LDPC Research Articles

Modulation and coding methods in 5th generation networks

The fifth generation (5G) of wireless communication networks represents a groundbreaking shift in the realm of connectivity, enabling a wide array of transformative applications and services. This article delves into the pivotal role played by modulation and coding methods in the context of 5G networks. It explores their significance, delves into recent research and publications within the field, and outlines the direction for future research endeavors. Modulation and coding (M&C) are fundamental for 5G networks, enhancing data rates, reliability, and reducing interference. This article delves into their role in 5G networks, addressing challenges, including fading channels, interference, and diverse user needs. Recent research explores advanced modulation schemes like 256-QAM and 1024-QAM, requiring error correction coding techniques like Turbo codes and LDPC codes. Massive MIMO, using multiple antennas at both ends, is supported by adaptive coding and modulation. Adaptive Modulation and Coding (AMC) dynamically adjusts schemes based on real-time channel conditions, balancing data rate and reliability. Non-Orthogonal Multiple Access (NOMA) accommodates massive device connectivity, allowing multiple users to share resources with different power levels and modulation schemes. The study aims to comprehensively analyze 5G's M&C methods, assess modulation schemes for higher data rates, evaluate error correction coding, investigate Massive MIMO and adaptive modulation for spectral efficiency, and scrutinize NOMA's potential for massive device connectivity. Results highlight the importance of advanced modulation schemes, efficient error correction coding, and adaptive techniques in realizing 5G objectives, enabling higher data rates, lower latency, and improved reliability. NOMA is promising for accommodating many connected devices in 5G. M&C are essential for efficient and reliable data transmission in 5G, with ongoing research refining techniques for 6G and beyond. Integrating machine learning and AI into M&C algorithms holds promise for enhancing network efficiency and reliability.

Full-Length Row-Multiplier QC-LDPC Codes With Girth Eight and Short Circulant Sizes

As a special case of a quasi-cyclic (QC) low-density parity-check (LDPC) code, a full-length row-multiplier (FLRM) QC-LDPC code is described by a compact exponent matrix based on two sequences of integers. The codes designed by a framework known as greatest-common-divisor (GCD) method, belong to a salient class of FLRM QC-LDPC codes, which can eliminate cycles of length up to six by carefully selecting a special sequence subject to a set of simple inequalities. However, the GCD method ensures the absence of these cycles only if circulant sizes are larger than a certain threshold. By combining the existing GCD method, novel sequences and a new analysis method (based on new lemmas of circulants and integers) for modulo equations, a group of novel FLRM QC-LDPC codes free of 4-cycles and 6-cycles are explicitly proposed for column weights from three to five in this paper, which possess circulant sizes much smaller than the forgoing threshold. Simulations show that the new FLRM QC-LDPC codes with shorter lengths perform almost the same as the existing FLRM QC-LDPC codes with longer lengths, and that the novel FLRM QC-LDPC codes noticeably outperform their counterparts with (nearly) identical lengths.

Analysis of LDPC Code in Hybrid Communication Systems

Free-space optical (FSO) communication is of supreme importance for designing next-generation networks. Over the past decades, the radio frequency (RF) spectrum has been the main topic of interest for wireless technology. The RF spectrum is becoming denser and more employed, making its availability tough for additional channels. Optical communication, exploited for messages or indications in historical times, is now becoming famous and useful in combination with error-correcting codes (ECC) to mitigate the effects of fading caused by atmospheric turbulence. A free-space communication system (FSCS) in which the hybrid technology is based on FSO and RF. FSCS is a capable solution to overcome the downsides of current schemes and enhance the overall link reliability and availability. The proposed FSCS with regular low-density parity-check (LDPC) for coding techniques is deliberated and evaluated in terms of signal-to-noise ratio (SNR) in this paper. The extrinsic information transfer (EXIT) methodology is an incredible technique employed to investigate the sum-product decoding algorithm of LDPC codes and optimize the EXIT chart by applying curve fitting. In this research work, we also analyze the behavior of the EXIT chart of regular/irregular LDPC for the FSCS. We also investigate the error performance of LDPC code for the proposed FSCS.

