This paper focuses on the design and performance analysis of faster-than-Nyquist (FTN) signaling employing enhanced 5G low-density parity-check (LDPC) codes, oriented toward the requirements of future 6G systems. We propose the extrinsic information transfer (EXIT) chart analysis for the LDPC-coded FTN system based on the Ungerboeck observation model, where the input-output mutual information function of the detector is approximated using least squares fitting. With the proposed EXIT chart analysis, we explore the thresholds and decoding performance of different LDPC codes (regular codes, irregular codes and protograph codes) in both Nyquist and FTN systems, revealing two important observational findings for FTN signaling: 1) Unlike Nyquist systems, where certain 5G New Radio (NR)-like information puncturing can enhance the decoding threshold and performance, we observe that in the FTN setting considered in this paper such puncturing leads to performance degradation; 2) Unlike Nyquist systems, the paritycheck matrix of LDPC codes optimized for FTN signaling tends to be relatively sparser within comparable ensembles, due to the intentionally introduced inter-symbol interference (ISI). Based on these findings, we develop tailored LDPC codes for FTN signaling by applying the masking operation to the base matrix of the standard 5G LDPC codes, aiming to achieve a lower decoding threshold and thereby better decoding performance. Moreover, the raptor-like structure and rate compatibility are preserved in the proposed LDPC codes, and the encoder and decoder are reused with only minor modifications. Numerical results show that: 1) All simulation results align with the decoding thresholds obtained by the proposed EXIT chart analysis, confirming the effectiveness of the analysis; 2) For the FTN system, the tailored LDPC codes outperform standard 5G LDPC codes, achieving over 0.4 dB coding gain and approaching (slightly exceeding) the constrained Nyquist capacity; 3) Under the same spectral efficiency, FTN with tailored LDPC codes performs better than standard 5G LDPC codes with Nyquist signaling, demonstrating a coding gain of up to 0.6 dB; 4) The proposed LDPC codes with the FTN signaling achieve better performance compared to existing high-performance codes specifically designed for FTN signaling.

In unsourced random access (URA) system, user pilot collisions are a key challenge when multiple users select identical pilot sequences, leading to poor activity detection and decoding performance. To address this issue, this paper develops a two-stage segmented pilot (TSSP) design for collision-resilient URA in massive multiple-input multiple-output (MIMO) system. The proposed scheme enables a substantial enlargement of the effective pilot space without increasing the physical codebook size and detection complexity. First, we construct a probabilistic collision model by leveraging the birthday-problem analogy, which provides theoretical characterization of collision events and closely matches the simulation results. Second, we propose a segmented pilot mapping and decoding framework in which the pilot bits are divided into two interconnected parts linked by common pilot bits. This structured segmentation allows the system to resolve partial collisions and reduce missed detection in high-density access scenarios. Third, we develop a joint-covariance linear minimum mean square error (JC-LMMSE) scheme that exploits the segmented pilot structure to suppress pilot contamination and improve estimation accuracy. Monte Carlo simulations show that the proposed TSSP framework achieves up to 3.5 dB gain in collision scenarios and approximately 1 dB gain in collision-free cases over existing methods, while maintaining comparable computational complexity.

This paper focuses on the analysis and design of improved 5G low-density parity-check (LDPC) codes for faster-than-Nyquist (FTN) signaling. We first propose the protograph-based extrinsic information transfer (PEXIT) chart analysis for the LDPC-coded FTN system using the sum-product algorithm (SPA) based on the Ungerboeck observation model, where the distribution of the output mutual information from the detector is approximately derived using least squares fitting. With the proposed PEXIT chart analysis, we then design the improved LDPC codes for the coded FTN signaling aiming to achieve a lower decoding threshold and thereby better error performance. The proposed codes are optimized based on the raptor-like structure of the 5G LDPC codes and also support rate compatibility. The proposed codes reveals two distinct LDPC code design criteria for FTN signaling, i.e., 1) no information bits should be punctured; 2) columns with high column weights should be removed in the base graph. The advantages of the proposed codes are explicitly verified by our numerical results, where noticeable coding gains compared to existing codes and coded Nyquist systems can be observed.

In this paper, we design a novel joint receiver that iteratively performs channel estimation (CE) and symbol detection for channel-coded multi-user multiple-input multiple-output systems with orthogonal time frequency space modulation (MIMO-OTFS). In particular, we first propose a two-stage CE method based on a single superimposed pilot (SP) with inter-user interference canceling (ICCE). The delay-Doppler domain SP is used to estimate path delays, Doppler shifts, and other channel parameters. Then the detected user symbols are utilized to update the channel parameters with mitigating inter-user and multipath interferences. Second, we construct a joint CE and signal detection scheme based on the expectation propagation (EP) algorithm (EP-ICCE). We exploit the relationship between CE and symbol detection, refining the estimated channel matrix with the detected data symbols. Finally, simulation results shows the proposed EP-ICCE can achieve performance gains up to 2 dB over the conventional methods for the different MIMO and modulations.

