2D Soft Output Viterbi Algorithm Research Articles

Long-Short Term Memory-Based Application on Adaptive Cross-Platform Decoder for Bit Patterned Magnetic Recording

Dynamic bit encoding and decoding of the magnetic recording process remain a challenge in that the process is restrained by the balance between reading and writing performance of the decoder’s bit error rate (BER). Sequential neural networks offer data streamflow for processes to reproduce recoded bits from signal distribution, overcoming the limitation of codeword mapping designed for each specific bit-patterned magnetic recording (BPMR) channel. Here, we implement the vanilla long short-term memory (LSTM) for adaptive modulation decoders in various BPMR channel designs within a single network, which benefits multi-channel decoder calibration tools with the same standardization. Signal information from media readback, a two-dimensional (2D) equalizer, 2D Viterbi, and a 2D soft-output Viterbi algorithm (SOVA) detector is arranged as a tensor that enables sequence-to-sequence bit prediction even with a highly complex data arrangement. Our adaptive model can predict recorded bits from readback with accuracies of approximately 97% for rate 4/5 decoding and 75% for crossing platforms, using a recently proposed single-reader/two-track reading (SRTR) system at an areal density of 4 Tb/in2 in a signal-to-noise ratio range of 1 to 8 dB. We conducted a BER simulation with the relevant results from conventional decoders and the LSTM model. Ultimately, our approach may demonstrate the limitation of supervised learning designed for BPMR systems and reveal a sequence data focus on LSTM that paves the way for sequential-type, unsupervised, mechanism-based, next-generation magnetic recordings.

An ant colony optimization aided two-dimensional soft output viterbi algorithm detection scheme for holographic data storage systems

In this paper, we propose an ant colony optimization (ACO) aided two-dimensional (2D) soft output Viterbi algorithm (SOVA) detection scheme for holographic data storage systems. The proposed detection scheme adopts the conventional 2D SOVA detection scheme which has two one-dimensional (1D) SOVA detectors for the horizontal and vertical directions, and employs an ACO detector with a reliability test. The proposed detection scheme operates in two stages. In the first stage, the data is detected by conducting the 2D SOVA detection scheme for the horizontal and vertical directions. In the second stage, the reliability test is taken to detect the less reliable bits in a data page by using the outputs of the horizontal and vertical 1D SOVA detectors from the first stage. If the less reliable bits are detected, the ACO detector is performed to improve the reliability of the unreliable bits. Otherwise, the sum of outputs from the horizontal and vertical 1D SOVA detectors is detected by a threshold detector. The bit error rate performances of the proposed detection scheme are compared to the conventional detection schemes. Simulation results show that the proposed detection scheme performing the ACO detector for only 0.3% of bits has more than 7 dB gains compared to the conventional 2D SOVA detection scheme when the grade of blur is 1.8.

Data page reconstruction method based on two-dimensional soft output Viterbi algorithm with self reference for holographic data storage

This study introduces a two-dimensional (2D) partial response maximum likelihood (PRML) method to reconstruct a degraded data page having 2D inter-symbol interference for holographic data storage. The proposed 2D PRML method consists of 2D partial response (PR) target, 2D equalizer using least mean square algorithm, and 2D soft output Viterbi algorithm (SOVA) having just two one-dimensional (1D) SOVAs in horizontal and vertical directions. To accurately organize a trellis diagram of the 1D SOVA in structural accordance with the 2D PR target, this study proposes the self-reference process for the extrinsic information in the 1D SOVA. Finally, simulation results show that the proposed method has bit error rate performance similar to that of modified 2D SOVA having four 1D SOVAs despite the relatively low computational complexity. Moreover, parallel processing is possible in the two 1D SOVAs through the self-reference process.

An iterative inter-track interference mitigation method for two-dimensional magnetic recording systems

At high recording density, the readback signal of two-dimensional magnetic recording is inevitably corrupted by the two-dimensional (2D) interference consisting of inter-symbol interference and inter-track interference (ITI), which can significantly degrade the overall system performance. This paper proposes an iterative ITI mitigation method using three modified 2D soft-output Viterbi algorithm (2D-SOVA) detectors in conjunction with an iterative processing technique to combat the 2D interference. The codeword of the outer code is divided and then written on three separate tracks. For every iteration, all 2D-SOVA detectors exchange the soft information to improve the reliability of the a priori information and use it in the branch metric calculation, before feeding the refined soft information to the outer decoder. Simulation results show that the proposed method outperforms the conventional receiver and the existing partial ITI mitigation method.

Two-Dimensional Soft Output Viterbi Algorithm with a Variable Reliability Factor for Holographic Data Storage

In a practical holographic data storage system, the reconstruction process for a data page should account for the processing time as well as the bit error rate (BER) performance. To improve both aspects, we introduce two-dimensional (2D) partial response maximum likelihood composed of a 2D partial response (PR) target including diagonal elements and a 2D soft output Viterbi algorithm (SOVA) with a variable reliability factor. The 2D SOVA performs two one-dimensional (1D) SOVAs in structural accordance with the 2D PR target where extrinsic information uses the expected value calculated on a synchronization pattern. Finally, the 2D SOVA exports a weighted average using the reliability factor that is updated similarly as the optimization scheme for each page. The simulation results show that the proposed method has superior BER performance, despite using only two 1D SOVAs as compared with the modified 2D SOVA composed of four 1D SOVAs.