Error Propagation Mitigation in Sliding Window Decoding of Spatially Coupled LDPC Codes

Error Propagation Mitigation in Sliding Window Decoding of Spatially Coupled LDPC Codes

Adaptive Quantized and Normalized MSA Based on Modified MET-DE and Its Application for 5G-NR LDPC Codes

Adaptive Quantized and Normalized MSA Based on Modified MET-DE and Its Application for 5G-NR LDPC Codes

An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes

An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes

The Cycle-Concentrating PEG Algorithm for Protograph Generalized LDPC Codes

The Cycle-Concentrating PEG Algorithm for Protograph Generalized LDPC Codes

Quasi-Cyclic LDPC Codes With Girth at Least Eight Based on Disjoint Difference Sets

A novel relationship between disjoint difference sets (DDS) and QC-LDPC codes without cycles of length up to six is established. Based on DDS with two sets, a class of column-weight-four QC-LDPC codes is constructed with girth at least eight. In the literature there are several explicit or semi-random methods which can yield column-weight-four QC-LDPC codes without 4-cycles and 6-cycles. Compared with these existing methods, the new DDS-based method is able to offer QC-LDPC codes with desirable decoding performance and flexible circulant sizes, and at the same time able to provide a large number of non-equivalent candidate codes. Moreover, by employing DDS with only one set, a class of column-weight-three QC-LDPC codes is constructed with short lengths and with girth at least eight.

Семейство асимптотически хороших квантовых и локально тестируемых классических LDPC-кодов

In this paper we study classical and quantum LDPC codes with constant rate obtained using tensor product operation over noncommutative group algebra for chain complexes. It is shown that these families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. The existence of asymptotically good families of locally testable codes with constant parameters of locality and soundness is also shown, which gives the solution of the known conjecture in the field of classical locally testable codes.

Multilayer perceptron-based detection for a coded two-dimensional magnetic recording

Recently, magnetic recording technology has been on the verge of reaching its recording density limit. Two-dimensional (2-D) magnetic recording (TDMR) is expected to be a candidate for next-generation magnetic recording because it provides powerful 2-D signal processing tools that are seamlessly compatible with the current technology. However, the degradation in signal quality due to 2-D interference when increasing the recording density far beyond the limit is inevitable even advanced signal processing tools cannot thoroughly handle such interference. In this work, we introduce two architectures of the multilayer perceptron (MLP)-based detection capable of producing soft information in the form of a log-likelihood ratio (LLR) for a coded TDMR system. This also enables turbo decoding capability to take place in the system, which further enhances the system performance. Such an architecture has two structures explicitly designed to execute before and during turbo decoding with a low-density parity-check code. In the first architecture, we employ triple MLP-based detection to process three readback sequences individually. For another architecture, it is designed to collectively process three readback sequences using just single MLP-based detection. The results show that both architectures of proposed detections outperform the systems using the conventional detection based on the Viterbi algorithm and single MLP-based detection achieves slightly better performance than triple MLP-based detection despite having much less complexity.

Development of a method for ensuring confidentiality and authenticity in wireless channels

The object of the research is the development of a method for ensuring the authenticity and integrity of data in wireless channels based on post-quantum cryptosystems. The development of modern digital technologies ensures the transition to smart technologies and the formation of Next Generation Networks. The formation of smart technologies, as a rule, uses wireless communication channel standards IEEE 802.11X, IEEE 802.15.4, IEEE 802.16, which use only authentication protocols and privacy mechanisms, which are formed on symmetric algorithms. In the conditions of the post-quantum period (the advent of a full-scale quantum computer), the stability of such algorithms is questioned. Such systems, as a rule, are formed on the basis of the synthesis of socio-cyber-physical systems and cloud technologies, which simplifies the conduct of Advanced Persistent Threat attacks, both on the internal circuit of execution systems and on external control systems. The creation of multi-circuit information protection systems allows for an objective assessment of the current state of the system as a whole and the formation of preventive measures to counter cyber threats. The proposed method of providing basic security services: confidentiality, integrity and authenticity based on crypto-code constructions takes into account the level of secrecy of information transmitted over wireless channels and/or stored in databases of socio-cyber-physical systems. The use of post-quantum algorithms – McEliece/Niederreiter crypto-code constructions on elliptic/modified elliptic/lossy/Low-density parity-check code provides the necessary level of stability in the post-quantum cryptoperiod (crypto-stability at the level of 1025–1035 group operations), speed and probability of information (Рerr not lower than 10-9–10-12). The proposed method of information exchange using wireless communication channels ensures their practical implementation on resource-limited devices (creating of CCC on the GF field (24–26).

