Partial Response Maximum Likelihood Detection Research Articles

Iterative Multihead Multitrack Detection Scheme for Bit-Patterned Media Recording

An iterative multi-head multi-track detection scheme for bit patterned media recording is proposed in this paper. The proposed scheme employs two iterative strategies with the multi-head multi-track detection where three tracks are simultaneously processed to accurately estimate the channel with TMR and effectively detect the data by using inter-track interference (ITI) information with high reliability. The first outer iteration aims to compensate for the track misregistration (TMR) effect, and the second inner iteration aims to improve the reliability of the data. In outer iteration, the TMR effect is compensated by modifying the generalized partial response (GPR) target to a channel that reflects the TMR estimated by a TMR estimator using expectation and maximization algorithm. In inner iteration, iterative equalization and decoding (IED) is conducted between the two-dimensional partial response maximum likelihood detector and the low-density parity check decoder based on the revised GPR target. Since each track has different channel performance according to the amount of ITI information in the multi-track detection, we design the GPR target and the code rate separately for each track to maximize the overall channel performance. The bit error rate performances of the proposed IED scheme are compared with the conventional IED scheme when areal density is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2 Tb/in^{2}$</tex-math></inline-formula> . Simulation results show that the proposed IED scheme has more than 2dB gains compared with the conventional IED scheme for 30 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> TMR.

Modulation Code and Multilayer Perceptron Decoding for Bit-Patterned Media Recording

In a bit-patterned media recording (BPMR) system, reducing the spacing between adjacent bit islands in the down- and cross-track directions increases areal density; however, two-dimensional (2-D) interference comprising intersymbol and intertrack interferences degrades the system performance. To mitigate error patterns that increase the 2-D interference in BPMRs, 2-D modulation coding schemes have been proposed. In this letter, we present a modulation code and its decoding using a multilayer perceptron (MLP) for BPMRs. Modulation decoding using an MLP can achieve significantly better performance than that using the minimum Euclidean distance, which is generally used to decode received modulated data. Similarly, when comparing the system performance at the same user density, modulation decoding using an MLP at 3 Tb/in2 shows better performance than an uncoded system (partial response maximum-likelihood detector) at 2 Tb/in2.

Three Typical Bit Position Patterns of Bit-Patterned Media Recording

Bit-patterned media recording (BPMR) is regarded as a promising candidate for next-generation magnetic storage systems in order to increase areal density. BPMR exhibits massive two-dimensional interference, however, that consists of horizontal intersymbol interference from neighboring bits and vertical intertrack interference (ITI) from adjacent tracks. In this letter, we investigate the performance of BPMR according to the spacing and position of magnetic islands when we use a partial-response maximum-likelihood detection scheme and low-density parity check code. We compare bit error rate performance when the islands are arranged in a regular array and when the islands are arranged in a staggered array. Simulation results show that substantially increased bit error rate performance can be achieved through the use of trigonal half-delayed layout island patterns that reduce the ITI.

A two-dimensional partial response maximum likelihood detection scheme for misalignment compensation in holographic data storage systems

A two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for misalignment compensation for holographic data storage systems is proposed. In the proposed detection scheme, a misalignment estimator and a predetermined table are added to the conventional 2D PRML scheme to estimate and reflect the effect of misalignment in the vertical and horizontal directions, respectively. In the vertical detection, the misalignment estimator located behind the vertical 2D equalizer and one-dimensional PRML detector estimates the misalignment by the adaptive least-mean-square algorithm (LMS). To improve the estimation accuracy, the misalignment is estimated iteratively by modifying the vertical equalizer coefficients reflecting the estimated misalignment. By considering the estimated misalignment, the vertical 2D equalizer coefficients, horizontal 2D equalizer coefficients, and 2D partial response (PR) target are selected among the predetermined table. In the predetermined table, the vertical and horizontal 2D equalizer coefficients for various misalignments were previously computed on the basis of the misalignment and 2D PR target by the LMS. By employing the horizontal 2D equalizer coefficients and 2D PR target reflecting the misalignment in the horizontal detection, the effect of misalignment is effectively mitigated. Simulation results show that the proposed scheme has more than 3 dB gains than the conventional scheme in the 10% misalignment in the horizontal and vertical directions.

