Search Results (112)

In this paper, we investigate the cycle structure inherent in the Tanner graphs of low-density parity-check (LDPC) codes constructed from balanced incomplete block designs (BIBDs). We begin by delineating the incidence structure of BIBDs and propose a methodology for constructing LDPC codes based on these designs. By analyzing the incidence relations between points and blocks within a BIBD, we prove that the resulting LDPC codes possess a girth of 6. Subsequently, we provide a detailed analysis of the cycle structure of the constructed LDPC codes and introduce a systematic approach for enumerating their short cycles. Using this method, we determine the exact numbers of cycles of lengths 6 and 8. Simulation results demonstrate that the constructed LDPC codes exhibit excellent performance. Full article

This study focuses on a 4FSK-modulated ultraviolet (UV) communication system, introducing an innovative symbol-level maximum likelihood decoding approach based on Poisson statistics. A forward error correction (FEC) coding mechanism is integrated to enhance system robustness. Through Monte Carlo simulations, the proposed decoding scheme and the error correction performances of Reed–Solomon (RS) and Low-Density Parity-Check (LDPC) codes are evaluated in UV channels. Both RS and LDPC codes significantly improve the Bit Error Rate (BER), with LDPC codes achieving superior gains under low SNR conditions. Hardware implementation and field tests validate the decoding algorithm and LDPC-optimized 4FSK system. Under non-line-of-sight (NLOS) conditions (10–45° transmit elevation angle), stable 60 m communication with BER < 10⁻³ is achieved. In line-of-sight (LOS) scenarios, the system demonstrates 900 m range with BER < 10⁻³, highlighting practical applicability in challenging atmospheric environments. Full article

The Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model’s objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes with penalty functions. To further enhance decoding efficiency and accuracy, We propose an LDPC code decoding algorithm based on the symmetric ADMM (S-ADMM). We also establish some contraction properties satisfied by the iterative sequence of the algorithm. Through simulation experiments, we evaluate the proposed S-ADMM decoder using three standard LDPC codes and three representative fifth-generation (5G) codes. The results show that the S-ADMM decoder consistently outperforms conventional ADMM penalized decoders, offering significant improvements in decoding performance. Full article

In Large Intelligent Surface (LIS) systems, achieving accurate channel estimation is essential for enhancing communication quality and system efficiency. The main focus of this study is on using the Least Squares (LS) method to estimate pilot-based channels. It also looks at more advanced methods, like using low-density parity-check (LDPC) codes, antenna selection, and optimized pilot design, to make the method more accurate and effective. We employ orthogonal pilot sequences to reduce signal interference and improve pilot power to enhance estimation performance. Additionally, LDPC codes play a crucial role in eliminating noise and interference effects, thereby improving system reliability. We also propose selective configurations of LIS antennas to balance high performance with reduced computational costs. Collectively, these strategies lead to a significant reduction in the Bit Error Rate (BER) and a remarkable improvement in the overall system performance, offering a practical solution for complex LIS deployments. Full article

This paper examines the iterative decoding of low-density parity check (LDPC) codes concatenated with continuous phase modulation (CPM). As relevant case studies, we focus on the family of three CPM waveforms that are embodied in the IRIG-106 aeronautical telemetry standard. Two of these CPMs have recently had LDPC codes designed for them for the first time, and thus the decoding complexity of these new schemes is of interest when considering adoption into the standard. We provide comprehensive numerical results that characterize the performance and iteration statistics of the joint LDPC–CPM decoder. These results identify the most advantageous decoder configurations and also expose a key design challenge, which is that LDPC-CPM decoders must deal with a large “peak to average” ratio in terms of global iterations. We show how a properly designed reference simulation can be used as a design tool to explore the performance of a large range of candidate systems without need for further simulation. We develop a real-time decoder architecture with fixed complexity and show how such a decoder can still achieve a relatively large maximum number of global iterations by introducing a trade-off between decoding latency and maximum global iterations. Our discussion shows that this scheme is generally applicable to LDPC-based schemes. We conclude with a comprehensive design study that demonstrates the accuracy of our methodology and its attractive performance–complexity trade-off. Full article

Underwater acoustic channel (UWAC) is characterized by significant multipath effects, strong time-varying properties and complex noise environments, which make achieving high-rate and reliable underwater communication a formidable task. To address the above adverse challenges, this study first presents a novel, robust and efficient polar code construction (NREPCC) method using the base-adversarial polarization weight (BPW) algorithm tailored for typical ocean channel models, including invariable sound velocity gradient (ISVG) channels, negative sound velocity gradient (NSVG) channels, and positive sound velocity gradient (PSVG) channels. Subsequently, a robust and reliable polar-coded UWAC system model based on the orthogonal frequency division multiplexing (OFDM) technique is designed using the $t$-distribution noise model in conjunction with real sea noise data fitting. Then, an enhanced time synchronization and packet detection algorithm based on $t$-distribution is proposed for the performance optimization of the polar-coded UWAC OFDM system. Finally, extensive numerical simulation results confirm the excellent performance of the proposed NREPCC method and polar-coded UWAC OFDM system under a variety of channel conditions. Specifically, the NREPCC method outperforms low-density parity-check (LDPC) codes by approximately 0.5~1 dB in PSVG and ISVG channels while maintaining lower encoding and decoding complexity. Moreover, the robustness of the NREPCC method under $t$-distribution noise with varying degrees of freedom is rigorously validated, which renders vital technical support for the design of high-precision and high-robustness UWAC systems. Full article