Study of Different Coding Methods of Polar code in 5G Communication system

Sure, most of you are aware that right now everyone is thinking or at least the industry and researchers are thinking about the next generation, the first generation of what will 5G be, and that a significant part of the 5G telecommunication standard has been finalised, in particular the error control codes that will be used in 5G telecommunication. One of the codes that will be used is called a Low-Density Parity Check code (or LDPC code for short), and the other is called Polar Code. These two famous and celebrated codes have distinct and fascinating histories. Both technologies are now capable of providing near-capacity results, making them formidable competitors in the race to become the 5G communication system's ultimate provider. In this paper, we zeroed in on the 5G Polar codes and their encoding methods.

Asymmetric Adaptive LDPC-Based Information Reconciliation for Industrial Quantum Key Distribution.

We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme combines the advantages of LDPC codes, a priori error rate estimation, rate-adaptive and blind information reconciliation techniques. We compare the performance of several asymmetric and symmetric error correction schemes using a real industrial QKD setup. The proposed asymmetric algorithm achieves significantly higher throughput, providing a secret key rate that is close to the symmetric one in a wide range of error rates. Thus, our approach is found to be particularly efficient for applications with high key rates, limited classical channel capacity and asymmetric computational resource allocation.

A bottom‐up design methodology of neural min‐sum decoders for LDPC codes

It is known the belief propagation variants of linear codes can be readily unrolled as neural networks, after assigning learnable weights on the message-passing edges. Contrary to the conventional top-down training process, where the distillation occurs in the form of pruning or sharing when downsizing model is required, a new bottom-up design methodology to augment performance of the raw min-sum decoder of LDPC codes is proposed, by introducing incrementally a few parameters in the specific positions of corresponding neural network. Then a novel postprocessing method, devised to further improve performance, can cope with decoding failures effectively. In the training process, a simplified scheme of generating training data is presented via exploiting an approximation to the targeted mixture density, and it is found the evaluation of trained parameters converges after sufficient iterations, indicating its generality with an arbitrary designated number of iterations. Lastly, an extensive simulation of three codes carried on the AWGN or Rayleigh fading channels demonstrates the design reaches a good tradeoff of low-complexity and comparable decoding performance.

IRS, LIS, and Radio Stripes-Aided Wireless Communications: A Tutorial

This is a tutorial on current techniques that use a huge number of antennas in intelligent reflecting surfaces (IRS), large intelligent surfaces (LIS), and radio stripes (RS), highlighting the similarities, differences, advantages, and drawbacks. A comparison between IRS, LIS, and RS is performed in terms of the implementation and capabilities, in the form of a tutorial. We begin by introducing the IRS, LIS, and RS as promising technologies for 6 G wireless technology. Then, we will look at how the three notions are applied in wireless networks. We discuss various performance indicators and methodologies for characterizing and improving the performance of IRS, LIS, and RS-assisted wireless networks. We cover rate maximization, power consumption reduction, and cost implementation concerns in order to take advantage of the performance increase. Furthermore, we extend the discussion to some cases of emerging use. In the description of the three concepts, IRS-assisted communication was introduced as a passive system, considering the capacity/data rate, with power optimization being an advantage, while channel estimation was a challenge. LIS is an active component that goes beyond massive MIMO; a recent study found that channel estimation issues in IRS had improved. In comparison to IRS, capacity enhancement is a highlight, and user interference showed a trend of decreasing. However, power consumption due to utilizing power amplifiers has restrictions. The third technique for increasing coverage is cell-free massive MIMO with RS, with easy deployment in communication network structures. It is demonstrated to have suitable energy efficiency and power consumption. Finally, for future work, we further propose expanding the conversation to include some cases of new uses, such as complexity reduction; design and simulation with LDPC code could be a solution to decreasing complexity.

