Gyuyeol Kong

Cell-to-cell interference compensation schemes using reduced symbol pattern of interfering cells for MLC NAND flash memory

Cell-to-cell interference compensation schemes using reduced symbol pattern of interfering cells for multilevel cell (MLC) NAND flash memory are proposed in this paper. The proposed schemes consist of three procedures, estimation of cell-to-cell interference, compensation for cell-to-cell interference, and generation of log-likelihood ratio (LLR). First, reduced symbol pattern of interfering cells is used to estimate cell-to-cell interference by modifying the levels of the threshold voltage shift from multi page programming to two levels. Second, based on this estimation, cell-to-cell interference is compensated by modifying the read voltage considering the estimated cell-to-cell interference in the proposed scheme 1 and by subtracting the estimated cell-to-cell interference from the sensed voltage in the proposed scheme 2. Finally, after conducting compensation, LLR is calculated for low-density parity check (LDPC) codes in the assumption of free cell-to-cell interference since interference between cells is mitigated by the compensation procedure. By using these techniques, cell-to-cell interference can be relaxed with a simple structure and a high reliability. The bit error rate (BER) performances of the proposed schemes are compared with the conventional schemes on 8-level MLC NAND flash memory. Simulation results show that the proposed schemes show the improved BER performances by more than an order of magnitude compared with the conventional LDPC scheme.

Performance Evaluation of the Reed Solomon and Low Density Parity Check Codes for Blu-ray Disk Channels

In this paper, we evaluate the performances of the Reed–Solomon (RS) and low density parity check (LDPC) codes in order to propose an efficient coding system for the outer code in high density optical recording channels. Hard decision decoding (HDD) RS code, iterative soft decision decoding (SDD) RS code or LDPC code is used as the outer code and LDPC code is used as the inner code. We compare the bit error rate (BER) performance of each coding system for various code rates, code lengths and burst errors. Simulation results show that the LDPC code has a better BER performance than the HDD RS and iterative SDD RS codes as the outer code in high density optical channels. Therefore, the LDPC code could be more attractive as the outer code than the RS code in high density optical channels.

Gaussian Sum Approximation Approach to Blu-ray Disc Channel Equalization

A new equalization method for Blu-ray (BR) recording channels is proposed. The proposed equalizer incorporates the Gaussian sum approximation (GSA) into a Kalman filtering framework to mitigate intersymbol interference in BR recording systems. The proposed equalizer consists of a bank of linear equalizers using the Kalman filtering algorithm and its output is obtained by combining the outputs of linear equalizers through the GSA. The proposed equalizer shows a better performance than the conventional equalizers and a similar performance with the only equalization technique to the partial response maximum likelihood methods in terms of bit-error-rate.

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.

Error Correcting Capable 2/4 Modulation Code Using Trellis Coded Modulation in Holographic Data Storage

An error correcting capable 2/4 modulation code scheme is proposed in holographic data storage (HDS) systems. We adopt trellis coded modulation (TCM) to obtain a good error correcting capability without loss of data rate in the HDS systems. To overcome loss of a data rate caused by a 1/2-rate convolutional code, we extend a 2/4 modulation code set the 3/4 modulation code set as high-order modulation in the proposed scheme. Additionally, we find an optimal mapping method of index numbers to maximize the free distance on the trellis and calculate the free distance according to each constraint length. The simulation results show that the proposed scheme with the same data rate has about 4 dB coding gains compared to the conventional 2/4 modulation coding scheme.

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.

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.

Two-Dimensional Iterative Decoding Schemes for Holographic Data Storage Systems

Two iterative decoding (ID) schemes, which are the ID using a single parity bit (ID-SPB) and ID using a modulation code (ID-MC), are proposed for holographic data storage systems. In the ID-SPB, a single two-dimensional parity bit is employed to conduct ID, whereas in the ID-MC, the inherent constraint of the modulation code is utilized to conduct ID. In both schemes, a data page is iteratively decoded by exchanging extrinsic information between the horizontal and vertical data bits in the page. In particular, in the ID-SPB, by adding more parity bits to each row and column of the interleaved page, we can conduct the ID within a page as well as between the original and interleaved pages. Thus, additional performance gain can be achieved in the ID-SPB. On the other hand, the ID-MC has a performance gain without loss of data rate since parity bits are not required for ID. The simulation results show that the proposed ID-SPB and ID-MC have about 2–4 and 1–2 dB performance gains in terms of bit error rate compared with the system without ID, respectively.

Soft-Decision Viterbi Decoding Scheme and a New Reliability Metric for 4/6 Modulation Code in Holographic Data Storage

A soft-decision Viterbi decoding for a 4/6 modulation code is proposed in a holographic data storage system. Since the previous proposed soft-decision Viterbi decoding does not support a higher rate modulation codes than 1/2 rate modulation codes, we propose a new reliability metric to support the 4/6 modulation code. The reliability metric is used to calculate the branch metric on the trellis. For a better coding gain, we find a symbol mapping method for the modulation code which provides a large free distance on the trellis to have the enhanced error correcting capability. Simulation results show that the proposed scheme has about 2 dB coding gains than the conventional soft-decision Viterbi decoding scheme.

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.