Bit error rate performance of iterative decoding in a perpendicular magnetic recording channel

The long-term bit error rate (BER) performance of partial response maximum likelihood (PRML) system in a perpendicular magnetic recording (PMR) channel with thermal decay is studied. A thermal decay model based on the experimental data for three CoPtCr-SiO2 PMR media with different thermal stability is obtained. Then, the performance of PR1ML channel for the 16/17(0,6/6) and 128/130(0,16/8) codes as a run-length-limited (RLL) code is evaluated by computer simulation using the model. Moreover, the relationships between the elapsed time and the BER are obtained for the combinations of two RLL codes and three PMR media and their performances are compared. The results show that for the combination of the 128/130(0,16/8) code and the medium with the poorest thermal stability, the degradation with the elapsed time is noticeable compared with the other combinations

Turbo decoding with an embedded autoregressive (AR) channel model is studied in an actual perpendicular magnetic recording channel. Performance of the a posteriori probability (APP) decoder is improved by applying an AR channel model in order to estimate the decoder input sequence. The bit-error-rate (BER) performance is obtained by read/write experiments using a spin stand with a perpendicular medium and an single-pole-type/giant magnetoresistive (SPT/GMR) head. The results show that our turbo coding and iterative decoding system using an AR channel model improves the BER performance.

Low-density parity-check (LDPC) codes are typically designed to avoid the length-4 cycles to ensure acceptable levels of performance. However, the turbo equalization, which relies on an interaction between an inner code such as an LDPC code and a soft-output Viterbi algorithm (SOVA) detector, exhibits a performance degradation due to the pseudo cycles. In this paper, we propose an interleaved modified array code (IMAC) that can reduce the number of pseudo cycles, hence, improving the gains from the iterative processing technique. The modification is made on the existing array-based LDPC codes named modified array codes (MAC) by introducing an additional interleaving matrix to the parity-check matrix. Simulation results on the perpendicular magnetic recording channels (PMRC) demonstrate that the IMAC outperforms both the MAC and the previously proposed random interleave array (RIA) codes for the partial-response targets under consideration. In addition, a subblock-based encoder design is proposed to reduce the encoding complexity of the IMAC and when compared with the RIA code, the IMAC exhibits a lower encoding complexity, and still maintains a comparable level of the decoding complexity.

In this work, we consider a perpendicular magnetic recording channel where the data is stored perpendicular to the plane of magnetic media. The perpendicular magnetic recording provides significant aerial density gain compared to the conventional longitudinal magnetic recording. This gain comes at the cost of adding a baseline wander noise which degrades the system performance and affects the data integrity. In this article, we propose a model for the baseline wander noise. The parameters of the proposed model are computed by posing the problem as minimizing the mean square error. We demonstrate that this problem can be appropriately simplified and posed as finding a least squares problem. The proposed model on the baseline wander noise requires the knowledge of information bits to estimate the noise but this information is unavailable at the time of decoding. We propose a novel technique to cancel the baseline wander effect on the Viterbi trellis. This cancellation is done on the fly in the trellis and obviates the need of the information bits yet provides the performance gain close to the genie performance. Simulation and experimental results corroborate the analysis of the proposed algorithm and demonstrate that the proposed algorithm provides the performance gain.

Performance improvement of partial-response maximum-likelihood (PRML) system in the perpendicular magnetic recording channel with jitter-like noise is studied. The performance of a Viterbi detector is improved by applying an autoregressive (AR) model in order to estimate the detector input sequence. The required signal-to-noise ratio to achieve a bit-error rate (BER) of 10/sup -4/ is obtained by computer simulation. In addition, a BER performance is also obtained by read/write experiments using a spin-stand. The results show that the proposed PRML system using an AR model exhibits better performance when compared with the normal PRML systems without an AR model.

Thermal asperity (TA) causes a major problem in data detection process. Without the TA detection and correction algorithm, the system performance (even with perfect synchronization) can be unacceptable, depending on how severe the TA effect is. This paper proposes a new method to suppress the TA effects in perpendicular magnetic recording channels. The TA detection is a threshold-based approach, while the TA correction is done by averaging the readback signal and applying a least-squares fitting technique to estimate the TA signal. Then, the corrected readback signal is obtained by subtracting the TA-affected readback signal by the reconstructed TA signal. Results indicate that the proposed method performs better than the existing one in terms of bit-error rate and is robust to changes in the peak TA amplitude.

Cheng (Doctoral Dissertation, CIT, Pasadena, California, 1997) introduced a class of linear codes called low-density generator matrix (LDGM) codes and studied its performance on a memoryless additive white Gaussian noise (AWGN) channel. In this paper, we study its performance on perpendicular magnetic recording channels. The results shown in this paper indicate that the bit-error rate (BER) performance of some LDGM-codes is comparable to that of low-density parity check (LDPC) codes of the same rate.

This paper studies the performance of iterative multiuser decoding, interference cancellation, and channel estimation techniques applicable to third generation WCDMA systems. The concept uses a posteriori probabilities of code symbols to enhance detection, decoding and channel estimation in an iterative fashion. The performance is analyzed in a multipath channel with simulations. It is seen that the proposed concept combats multiuser interference effectively and performs almost as well as single user systems.

In recent years, shingled magnetic recording (SMR) has attracted attention as a new recording system of the hard disk drives. Although SMR can realize narrow track by overwriting data track like tile roofing, it has remarkable performance deterioration due to the influence of inter-track interference. Therefore, the performance improvement of the low-density parity-check (LDPC) coding and iterative decoding system using the sum-product decoding is required. In this paper, we propose the LDPC encoding and iterative decoding system with the log-likelihood ratio modulator and show the error floor is eliminated and improvement of signal-to-noise ratio to achieve the error free is obtained in the SMR under an areal recording density of 4 Tbits/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> specification for the channel bit sequence coded by run-length limited and LDPC encoders by computer simulation. Therefore, the channel bit is composed bit about five magnetic grains.