Two-Track Reading With a Wide-Track Reader for Shingled Track Recording

In order to avoid the requirement for a narrow track reader in high track density shingled recording, decoding schemes for two-track simultaneous reading, which allows a wide-track reader to be used, are investigated. The strong intertrack interference (ITI) is a major difficulty to be overcome. To avoid ITI, the recorded magnetization in the two tracks should be staggered. Two possible 2-D decoding techniques are provided: 1) recursive decoding by oversampling and 2) Partial Response Maximum Likelihood (PRML) detection. Because data in two track are read simultaneously, the data transfer rate is two times higher than in regular single-track reading. Despite the high data rate, the requirement on the reader for high readback resolution, such as a small shield gap length, magnetic spacing, can be mitigated.

Generalized Partial Response Equalization and Data-Dependent Noise Predictive Signal Detection Over Media Models for TDMR

Two-dimensional magnetic recording (2-D TDMR) is an emerging technology that aims to achieve areal densities as high as 10 Tb/in2 using sophisticated 2-D signal-processing algorithms. High areal densities are achieved by reducing the size of a bit to the order of the size of magnetic grains, resulting in severe 2-D intersymbol interference (ISI). Jitter noise due to irregular grain positions on the magnetic medium is more pronounced at these areal densities. Therefore, a viable read-channel architecture for TDMR requires 2-D signal-detection algorithms that can mitigate 2-D ISI and combat noise comprising jitter and electronic components. Partial response maximum likelihood (PRML) detection scheme allows controlled ISI as seen by the detector. With the controlled and reduced span of 2-D ISI, the PRML scheme overcomes practical difficulties such as Nyquist rate signaling required for full response 2-D equalization. As in the case of 1-D magnetic recording, jitter noise can be handled using a data-dependent noise-prediction (DDNP) filter bank within a 2-D signal-detection engine. The contributions of this paper are threefold: 1) we empirically study the jitter noise characteristics in TDMR as a function of grain density using a Voronoi-based granular media model; 2) we develop a 2-D DDNP algorithm to handle the media noise seen in TDMR; and 3) we also develop techniques to design 2-D separable and nonseparable targets for generalized partial response equalization for TDMR. This can be used along with a 2-D signal-detection algorithm. The DDNP algorithm is observed to give a 2.5 dB gain in SNR over uncoded data compared with the noise predictive maximum likelihood detection for the same choice of channel model parameters to achieve a channel bit density of 1.3 Tb/in2 with media grain center-to-center distance of 10 nm. The DDNP algorithm is observed to give $\sim$ 10% gain in areal density near 5 grains/bit. The proposed signal-processing framework can broadly scale to various TDMR realizations and areal density points.

Novel Joint Detection and Decoding Schemes for TDMR Channels

Two-dimensional magnetic recording (TDMR) relies on advanced signal processing and coding techniques to enable storage of data at higher densities. Various detection and decoding schemes have been proposed in the literature. In this paper, a recently proposed joint detection and decoding scheme known as the joint Viterbi detector decoder (JVDD) is presented for TDMR channels. The JVDD operates on a trellis and attempts to find a sequence in the trellis that belongs to a legal codeword with minimum metric. It does so by using a metric thresholding and parity checking technique over the same trellis structure. The iterative detector/decoder consisting of a soft-output Viterbi algorithm detector and low-density parity check decoder is used as a performance benchmark for the JVDD. In this paper, we perform the comparison with various equalization/detection techniques consisting of: 1) a 1-D general partial response equalization scheme followed by a 1-D-detector as used in today’s Partial Response Maximum Likelihood Detection (PRML) channels; 2) a 2-D equalization scheme that equalizes to a 1-D target [fully equalizing away the intertrack interference (ITI)], followed by a series of parallel 1-D-detectors to handle the intersymbol interference (ISI); and 3) a 2-D-equalization scheme followed by 2-D detector to combat both ITI and ISI.

Improved partial response maximum likelihood method combining modulation code for signal waveform modulation multi-level disc

In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code for signal waveform modulation multi-level disc. This improved adaptive PRML method employs partial response equalizer and adaptive viterbi detector combining modulation code. Compared with the traditional adaptive PRML detector, the improved PRML detector additionally employs illogical sequence detector and corrector. Illogical sequence detector and corrector can avoid the appearance of illogical sequences effectively, which do not follow the law of modulation code for signal waveform modulation multi-level disc, and obtain the correct sequences. We implement the improved PRML detector using a DSP and an FPGA chip. The experimental results show good performance. The higher efficient and lower complexity can be obtained by using the improved PRML method than by using the previous PRML method. Meanwhile, resource utilization of the improved PRML detector is not changed, but the bit error rate (BER) is reduced by more than 20%.

