J. R. Cruz

Reduced-complexity decoding of Q-ary LDPC codes for magnetic recording

Binary low-density parity-check (LDPC) codes perform very well on magnetic recording channels (MRCs) with additive white Gaussian noise (AWGN). However, an MRC is subject to other impairments, such as media defects and thermal asperities. Binary LDPC codes may not be able to cope with these impairments without the help of a Reed-Solomon code. A better form of coding may be Q-ary LDPC codes, which have been shown to outperform binary LDPC codes and Reed-Solomon codes on the AWGN channel. In this paper, we report on our investigation of Q-ary LDPC coded MRCs, both with AWGN and with burst impairments, and we present a new reduced-complexity decoding algorithm for Q-ary LDPC codes. We show that Q-ary LDPC codes outperform binary LDPC codes in the presence of burst impairments.

Inter-Track Interference Mitigation for Bit-Patterned Magnetic Recording

In bit-patterned magnetic recording (BPMR), inter-track interference (ITI) becomes a major impairment due to the small track pitch. One way to mitigate the ITI is to equalize the read channel to a two dimensional (2D) partial-response (PR) target. However, we find that the channel detection on the center track cannot take advantage of the 2D target without good estimation of the data on the sidetracks. Therefore, we propose a multi-track detection technique, where the detection on the center track is aided by the information obtained from the detection of the sidetracks. This technique works with any equalizer capable of equalizing the channel to a 2D target. We apply this method to joint-track equalized and 2D equalized BPMR channels. Our simulation results show that the proposed technique provides a significant performance improvement.

Reliability-Based Reed-Solomon Decoding for Magnetic Recording Channels

The performance of soft-decision Reed-Solomon decoding using belief propagation (BP) is investigated on partial-response equalized magnetic recording channels. A simplification of the BP algorithm, which can be viewed as a Chase-type algorithm, is presented and analyzed

Low density parity check codes for magnetic recording channels

We propose a system for magnetic recording, using a low density parity check (LDPC) code as the error-correcting-code, in conjunction with a rate 16/17 quasi-maximum-transition-run channel code and a modified E/sup 2/PR4-equalized channel. Iterative decoding between the partial response channel and the LDPC code is performed. Simulations show that this system can achieve a 5.9 dB gain over uncoded EPR4. The algorithms used to design this LDPC code are also discussed.

Nonbinary LDPC Codes for 4-kB Sectors

The performance of nonbinary LDPC codes on perpendicular magnetic recording channels (PMRCs) with 4-kB sectors is investigated. Each sector is encoded by either 4- or 0.5-kB-long codes. Both quasi-cyclic (QC) and nonquasi-cyclic (non-QC) nonbinary low-density parity-check (LDPC) codes are designed, and a set of simulations in a mixture of 10% additive white Gaussian noise (AWGN) and 90% position jitter noise power, with and without turbo equalization and with a rereading technique, is presented. The results show that sector-long codes perform better than 0.5-kB codes for all decoding schemes considered. In addition, the erasure correction capabilities of these nonbinary LDPC codes are calculated under both maximum-likelihood decoding and iterative decoding, and, as expected, longer codes can correct longer erasures. QC and non-QC nonbinary LDPC codes exhibit similar performance and have almost the same erasure correction capability under iterative decoding. Because of their efficient encoding, QC nonbinary LDPC codes are a good choice for perpendicular recording channels with 4-kB sectors, and offer a tradeoff between performance and code length.

Signal-to-noise ratio mismatch for low-density parity-check coded magnetic recording channels

Signal-to-noise ratio (SNR) mismatch is found in simulations to have great influence on the performance of low-density parity-check coded magnetic recording channels. While an inappropriate SNR mismatch degrades the performance dramatically, a properly selected optimum SNR mismatch can improve it significantly. In this paper we analyze the causes of this phenomenon and find optimum SNR mismatch values for specific magnetic recording systems with physical impairments such as electronic and media noise as well as erasures, using both density evolution analysis and Monte Carlo simulations. We observed that two characteristics of the probability density function (pdf) of the channel message, namely, the Gaussianity and the variance-to-mean ratio (VMR) have a major effect on the SNR mismatch. Generally speaking, if the channel message is approximately Gaussian-distributed and the VMR is larger than two, a negative SNR mismatch substantially improves the system performance. Numerical results show that for a magnetic recording channel with additive white Gaussian noise (AWGN), the optimum SNR mismatch is about -3 to -2 dB, while for a channel with 10% AWGN and 90% media noise, is about -10 to -8 dB, whether erasures are present or not.

Applications of low-density parity-check codes to magnetic recording channels

We consider the use of high-rate low-density parity-check (LDPC) codes for magnetic recording. We design and evaluate the performance of a magnetic recording system, which uses an LDPC code as the error-correcting code, in conjunction with a rate 16/17 quasimaximum-transition-run (QMTR) channel code on a modified E/sup 2/PR4 (ME/sup 2/PR4)-equalized channel. Iterative decoding between the partial response channel and the LDPC code is performed. Simulations show that an additional four-dB gain over the QMTR code can be obtained by the LDPC code. The algorithms used to design this LDPC code are also discussed.

Signal processing for perpendicular recording channels with intertrack interference

Signal processing techniques for perpendicular magnetic recording channels with intertrack interference (ITI) are studied in this paper. Both single-track and joint-track equalization and detection algorithms are considered. Modified minimum mean-square error equalization methods are used to select optimum generalized partial response targets for ITI channels with either dominant additive white Gaussian noise or media noise. Simulation results show that good targets for single-track detection of ITI-free channels may not be acceptable for channels with ITI. Short targets are just slightly worse than longer targets for joint-track detection, making it possible its use in practical systems with ITI.

Two-Dimensional Voronoi-Based Model and Detection for Shingled Magnetic Recording

In this paper, we present a model of a shingled magnetic recording system, where Voronoi regions are used to model the grains of the magnetic medium. A probabilistic model is used to represent imperfections in the write process, i.e., the head failing to write some grains correctly. A two-dimensional model of the head response is used to calculate the signal read back by the head over any place on the medium, thereby including both intertrack and intersymbol interference effects in the model. We also present simulation results from tests of this model using a multitrack detector and an intertrack interference canceller and give performance results of the channel/detector combination for various track offsets.

Performance and Decoding Complexity of Nonbinary LDPC Codes for Magnetic Recording

We consider a group of high-performance q-ary low-density parity-check (LDPC) coded perpendicular magnetic recording channels (PMRCs) with optimized targets and codes over various field sizes. We show that the nonbinary LDPC-coded PMRCs provide 1-dB coding gain over a practical implementation of a good binary LDPC-coded PMRC at user density of 1.22, and evaluate the decoding complexities of these systems in terms of both the number of floating-point (FLP) operations and the computational time. Decoding complexity ratios of nonbinary LDPC-coded PMRCs to the binary LDPC-coded system are presented. After careful analysis, we conclude that the time complexity ratios are always smaller than the ratios obtained by the number of FLP operations, which do not exceed 7.42. Furthermore, experimental results show that the size of the Galois field does not affect the decoding complexity.