Two-Dimensional Partial Response Maximum Likelihood at Rear for Bit-Patterned Media

Bit-patterned media (BPM) storage can have ultrahigh capacity, whereas the readback signal for the BPM storage is deteriorated by intersymbol interference in both the along- and across-track directions. As a detection method considering the two-dimensional (2D) interference, we propose a new structure of 2D partial response maximum likelihood (PRML) method based on a 2D partial response (PR) target and a 2D soft output Viterbi algorithm (SOVA) composed of two one-dimensional SOVAs. For the purpose of improving the bit error rate (BER) performance and reducing the computational complexity, the proposed method applies a 2D equalizer estimating the binary data recorded on the BPM instead of the output data of the 2D PR target. For this reason, the 2D PRML is located behind the 2D equalizer. Consequently, the proposed method has a superior BER performance as well as a low computational complexity. In addition, we carry out comparison of the BER performance in the 2D PRML according to the use of the least mean square and recursive least square algorithms in the 2D equalizer.

Two-Dimensional Soft Output Viterbi Algorithm With Dual Equalizers for Bit-Patterned Media

This study proposes a two-dimensional (2D) detection method using partial response maximum likelihood (PRML) for bit-patterned media (BPM) storage. Because the readback signals are deteriorated by 2D channel effect, that is, intersymbol interference along the track direction and intertrack interference across the track direction, it is necessary to use “2D” PRML in order to improve the bit error rate (BER) performance. The 2D PRML in the proposed method is based on the 2D soft output Viterbi algorithm (SOVA), which is composed of two one-dimensional SOVAs. In addition, we propose a 2D SOVA for a 2D partial response (PR) target using dual equalizers: one estimates the correlated signal (output data of the PR target), used as the main information with encoding rule, and the other estimates the binary signal (binary data recorded on BPM), used as extrinsic information on the other direction's neighboring bits. The simulation results show that the proposed method improves the BER performance at a low computational complexity.

Modified Two-Dimensional Soft Output Viterbi Algorithm with Two-Dimensional Partial Response Target for Holographic Data Storage

The previously modified two-dimensional (2D) soft output Viterbi algorithm (SOVA) for holographic data storage (HDS) consists of four one-dimensional (1D) SOVAs in accordance with two different 1D partial response (PR) targets (vertical and horizontal directions). In this study, we propose a detection method in structural accordance with a 2D PR target through the use of the modified 2D SOVA. The proposed method shows superior bit error rate performance owing to the use of a 2D PR target that contains more information than the 1D PR target. Moreover, a reduction in power consumption, computational complexity, and the system-on-chip size for HDS system can be expected as a result of the use of only one 2D equalizer.

Two-dimensional soft output Viterbi algorithm with noise filter for patterned media storage

We introduce a two-dimensional (2D) soft output Viterbi algorithm (SOVA) using two 1D SOVAs, which apply two noise filters corresponding to horizontal and vertical directions, respectively, for patterned media storage. Patterned media storage has 2D intersymbol interference (ISI), which includes ISI from neighboring symbols and intertrack interference from adjacent tracks, since there is a small space between adjacent tracks and neighborhood symbols. Noise filter replaces colored noise with white noise. As a result, the noise filter can reduce the noise power, so that performance can be improved. As shown in the simulation results, when there is no off-track, the 2D SOVA using a noise filter is approximately 0.4 dB better than not using a noise filter at a 10−6 bit error rate; when there is 20% off-track, it has about a 1 dB gain.

Two-Dimensional SOVA and LDPC Codes for Holographic Data Storage System

We introduce partial response maximum likelihood (PRML) with the two-dimensional (2D) soft output Viterbi algorithm (SOVA) and 2D equalizer for holographic data storage (HDS) channel. The 2D SOVA output is the average of two 1D SOVAs that are separately operated in horizontal and vertical directions. The complexity of the proposed 2D SOVA is increased only twice compared with 1D SOVA while its performance is superior to that of 1D SOVA. Since the 2D SOVA outputs soft decision value, LDPC can be utilized by the soft-in hard-out decoding. We study for different PR target, comparing 1D Viterbi detection with 2D SOVA detection, different misalignments, and two kinds of LDPC codes.

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.

Two-Dimensional 5:8 Modulation Code for Holographic Data Storage

We present a two-dimensional (2D) 5:8 modulation code which does not allow isolated pixel patterns for holographic data storage. We compare it with 6:8 code and uncoded cases. Bit error rates (BERs) are measured by the threshold detection and the 2D soft-output Viterbi algorithm (SOVA) collaborated with 2D equalizer at the blur of 1.85. The proposed 2D 5:8 modulation code is simpler than conventional 6:8 code and removes all the isolated 2D ISI patterns. As a result, when the 2D SOVA is applied and the data is quantized to 1 or 2 bits, the SNR of the proposed 5:8 code is approximately 3 dB better than that of the 6:8 code at 10-5 BER. When the data is quantized to 3 or 4 bits, both codes show similar performance.