A 6/9 Four-Ary Modulation Code for Four-Level Holographic Data Storage

A holographic data storage (HDS) system can provide high storage capacity, faster transmission, and shorter access time. However, there are two major concerns with such systems: two-dimensional (2D) inter-symbol interference (ISI) and inter-page interference (IPI). The use of existing partial response maximum likelihood (PRML) detection can somewhat mitigate the problem of ISI. However, if the channel is subject to misalignment, the performance of PRML detection can be degraded. This problem can be remedied by a modulation code. Thus, this paper proposes a 6/9 modulation code, which mitigates ISI, and a modulation/demodulation scheme.

Two-Dimensional Equalization Using Bilinear Recursive Polynomial Model for Holographic Data Storage Systems

In this paper, we propose new two-dimensional (2D) nonlinear equalizers developed on the basis of a bilinear recursive polynomial (BRP) model for holographic data storage (HDS) systems. The 2D BRP equalizer (BRPE) and the 2D BRP decision feedback equalizer (BRPDFE) are proposed. The bit error rate (BER) performances of the proposed schemes are studied in the electrical-noise-dominant channel (ENDC) and the optical-noise-dominant channel (ONDC). The proposed schemes are compared with the conventional adaptive DFE and the partial response maximum likelihood (PRML) detector. The simulation results show that the proposed schemes outperform the adaptive DFE and the PRML detector. In particular, the BRPDFE shows the best BER performance in both the ENDC and the ONDC.

Turbo Equalization Scheme between Partial Response Maximum Likelihood Detector and Viterbi Decoder for 2/4 Modulation Code in Holographic Data Storage Systems

A turbo equalization scheme for holographic data storage (HDS) systems is proposed. The proposed turbo equalization procedure is conducted between a one-dimensional (1D) partial response maximum likelihood (PRML) detector and the joint Viterbi decoder by exchanging a priori and extrinsic information. In the joint Viterbi decoder, the modulation and convolutional decoding is performed simultaneously by mapping a 2/4 modulation symbol onto the trellis of the convolutional code to reduce the complexity of the decoding procedure and improve the decoding capability for the iterative equalization and decoding. In addition, since the channel model is described as the two-dimensional convolution in HDS systems, the 1D PRML detector is performed in the vertical direction and the joint Viterbi decoder is performed in the horizontal direction to maximize the performance gains. The simulation result shows that the proposed turbo equalization scheme has the better bit error rate performances as the number of iterations increases.

Turbo Equalization Scheme between Partial Response Maximum Likelihood Detector and Viterbi Decoder for 2/4 Modulation Code in Holographic Data Storage Systems

A turbo equalization scheme for holographic data storage (HDS) systems is proposed. The proposed turbo equalization procedure is conducted between a one-dimensional (1D) partial response maximum likelihood (PRML) detector and the joint Viterbi decoder by exchanging a priori and extrinsic information. In the joint Viterbi decoder, the modulation and convolutional decoding is performed simultaneously by mapping a 2/4 modulation symbol onto the trellis of the convolutional code to reduce the complexity of the decoding procedure and improve the decoding capability for the iterative equalization and decoding. In addition, since the channel model is described as the two-dimensional convolution in HDS systems, the 1D PRML detector is performed in the vertical direction and the joint Viterbi decoder is performed in the horizontal direction to maximize the performance gains. The simulation result shows that the proposed turbo equalization scheme has the better bit error rate performances as the number of iterations increases.

Sequential Two-Dimensional Partial Response Maximum Likelihood Detection Scheme with Constant-Weight Constraint Code for Holographic Data Storage Systems

A sequential two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for holographic data storage (HDS) systems is proposed. We use two complexity reduction schemes, a reduced-state trellis and a constant-weight (CW) constraint. In the reduced-state trellis, the limited candidate bits surrounding the target bit are considered for the 2D PRML detector. In the CW constraint, the trellis transitions that violate the CW condition that each code-word block has only one white bit are eliminated. However, the 2D PRML detector using the complexity reduction schemes, which operates on 47 states and 169 branches, has performance degradation. To overcome performance degradation, a sequential detection algorithm uses the estimated a priori probability. By the sequential procedure, we mitigate 2D intersymbol interference with an enhanced reliability of the branch metric. Simulation results show that the proposed 2D PRML detection scheme yields about 3 dB gains over the one-dimensional PRML detection scheme.

