Quasi-cyclic low-density parity-check (QC-LDPC) codes constructed by using algebraic approaches, such as finite geometry and finite field, generally have good structural properties and very low error-floors, and facilitate hardware implementation. Irregular QC-LDPC codes constructed from such QC-LDPC codes by using the masking technique, when decoded with the sum-product algorithm (SPA), have low decoding complexity, but often show early error-floors. In this paper, the relationship of cycle, girth and approximate cycle EMD (ACE) between the masking matrix and masked matrix is investigated, and the ACE algorithm is modified and used to construct the masking matrix for irregular QC-LDPC codes. Simulations demonstrate that the codes constructed by masking with ACE optimization exhibit much improved waterfall performance and lower error floors.

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 10⁴ bits optimized for a 2-D ISI channel corresponding to 4 Tb/in² 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.

The differential chaos shift keying with code index modulation (CIM-DCSK) using Walsh codes can increase the data rate, but error rate performance degrades over practical multipath channel with high delay spread. To tackle this drawback, this paper proposes a parallel CIM-DCSK (PT-CIM-DCSK), where the first time slot is used to transmit the chaotic reference sequence, and the second slot is used to transmit the multiple sequences carrying data bits. In particular, multiple $q$ chaotic sequences are added for data transmission in parallel, and each sequence is modulated by CIM-DCSK with $m_{c}$ bits. By exploiting the quasi-orthogonal characteristics of permuted chaotic signals, the interference between $q$ sequences can be remarkably suppressed. In this way, given the data rate, PT-CIM-DCSK can achieve a larger length of Walsh segment than the CIM-DCSK, since its parallel transmission compensates the rate. In addition, the error performance of the proposed scheme over the multipath Rayleigh fading channel is theoretically analyzed. The theoretical and consistent simulation results demonstrate that the PT-CIM-DCSK can obtain significant performance gains over the conventional CIM-DCSK, and the gain can be up to 5 dB in multipath fading channel with high delay. This is because the larger Walsh segment of PT-CIM-DCSK provides the enhanced robustness against multipath effect. The performance superiority of the proposed scheme is further verified in practical ultra-wideband (UWB) wireless industrial scenarios, which suggests promising for low-cost and low-complexity wireless communication applications.

2-D inter-symbol-interference (2-D-ISI), consisting of ISI in the down track direction and inter-track interference along the cross-track direction, is a major factor that severely degrades the performance of ultra-high density magnetic recording systems. Due to its superior performance and the protograph structure which facilitates high-speed encoding and decoding, the protograph codes have shown a high potential to tackle 2-D-ISI. However, so far, no work has been reported on the design of non-binary protograph-based low-density parity-check (NP-LDPC) codes for 2-D-ISI channels. In this paper, we first propose a modified protograph extrinsic information transfer analysis. In conjunction with the asymptotic ensemble weight distribution analysis, they both serve as theoretical tools to analyze the performance of NP-LDPC codes designed for the 2-D-ISI channels. By further applying a fast search approach, we construct two types of NP-LDPC codes for 2-D-ISI channels. Both theoretical analyses and simulated results show that the proposed codes outperform the existing binary LDPC codes that optimized for 2-D-ISI channels as well as the non-binary quasi-cyclic LDPC code, at both low and high SNR regions.

This paper investigates the performance of the protograph-based low-density parity-check (LDPC) codes for 2-D intersymbol interference (ISI) channels with magnetic recording density. The protograph LDPC codes have been shown to possess simple hardware implementation and excellent error performance over additive white Gaussian noise channels and over partial response channels. We propose a design scheme and construct two new protograph LDPC codes for 2-D ISI channel, with the help of extrinsic information transfer chart analysis and asymptotic ensemble weight distribution analysis. The theoretical analyses and simulated results show that the proposed codes outperform the previously optimized irregular LDPC code in both low- and high-SNR regions. Thus, the proposed codes are good alternatives compared with other error-correction codes for the use in magnetic recording systems.

The performance of classical channel decoding algorithms in resistive random access memory (ReRAM) channels is severely degraded due to the sneak path interference (SPI) caused by the crossbar array structure. In this letter, we first propose a sneak path-aware reliability-based iterative majority-logic decoding (SPR-IMLGD) algorithm for low-density parity-check (LDPC) codes by integrating the sneak path information into reliability metrics. In particular, we introduce the sneak path distance, derived from the associated sneak path probability, which provides a desirable characterization of the presence and extent of sneak paths within a given memory cell. Moreover, we present an enhanced version of the SPR-IMLGD algorithm (ESPR-IMLGD) that further improves the error correction performance. We also optimize the calculation of sneak path distance, ensuring that the SPR-IMLGD and ESPR-IMLGD algorithms have the same level of computational complexity. Simulation results demonstrate that the SPR-IMLGD and ESPR-IMLGD algorithms can achieve better performance with lower computational cost compared with the existing methods.