Constrained coding for binary channels with high intersymbol interference

Recording media written-in transition jitter noise can limit magnetic recording systems. Read channel intersymbol interference (ISI) modulates media jitter in a head/disk/channel, attenuating jitter at low linear density due to classical ISI but amplifying at high density. This paper assesses whether jitter modulation is significant in typical disk drive peak detect (PD) and partial response (PR) channel design, where maximum linear bit density is sought at a specified bit error rate (BER). Experimental isolated pulse data, transition noise, and electronic noise measurements from a 65 mm head/disk recording design are used as inputs to a Matlab simulation of PD and PR Lorentzian channel low pass and boost filters, PD differentiator filter, PR digital filter, and PD/PR bit detectors. The goal of such models is optimizing the designable PD and PR channel parameters for realistic maximum linear density prediction. However their complexity obscures the jitter modulation contribution, which is demonstrated here by the shift in the EER versus density curves, when the jitter modulation is mathematically turned off. Jitter modulation is thereby shown to be significant but not dominant in (1,7) PD density limits. About an order of magnitude BER loss due to jitter modulation can occur at typical PD linear channel bit densities P/sub 50//T/spl ap/2. Jitter amplification in PD channels can occur at channel density 3.8 (above usable PD limits). PR channels only amplify media jitter, degrading EER by about an order of magnitude at typical (0, k) PR4 densities, and degrading timing channel accuracy twice as fast as channel density increases. Lorentzian isolated pulse (ISOP) modeling is compared to recording physics mathematical pulses, and simulation statistical validity checks are made.

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.

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.

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.

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.

We study the performance of turbo codes for magnetic recording channels using realistic channel models. The main objective is to provide a benchmark for the future studies on the subject. We examine a variety of schemes including the use of parallel concatenated turbo codes with and without turbo equalization and convolutional codes with an interleaver (can be regarded as a serial concatenation of convolutional codes with the partial response channel). We investigate the effect of the (turbo) code block length, the use of different code structures, and the effects of precoding and the media noise on the system performance. We assume that the partial response target is EPR4.

Using a semianalytic technique based on the work of Agazzi and Seshadri, we compare the performance of PR1, PR4, and EPR4 partial response schemes on a magnetic recording channel. The technique includes the effect of imperfect equalization and, in the PR4 case, the effect of employing two interleaved Viterbi detectors. Assuming the Lorentzian channel model and superposition, we use this technique to compare these signaling schemes at medium and high recording densities. It is observed that, even with the trivial DC-free code employed, PR1 is superior to PR4 at recording densities beyond about S/sub c/=2.4 and superior to EPR4 beyond about S/sub c/=2.9. In addition, PR1 lends itself to difference metric Viterbi detection. Our analytical results are supported by computer simulations.

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.

High data-rate upstream transmission in wavelength division multiplexed passive optical network (WDM-PON) based on reflective semiconductor optical amplifier (RSOA) is limited by severe inter-symbol interference (ISI), owing to low-bandwidth transmitter and fiber dispersion. To overcome the limitations in RSOA-based WDM-PON, we propose a novel receiver based on partial response maximum likelihood (PRML) equalization which combines the use of partial response (PR) signaling with maximum likelihood sequence estimation (MLSE). MLSE has been long considered as the optimal reception technique to overcome various types of impairment in optical transmission such as dispersions. It is demonstrated in this paper that PRML surpasses standard MLSE in ISI and reflection suppression with reduced complexity for RSOA-based WDM-PON system. 150 km unidirectional distance is demonstrated for 10 Gb/s uplink, while bidirectional uplinks up to 50 km and 20 km are achieved for data rate of 10 Gb/s and 20 Gb/s respectively, in WDM-PON using PRML. Furthermore, the impacts of discrete reflections on various equalization techniques are investigated, where PRML also shows superiority over MLSE.

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.

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.

Optical wireless communication (OWC) has received increasing attention recently. One application of OWC uses image sensor as optical receiver, which is known as optical camera communication (OCC). Rolling shutter mode in OCC allows data rate higher than the camera frame-rate operation. However, the row by row exposure delay will create decoding challenge, and high inter-symbol interference (ISI) can be observed in the rolling shutter pattern. In this work, we propose and demonstrate an OCC system employing pixel-per-bit (PPB) as label for the deep neural network (PPB-NN). Besides, two rolling shutter patterns emitted by two LED light panels can be decoded simultaneously. The proposed PPB-NN is also compared with other decoding schemes in the literature, and the experimental results revealed that the proposed scheme can achieve a better bit-error ratio (BER) performance.

Diffusion-based molecular communication system (DBMC) is a system in which information-carrying molecules are sent from the transmitter and passively transported to the receiver in a fluid environment. Nanomachines, which are the main part of this system, have limited processing capacity. Besides, at the receiver, high inter-symbol interference (ISI) occurs due to free movement of molecules and the variance of the observation noise is signal dependent. Hence, it is important to design high-performance and low complexity receiver detection methods. In this paper, finite impulse response (FIR) Wiener filter is introduced for the first time, which has considerably less computational complexity compared to the minimum mean square error (MMSE) algorithm proposed in the literature. Moreover, extended Kalman filter is introduced for the first time to DBMC as a receiver detection method. Finally, Viterbi algorithm is modified and used as a benchmark for performance evaluation.

The magnetic recording channel is often equalised to the PR4 partial response. Viterbi detection is used to detect the recorded data, but suffers a loss owing to the effects of noise correlation. The use of coding on the PR4 magnetic recording channel to reduce the effects of noise correlation is proposed. This is shown to achieve a gain in effective SNR over an uncoded channel. Parity codes are shown to be one method of achieving this. The read data is decoded with a soft decision Viterbi detector. The performance of the method is verified through simulations.

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.