Sequential Two-Dimensional Partial Response Maximum Likelihood Detection Scheme with Constant-Weight Constraint Code for Holographic Data Storage Systems

Sequential Two-Dimensional Partial Response Maximum Likelihood Detection Scheme with Constant-Weight Constraint Code for Holographic Data Storage Systems

Effective Two-Dimensional Partial Response Maximum Likelihood Detection Scheme for Holographic Data Storage Systems

An effective two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for holographic data storage (HDS) systems is proposed. The proposed scheme adopts the simplified trellis diagram, uses a priori information, and detects the data in two directions from the previously proposed detection schemes. The simplified trellis diagram which has 4 states and 8 branches yields a dramatic complexity reduction while the simplified 2D PRML detector shows serious performance degradation in the high density HDS channels. To prevent performance degradation, the proposed detector uses a priori information in order to give higher reliability to the branch metric. Furthermore, the proposed scheme detects the data in the vertical and horizontal directions to fully utilize the characteristics of the channel detection with a 2D partial response target. By effective combination of these three techniques, the proposed scheme with a simple structure has more than 2 dB gains compared to the conventional detection schemes.

Effective Two-Dimensional Partial Response Maximum Likelihood Detection Scheme for Holographic Data Storage Systems

An effective two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for holographic data storage (HDS) systems is proposed. The proposed scheme adopts the simplified trellis diagram, uses a priori information, and detects the data in two directions from the previously proposed detection schemes. The simplified trellis diagram which has 4 states and 8 branches yields a dramatic complexity reduction while the simplified 2D PRML detector shows serious performance degradation in the high density HDS channels. To prevent performance degradation, the proposed detector uses a priori information in order to give higher reliability to the branch metric. Furthermore, the proposed scheme detects the data in the vertical and horizontal directions to fully utilize the characteristics of the channel detection with a 2D partial response target. By effective combination of these three techniques, the proposed scheme with a simple structure has more than 2 dB gains compared to the conventional detection schemes.

Adaptive Trellis Using Interim Maximum-Likelihood Detector Output for a Holographic Storage System

The performance of partial response maximum likelihood (PRML) for holographic data storage can be reduced by asymmetric channel characteristics such as radial/tangential tilts. Therefore, we proposed the adaptive trellis scheme to improve performance. The proposed algorithm updates the reference branch values through using interim maximum-likelihood detector output, using the changed channel condition. Thus, this system guarantees better bit error rate performance than conventional PRML detection.

Read channel for signal waveform modulation multi-level disc

A novel read channel for signal waveform modulation multi-level disc is presented in this paper. This read channel employs timing recovery system and partial response maximum likelihood detector. Compared to the previous read channel composed of level detection and run-length detection, the present read channel shows superiority in capacity increase and robust performance. Especially, relying on the partial response maximum likelihood detection, lower bit error rate can be obtained.

Performance of Advanced Data-Detection Schemes on Barium-Ferrite Particulate Media

Noise-predictive maximum likelihood (NPML) detection has become state of the art in modern hard-disk drive (HDD) systems. Tape drive systems, in contrast, have typically adopted a traditional partial-response maximum likelihood detection approach, a fact that mainly reflects the large disparity in areal recording density between tape drives and HDDs. However, tape drive systems maintain a growth rate in areal recording density that is similar to that of HDDs, which implies that in future tape storage systems also advanced detection schemes need to be employed. This paper investigates the performance achieved by NPML, in particular, data-dependent NPML for data detection on barium-ferrite (BaFe) particulate tape media. Using actual readback waveforms, it is found that these advanced detection techniques are fairly efficient in improving the bit-error-rate performance of the read channel. Therefore, they enable, in combination with the BaFe media, a significant increase in linear recording density over that of state-of-the-art tape systems.

Partial Response Maximum Likelihood Detections Using Two-Dimensional Soft Output Viterbi Algorithm with Two-Dimensional Equalizer for Holographic Data Storage

We present partial response maximum likelihood (PRML) detection with two-dimensional (2D) equalizer scheme and introduce 2D soft output Viterbi algorithm (SOVA) detection for holographic data storage (HDS) channel. We also propose the 2D PR target for the HDS channel varying the grade of blur. Simulation results show that the proposed schemes outperform the nearest neighbor detection.