In this paper, we consider how to partition the parity-check matrices (PCMs) to reduce the hardware complexity and increase decoding throughput for the row layered decoding of quasi-cyclic low-density parity-check (QC-LDPC) codes. First, we formulate the PCM partitioning as an optimization problem, which targets to minimize the maximum column weight of each layer while maintaining a block cyclic shift property among different layers. As a result, we derive all the feasible solutions for the problem and propose a tight lower bound ωLBon the minimum possible maximum column weight to evaluate a solution. Second, we define a metric called layer distance to measure the data dependency between consecutive layers and further illustrate how to identify the solutions with desired layer distance from those achieving the minimum value of ωLB= 1, which is preferred to reduce computation delay. Next, we demonstrate that up-to-now, finding an optimal solution for the optimization problem with polynomial time complexity is unachievable. Therefore, both enumerative and greedy partition algorithms are proposed instead. After that, we modify the quasi-cyclic progressive edge-growth (QC-PEG) algorithm to directly construct PCMs that have a straightforward partition scheme to achieve ωLBor the desired layer distance. Simulation results showed that the constructed codes have better error correction performance and achieve less average number of iterations than the underlying 5G LDPC codes.

In this paper, we propose a mutual information-maximizing quantized layered min-sum (MIM-QLMS) decoder for quasi-cyclic low-density parity-check (QC-LDPC) codes. Our proposed decoder operates similarly to a layered min-sum decoder with additional reconstruction and quantization operations by using single-input lookup tables (LUTs). In particular, we first develop the protograph-based MIM density evolution to design the LUTs, which may differ for each iteration and each edge in the protograph of the QC-LDPC codes. Furthermore, to minimize the memory requirement for storing the LUTs, we propose an optimization method to unify all LUTs into only four distinct LUTs, which can be used for all decoding iterations. To the best of our knowledge, the proposed MIM-QLMS decoders are the first class of layered finite alphabet iterative decoders (FAIDs) that are designed based on accurately tracking the probability distributions of the exchanged messages. Simulation results show that for 3-bit (resp. 4-bit) exchanged message precision, the proposed MIM-QLMS decoders can reasonably (resp. generally) outperform the state-of-the-art layered FAIDs and the layered normalized min-sum decoder, in terms of both the error rate performance and the average number of iterations.

We propose a two-dimensional modified min-sum algorithm for the LDPC codes in the fifth generation (5G) networks standard to approach the error performance of the sum-product algorithm (SPA). In the proposed decoding algorithm, we adopt a partial self-correction method followed by message amplification to improve the reliability of the variable-to-check (V2C) messages. To further approach the performance of the maximum likelihood decoding for 5G short LDPC codes, we propose an enhanced quasi-maximum likelihood (EQML) decoding method. The proposed decoding method performs multiple rounds of decoding tests once the first decoding attempt fails, where the decoder inputs of the selected unreliable variable nodes are modified in each decoding test. A novel node selection method based on the sign fluctuation of V2C messages is proposed for the EQML decoding method. We also present a partial pruning stopping (PPS) rule to reduce the decoding complexity by deactivating part of the decoding tests once a valid codeword is found. A lower bound on the error performance is also derived by using the semi-analytical method. Simulation results show that the EQML decoding method outperforms the SPA with the same decoding complexity and other QML decoding methods, and it approaches the Polyanskiy-Poor-Verdú bound within 0.4 dB.

In this paper, we propose an enhanced quasi-maximum likelihood (EQML) decoder for short LDPC codes. The proposed EQML decoder selects unreliable variable nodes (VNs) and performs the reprocessing if the first belief propagation (BP) decoding attempt fails. To improve the decoding error rate performance, we propose a novel node selection method based on the sign fluctuation of VNs' extrinsic messages. We also present a partial pruning stopping (PPS) rule to reduce the decoding complexity by deactivating part of the decoding tests once a valid codeword is found. Simulation results show that the proposed PPS rule achieves 20% lower decoding complexity compared to the full list decoding without sacrificing the error rate performance. In addition, the proposed EQML decoder outperforms the augmented BP decoder for short LDPC codes and approaches the performance of the ML decoder within 0.3 dB in terms of the frame error rate.

In this paper, we construct binary spatially coupled (SC) low-density parity-check (LDPC) codes based on Euclidean geometry (EG) LDPC codes for storage applications, where high error correction capability, extremely low uncorrectable bit error rate (UBER), and low decoding complexity are required. We propose a systematic way to construct the families of SC LDPC codes from (m,2s) EG LDPC codes, which are termed EG-SC LDPC codes. In the construction method, we propose a 2-D edge-spreading process to construct the base matrix of EG-SC LDPC codes, which consists of matrix unwrapping and periodically time-varying of a protograph. A lower bound on the rank of the parity-check matrix of an EG-SC LDPC code is derived. We evaluate the error rate performance of the constructed EG-SC LDPC codes by using a weighted bit-flipping decoding algorithm for its low decoding complexity. Numerical results show that the UBER performance of the constructed EG-SC LDPC codes is superior to that of their EG LDPC code counterparts, and show no error floor compared with the constructed protograph SC LDPC codes and regular LDPC codes.