In this paper, we introduce a novel gradient descent bit-flipping algorithm with a finite state machine (GDBF-wSM) for iterative decoding of low-density parity-check (LDPC) codes. The algorithm utilizes a finite state machine to update variable node potentials—for each variable node, the corresponding finite state machine adjusts the update value based on whether the node was a candidate for flipping in previous iterations. We also present a learnable framework that can optimize decoder parameters using a database of uncorrectable error patterns. The performance of the proposed algorithm is illustrated for various regular LDPC codes, both in a binary symmetric channel (BSC) and the channel with additive white Gaussian noise (AWGN). The numerical results indicate a performance improvement when comparing our algorithm to previously proposed GDBF-based approaches. Full article

This paper focuses on the Low-Density Algebra-Check (LDAC) code, a novel low-rate channel code derived from the Low-Density Parity-Check (LDPC) code with expanded algebra-check constraints. A method for optimizing LDAC code design using Extrinsic Information Transfer (EXIT) charts is presented. Firstly, an iterative decoding model for LDAC is established according to its structure, and a method for plotting EXIT curves of the algebra-check node decoder is proposed. Then, the performance of two types of algebra-check nodes under different conditions is analyzed via EXIT curves. Finally, a low-rate LDAC code with enhanced coding gain is constructed, demonstrating the effectiveness of the proposed method. Full article

With its high area density, bit-patterned media recording (BPMR) is emerging as a leading technology for next-generation storage systems. However, as area density increases, magnetic islands are positioned closer together, causing significant two-dimensional (2D) interference. To address this, detection methods are used to interpret the received signal and mitigate 2D interference. Recently, the maximum a posteriori (MAP) detection algorithm has shown promise in improving BPMR performance, though it requires extrinsic information to effectively reduce interference. In this paper, to solve the 2D interference and improve the performance of BPMR systems, a model using low-density parity-check (LDPC) coding was introduced to supply the MAP detector with the needed extrinsic information, enhancing detection in a joint decoding model we call MAP–LDPC. Additionally, leveraging similarities between LDPC codes and graph neural networks (GNNs), we replace the traditional sum–product algorithm in LDPC decoding with a GNN, creating a new model, MAP–GNN. The simulation results demonstrate that MAP–GNN achieves superior performance, particularly when using the deep learning-based GNN approach over conventional techniques. Full article

Low-density parity-check (LDPC) codes form part of the IRIG-106 standard and have been successfully deployed for the Telemetry Group version of shaped-offset quadrature phase shift keying (SOQPSK-TG) modulation. Recently, LDPC code solutions have been proposed and optimized for continuous phase modulations (CPMs), including pulse code modulation/frequency modulation (PCM/FM) and the multi-h CPM developed by the Advanced-Range TeleMetry program (ARTM CPM), the latter of which was shown to perform around one dB from channel capacity. In this paper, we consider the effect of the random puncturing and shortening of these LDPC codes to further improve spectrum efficiency. We perform asymptotic analyses of the ARTM0 code ensembles and present numerical simulation results that affirm the robust decoding performance promised by LDPC codes designed for ARTM CPM. Full article

This work presents a novel fully parallel decoder architecture designed for high-throughput decoding of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes within the context of 5G New-Radio (NR) communication. The design uses the layered Min-Sum (MS) algorithm and focuses on increasing throughput to meet the strict needs of enhanced Mobile BroadBand (eMBB) applications. We incorporated a Sub-Optimal Low-Latency (SOLL) technique to enhance the critical check node processing stage inherent to the MS algorithm. This technique efficiently computes the two minimum values, rendering the architecture well-suited for specific Ultra-Reliable Low-Latency Communication (URLLC) scenarios. We design the decoder to be reconfigurable, enabling efficient operation across all expansion factors. We rigorously validate the decoder’s effectiveness through meticulous bit-error-rate (BER) performance evaluations using Hardware Description Language (HDL) co-simulation. This co-simulation utilizes a well-established suite of tools encompassing MATLAB/Simulink for system modeling and Vivado, a prominent FPGA design suite, for hardware representation. With 380,737 Look-Up Tables (LUTs) and 32,898 registers, the decoder’s implementation on a Virtex-7 XC7VX980T FPGA platform by AMD/Xilinx shows good hardware utilization. The architecture attains a robust operating frequency of 304.5 MHz and a normalized throughput of 49.5 Gbps, marking a 36% enhancement compared to the state-of-the-art. This advancement propels decoding capabilities to meet the demands of high-speed data processing. Full article