Doped low-density parity-check codes

In this paper, we propose a doping approach to lower the error floor of Low-Density Parity-Check (LDPC) codes. The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code. Accordingly, an algorithm for selecting the information bits of the short code is proposed, and a specific two-stage decoding algorithm is presented. Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 ​dB gain compared with the original LDPC code at a frame error rate of 10−6. Furthermore, the proposed design can lower the error floor of original LDPC codes.

Blind recognition of sparse parity‐check matrices of low‐density parity‐check codes in the presence of noise

This paper studies the blind recognition method of the sparse parity-check matrices of low-density parity-check codes in noncooperative communication, which is critical to the reverse analysis of communication protocols using LDPC codes. In this paper, two improvements are made to the algorithm of Liu Qian et al. (2021) for this problem. Firstly, a Gaussian elimination method based on random column exchange and soft information is proposed to enhance the fault tolerance of the elimination process. Secondly, according to the sparse property of the parity-check matrices of LDPC codes, a random extraction method is proposed to further improve the fault tolerance of the algorithm, and it is verified theoretically. Finally, simulations verify the superior performance of the algorithm proposed in this paper.

Fully Absorbing Set Enumerators for Protograph-Based LDPC Code Ensembles

The average finite-length (elementary) fully absorbing set enumerators for binary protograph-based low-density parity-check (LDPC) code ensembles are derived. The method relies on generating functions, and it provides an efficient mean to obtain the normalized logarithmic asymptotic distribution of (elementary) fully absorbing sets. Using these results, the asymptotic distribution of (elementary) fully absorbing sets is evaluated for some protograph-based LDPC code ensembles. Numerical results show how the distributions can be used to estimate the error floor performance of protograph LDPC codes.

Multi-Layer Progressive Tree-Structured Edge Growth Algorithm for Nested Lifting Design of 5G-NR-Like LDPC Codes

We proposed an algorithm called multi-layer progressive tree-structured edge growth, to design rate-compatible length-scalable raptor-like quasi-cyclic LDPC codes with nested base matrices and nested lifting, like 5G new radio (NR) LDPC codes. The nested lifting design is mainly investigated in this letter. To deal with the complicated dependency of the performance for nested base matrices and lifting sizes simply and effectively, the design of nested lifting is decomposed into the lifting design of each lifting size, which is called a layer. In each layer, the lifting of nested base matrices is designed via progressive tree-structured edge growth algorithm, where tree structure is employed to reserve diversified intermediate results and achieve better trade-off of error floor performance among nested base matrices. The criterion composed of improved cycle classification, minimum distance test and performance evaluation is employed for tree pruning, which could better optimize the error floor performance under acceptable complexity. The effectiveness of the proposed algorithm is demonstrated via construction and simulation.

Decoding Short LDPC Codes via BP-RNN Diversity and Reliability-Based Post-Processing

This paper investigates decoder diversity architectures for short low-density parity-check (LDPC) codes, based on recurrent neural network (RNN) models of the belief-propagation (BP) algorithm. We propose a new approach to achieve decoder diversity in the waterfall region, by specializing BP-RNN decoders to specific classes of errors, with absorbing set support. We further combine our approach with an ordered statistics decoding (OSD) post-processing step, which effectively leverages the bit-error rate optimization deriving from the use of the binary cross-entropy loss function. We show that a single specialized BP-RNN decoder combines better than BP with the OSD post-processing step. Moreover, combining OSD post-processing with the diversity brought by the use of multiple BP-RNN decoders, provides an efficient way to bridge the gap to maximum likelihood decoding.