partial response channels that can impair several known joint optimization methods. Simulation results corroborate the analysis that joint transmitter-receiver optimization can achieve significant performance improvement over inverse filter receiver and receiver optimization schemes.

In this paper, a physical model of readback signals from a hybrid magneto-optical (MO) recording using magnetic flux detection is presented. The minimum mean-square error (MMSE) technique has been used to design generalized partial response (GPR) targets in order to facilitate the application of the trellis based channel detector. A PR target with integer coefficients is proposed as a good approximation to the GPR target. We also address the application of turbo codes and LDPC codes with iterative soft decoding structure to the hybrid magneto-optical (MO) recording channel. The effects of bloom, transition noise and giant magneto-resistive (GMR) sensor nonlinearity on the bit error rate (BER) performance are investigated both for uncoded partial response maximum likelihood (PRML) and iterative soft decoded recording channels. Our results for the hybrid recording channels indicate that turbo/LDPC codes of rate 16/17 can achieve coding gains of about 5 dB over PRML methods for a 10/sup -5/ target BER at the normalized density S=1.5. Turbo codes with iterative soft decoding are seen to be robust to transition noise.

The partial response channel can be viewed as a rate-1 encoder in which the output alphabet differs from the input alphabet. In serially concatenated coding schemes, the partial response channel can serve as the inner encoder. Recent works on the application of turbo decoding techniques to partial response channels have used channel models to investigate system performance. While the models provided some insight into the performance of turbo decoding techniques, performance in a real system, with electronic and signal-dependent media noise, remained unknown. This paper will demonstrate the performance of turbo decoding techniques using real and modeled spinstand data. A simple serial concatenation system will be presented that uses as its outer code a single convolutional code and as its inner code the partial response channel. Significant gains will be shown over QMTR coded systems.

We demonstrated near-field recording with the combination of a GaN laser diode and a 1.5 NA objective lens. The realized linear bit density was less than 90 nm (corresponding to the areal recording density over 40 Gbit/in/sup 2/) regardless of using a small 1.0 mm-diameter super-hemispherical solid immersion lens (SIL). Further improvement of a near-field phase-change optical disk will enable a linear bit density of 80 nm or less. In this talk we shall also report the fabrication process of the plateau, and of the electrode on the SIL.

By dividing the available spectrum into multiple bands, multi-band ultra-wideband (UWB) systems possess many advantages, such as the flexibility to eliminate possible interference and coexistence problems with available wireless standards. UWB channels have large delay spread, causing inter- symbol interference (ISI) in high rate systems. The RAKE receiver is often used to capture multipath energy, but it is incapable of ISI compensation, causing severe bit error rate (BER) degradation in practical UWB channels. This paper proposes an over-sampling multi-channel equalizer per sub-band for multi-band UWB. The performance of the proposed receiver is compared with the RAKE receiver through analytical and simulation studies. The proposed equalizer has been shown to be able to handle ISI under any channel conditions or data rate presented, with an acceptable BER. In addition, the rich multipath diversity of the UWB channels is harnessed by the over-sampling scheme, for output SNR improvement. one. Therefore, equalization receiver based on adaptive algorithms seems to be an effective way to recover the transmitted data. With this consideration, we propose an over-sampling multi-channel equalizer per sub-band for a multi-band UWB system, which provides more effective inter-symbol interference (ISI) suppression compared with the conventional RAKE receiver when operating in channels with large delay spread. Through detailed theoretical analysis and extensive simulations, we are able to show that the proposed 4-arm equalizer scheme is superior to a 4-arm conventional RAKE receiver in the presence of ISI at all signal-to-noise ratios (SNRs). Based on the method presented in (4), the simulated performance is shown to conform to analytical predictions. The RAKE receiver is incapable of ISI compensation, and a moderate level of ISI is shown to cause severe bit error rate (BER) degradation. The proposed over-sampling equalizer, on the other hand, is able to handle ISI under any channel conditions or data rate, with an acceptable BER. Over- sampling is shown to be able to achieve diversity gain, and improves the output SNR.

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.

In this paper, the combined normalized and offset min-sum algorithm is proposed for efficient decoding of low-density parity-check (LDPC) codes in optical and magnetic storage systems. The proposed algorithm can be considered as a general case of the normalized and offset algorithms, and offers better BER performance compared to them. The performance improvement is presented for a partial response magnetic recording channel. Our simulations are based on an LDPC code from the class of finite-geometry LDPC codes. It will be shown that the proposed method has a performance very close to that of the belief propagation algorithm which has a much higher complexity.