We examine the performance of a rate-0.9 structured irregular repeat-accumulate (S-IRA) code on a perpendicular magnetic recording (PMR) channel with media noise. To account for the presence of data-dependent media noise, a pattern-dependent-noise-predictive (PDNP) channel detector is employed, in which the prediction filters are trained using the LMS algorithm. We compare the error rate performance of the S-IRA code with that of a Reed-Solomon (RS) code of the same length and rate, with the PDNP detector present in both cases. Our results show that the S-IRA code achieves a gain of over 1 dB relative to the RS code for sector error rates down past 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> , but only if the columns of its H-matrix are properly permuted. We have also estimated that the linear density gain attainable by the S-IRA code relative to the RS code is about 8% for the operating point we have chosen.

In this paper, new schemes have been proposed for the estimation of the additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) in an iterative equalization and decoding system using low-density parity check (LDPC) codes. This article explores the use of the least squares algorithm in various scenarios. For example, the impulse response of the AWGN channel h was initially estimated using a training sequence. Subsequently, the impulse response was calculated based on the training sequence and then re-estimated once using the sequence estimated from the output of the LDPC decoder. Lastly, the impulse response was calculated based on the training sequence and re-estimated twice using the sequence estimated from the output of the LDPC decoder. Comparisons were made between the performances of the three mentioned situations, with the situation in which a perfect estimate of the impulse response of the channel is assumed. The performance analysis focused on how the bit error rate changes in relation to the signal-to-noise ratio. The BER performance comes close to the scenario of having a perfect estimate of the impulse response when the estimation is performed based on the training sequence and then re-estimated twice from the sequence obtained from the output of the LDPC decoder.

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by symmetric Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes is analyzed by examining whether a signal-to-noise ratio (SNR) for the extrinsic information keeps growing with iterations. We define a for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded by a number below zero dB. By decomposing the code's noise figure into individual curves of output SNR versus input SNR corresponding to the individual constituent codes, we gain many new insights into the performance of the iterative decoder for different constituents. Many mysteries of turbo codes are explained based on this analysis. For example, we show why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are crystallized. The analysis is generalized to serial concatenations of mixtures of complementary outer and inner constituent codes. Design examples are given to optimize mixture codes to achieve low iterative decoding thresholds on the signal-to-noise ratio of the channel.

Çok taşıyıcılı (MC) telsiz iletişim sistemlerinin en büyük dezavantajlarından birisi yüksek tepe-ortalama güç oranı (PAPR)’dır. Pek çok standartta kabul edilen dikgen frekans bölmeli çoğullama (OFDM) sistemi de bu dezavantajdan etkilenmektedir. Araştırma literatüründe MC telsiz iletişim sistemlerinin yüksek PAPR seviyelerini azaltmak için genlik kırpma (AC) ve filtreleme, kodlama, serpiştirme, ton rezervasyonu (TR), ton ekleme (TI), kısmi iletim dizisi (PTS) ve seçilmiş haritalama (SLM) teknikleri gibi pek çok yöntem sunulmuştur. Bunlara ek olarak, bu PAPR azaltma yöntemlerini kullanan MC telsiz iletişim sistemlerinin diğer performanslarının iyileştirilmesi amacıyla sistemlere uygulanan hızlı Walsh Hadamard dönüşümü (FWHT) ve ayrık dalgacık dönüşümü (DWT) gibi dönüşümlerde sunulmuştur. Bu çalışmada, MC telsiz iletişim sistemlerinin hem bit hata oranı (BER) performansını hem de PAPR başarımını iyileştirmek için PTS ve AC tekniği ile Lazy dalgacığını kullanan Lifting dalgacık dönüşümünün (LLWT) birleştirilmesi önerilmektedir. Bu makalede, ilk defa bu çalışmada önerilen PTS ve AC tekniği ile LLWT dönüşümünün birleşimi olan LLWT-PTS-AC yöntemi, MC telsiz iletişim sistemlerinin dezavantajlarını ortadan kaldırmak için klasik OFDM dalga formuna uygulanmıştır ve kayda değer sonuçlar elde edilmiştir. Sonuçlar incelendiği zaman, klasik OFDM sisteminin PAPR ve BER başarımlarının tatmin edici ölçüde arttığı görülmektedir.

A new method for adjusting positions of signal points of a traditional signal constellation used in the BICM-ID (Bit-Interleaved Coded Modulation with Iterative Decoding) system is proposed. Optimal rotation angle versus SNRs (Signal-to-Noise Power ratios) in the sense of providing the system with attainable lowest BER (Bit Error Rate) are reported.

The edge connections in factor graphs of quasi-cyclic (QC) LDPC codes, which affect their iterative decoding performance, are determined by their base matrices. In this paper, the effects of base matrices on the iterative decoding performance of QC-LDPC codes are investigated by using the recently proposed EXIT chart tool for protograph LDPC codes. Extensive experiments have been carried out and iterative decoding thresholds of QC-LDPC codes with the same degree distribution pair but base matrices having different structures and different dimensions have been obtained and compared. Experimental results show that 1) the base matrix structure affects not only the waterfall performance but also the error floor performance; base matrices having good waterfall performance may exhibit rather poor error floor performance. 2) by increasing the dimensions of base matrices for a given degree distribution, the threshold means are reduced while the ranges of threshold distributions are increased. 3) similar to the case of detailed represented LDPC codes, base matrices with sufficiently large dimensions may have thresholds surpassing the conventional ensemble threshold with the same degree distribution pair. Moreover, as a concrete example, an improved base matrix is designed for a rate-1/2 WiMax LDPC code.