As high-speed big-data communications impose new requirements on storage latency, low-density parity-check (LDPC) codes have become a widely used technology in flash-memory channels. However, the iterative LDPC decoding algorithm faces a high decoding latency problem due to its mechanism based on iterative message transmission. Motivated by the unbalanced bit reliability of codeword, this paper proposes two technologies, i.e., serial entropy feature-based layered normalized min-sum (S-EFB-LNMS) decoding and parallel entropy feature-based layered normalized min-sum (P-EFB-LNMS) decoding. First, we construct an entropy feature vector that reflects the real-time bit reliability of the codeword. Then, the reliability of the output information of the layered processing unit (LPU) is evaluated by analyzing the similarity between the check matrix and the entropy feature vector. Based on this evaluation, we can dynamically allocate and schedule LPUs during the decoding iteration process, thereby optimizing the entire decoding process. Experimental results show that these techniques can significantly reduce decoding latency. Full article

Due to the limited payload and power of drones, the computational overhead, storage overhead and communication overhead that can be used for secure communication are restricted, making it difficult to apply some complex but fairly secure authentication protocols on drones. In this paper, we propose a low-complexity protocol for storing identity information in a resource-unconstrained device that does not require the UAV to store the information, thereby enhancing the UAV’s resistance to capture. The protocol in this paper mainly consists of quasi-cyclic low-density parity-check (QC-LDPC) codes, physical unclonable functions (PUFs) based on random-access memory (RAM), “XOR” operations, and hash computation. The protocol in this paper is an authentication architecture in which the drone is guided by the ground station to read its identity information, and the drone does not store any identity information in advance. The protocol is divided into two phases: 1. fuzzy authentication of fingerprint PUF and 2. uniqueness authentication accomplished while guiding the recovery of identity PUF. Recovering identity PUF in this paper, QC-LDPC is used as the error control module, and the optimization of bit-flip decoding significantly reduces the probability of decoding failure. After the comparative security analysis and comparative overhead analysis of this paper’s protocol, it can be concluded that this paper’s protocol can withstand common attacks (including attacks attempting to pass authentication, attacks attempting to interfere with authentication, and physical capture attacks), and the storage and communication overhead is small in the case of large time overhead. Full article

In this paper, new schemes have been proposed for the estimation of the additive white Gaussian noise (AWGN) channel with intersymbol interference (ISI) in an iterative equalization and decoding system using low-density parity check (LDPC) codes. This article explores the use of the least squares algorithm in various scenarios. For example, the impulse response of the AWGN channel h was initially estimated using a training sequence. Subsequently, the impulse response was calculated based on the training sequence and then re-estimated once using the sequence estimated from the output of the LDPC decoder. Lastly, the impulse response was calculated based on the training sequence and re-estimated twice using the sequence estimated from the output of the LDPC decoder. Comparisons were made between the performances of the three mentioned situations, with the situation in which a perfect estimate of the impulse response of the channel is assumed. The performance analysis focused on how the bit error rate changes in relation to the signal-to-noise ratio. The BER performance comes close to the scenario of having a perfect estimate of the impulse response when the estimation is performed based on the training sequence and then re-estimated twice from the sequence obtained from the output of the LDPC decoder. Full article

Relaying with network coding forms a basis for a variety of collaborative communication systems. A linear block coding framework for multi-way relaying using network codes introduced in the literature shows great promise for understanding, analyzing, and designing such systems. So far, this technique has been used with low-density parity check (LDPC) codes and belief propagation (BP) decoding. Polar codes have drawn significant interest in recent years because of their low decoding complexity and good performance. Our paper considers the use of polar codes also as network codes with differential binary phase shift keying (DBPSK), bypassing the need for channel state estimation in multi-way selective detect-and-forward (DetF) cooperative relaying. We demonstrate that polar codes are suitable for such applications. The encoding and decoding complexity of such systems for linear block codes is analyzed using maximum likelihood (ML) decoding for LDPC codes with log-BP decoding and polar codes with successive cancellation (SC) as well as successive cancellation list (SCL) decoding. We present Monte-Carlo simulation results for the performance of such a multi-way relaying system, employing polar codes with different lengths and code rates. The results demonstrate a significant performance gain compared to an uncoded scheme. The simulation results show that the error performance of such a system employing polar codes is comparable to LDPC codes with log-BP decoding, while the decoding complexity is much lower. Furthermore, we consider a hard threshold technique at user terminals for determining whether a relay transmits or not. This technique makes the system practical without increasing the complexity and can significantly reduce the degradation from intermittent relay transmissions that is associated with such a multi-way relaying protocol. Full article