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Due to the rapid growth in the global volume of data, deoxyribonucleic acid (DNA) data storage has emerged. Error correction in DNA data storage is a key part of this storage technology. In this paper, an improved marker code scheme is proposed to correct insertion, deletion, and substitution errors in deoxyribonucleic acid (DNA) data storage. To correct synchronization (i.e., insertion and deletion) errors, a novel base-symbol-based synchronization algorithm is proposed and used. In the improved scheme, the marker bits are encoded as the information part of the LDPC code, and then mapped into marker bases to correct the synchronization errors. Thus marker bits not only assist in regaining synchronization, but also play a role in LDPC decoding to improve decoding performance. An improved low-complexity normalized min-sum (INMS) algorithm is proposed to correct residual substitution errors after regaining synchronization. The simulation results demonstrate that the improved scheme provides a substantial performance improvement over the concatenated marker code scheme and concatenated watermark code scheme. At the same time, the complexity of the INMS algorithm was reduced, while its bit error rate (BER) performance was approximate to that of the belief propagation (BP) algorithm. [ABSTRACT FROM AUTHOR]

As one of the most classical data-storage systems, magnetic recording (MR) systems have attracted a significant amount of research attention in the past several decades due to the advantages of low cost and high storage density. Along with the continual increase of areal density of modern MR devices, more severe inter-symbol interference (ISI) and noise appear and thus reliable storage becomes more difficult. To address this challenging problem, turbo detections and error-correction codes (ECCs) have been applied to MR systems so as to significantly improve the overall data-storage reliability. Among all the existing ECCs, low-density parity-check (LDPC) codes are of particular interest because they can offer excellent error performance with relatively low encoding and decoding complexity. This paper presents a comprehensive survey of the latest research advancements in LDPC-code design for MR systems from the perspectives of code construction, decoder design, as well as asymptotic performance-evaluation methodology. More specifically, we summarize the design guidelines of LDPC encoder and decoder over both one-dimensional (OD) ISI and two-dimensional (TD) ISI channels, which are commonly used to characterize MR systems with different areal densities. We also concisely portray the research progress in the design of some LDPC-code variants, such as protograph codes, repeat-accumulate codes, spatially coupled codes, and their non-binary counterparts over the aforementioned ISI channels. In particular, we restrict our attention to the reading process and ignore the written-in errors in MR systems unless otherwise stated. Hopefully, this survey will inspire more research activities in the area of LDPC-coded MR systems. [ABSTRACT FROM AUTHOR]

In this paper, protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes are proposed for the efficient structure coding of LDPC codes in 2-D intersymbol interference (ISI) ultrahigh density magnetic recording channels, such as bit-patterned magnetic recording and 2-D magnetic recording, where a reduced-complexity 2-D detector based on the iterative row–column soft detection feedback with Gaussian approximation is employed instead of the full 2-D Bahl–Cocke–Jelinek–Raviv detector. The proposed protograph-based codes, whose base matrices are constructed according to the degree sequences for 2-D-ISI channels, have a low-complexity QC encoder structure with a readily parallelizable protograph decoder structure. Simulation results show that the proposed protograph-based QC-LDPC codes outperform the random LDPC codes optimized for additive white Gaussian noise channels. Furthermore, the performance of the QC codes is similar to that exhibited by ISI-optimized random LDPC codes designed for 2-D-ISI channels, while retaining the implementational benefits. [ABSTRACT FROM AUTHOR]

In this paper, we present a new error-correction scheme, referred to as embedded marker code scheme (EMCS), for channels corrupted by insertions, deletions and additive white Gaussian noise (AWGN). The EMCS uses the pinning bits, which have the potential to lower the error floors of the outer low-density parity-check (LDPC) codes, for both resynchronization and improving error-correction performance. Furthermore, the soft-input synchronization for the inner decoder and the joint iterative decoding between the inner decoder and the outer decoder is employed to further improve the overall performance of the new scheme. Simulations show that the proposed EMCS reduces the code rate loss as compared with the conventional marker code scheme and achieves a better tradeoff between the error performance and the decoding complexity. Therefore, the new scheme can reduce code rate loss and improve storage efficiency when it is used in bit-patterned media recording (BPMR) systems. [ABSTRACT FROM PUBLISHER]

In this paper, optimization of low-density parity-check (LDPC) codes to approach the symmetric information rate (SIR) of two-dimensional (2-D) intersymbol interference (ISI) channels is proposed for high-density magnetic recording, such as bit-patterned magnetic recording (BPMR) and 2-D magnetic recording (TDMR). The code design makes use of the modified Extrinsic Information Transfer (EXIT) chart, where the optimal variable node degree is searched by selecting the best check node degree to fit the check node decoder (CND) EXIT curve to the EXIT curve of the variable node decoder (VND) curve combined with 2-D detector. Simulation results show that LDPC codes with code length 10^4 bits optimized for a 2-D ISI channel corresponding to 4 \Tb/in^2 recording density can achieve bit error rate 10^-5 at signal-to-noise ratio 0.33 dB away from the SIR. To our knowledge, this is the first capacity-approaching LDPC code successfully optimized for a 2-D ISI channel. [ABSTRACT FROM PUBLISHER]

Scheduling strategy is considered an important aspect of belief-propagation (BP) decoding of low-density parity-check (LDPC) codes because it affects the decoder's convergence rate, decoding complexity and error-correction performance. In this paper, we propose two new scheduling strategies for the BP decoding of non-binary LDPC (NB-LDPC) codes. Both the strategies are devised based on the concept of check node reliability and employ a heuristically defined threshold which can adapt to the communication channel variations. As the scheduling strategies only update a subset of the check nodes in each iteration, they result in reduced iteration cost. Furthermore, since the BP performs suboptimally for finite-length LDPC codes, especially for short-length LDPC codes, by enhancing the message propagation over the Tanner Graphs of short-length NB-LDPC codes, the new scheduling strategies can even improve the error-correction performances of BP decoding. Simulation results demonstrate that the new scheduling strategies provide good performance/complexity tradeoffs. [ABSTRACT FROM AUTHOR]