LDPC Research Articles

Construction of LDPC Codes Using Cole's Modified Importance Sampling Method

Purpose of research is a modification of Cole's importance sampling method for finding trapping sets in an LDPC code to speed up their search.Methods. Cole proposed a method for searching for trapping sets in an LDPC code by using a Monte Carlo method that causes the decoding algorithm to fail at nodes potentially contained in trapping sets. His method makes it possible to accelerate the study of the efficiency of medium-length LDPC codes in the region of large SNRs. The modified method uses the properties of automorphisms of Tanner graphs, which make it possible to exclude a significant number of symbolic nodes from the enumeration. The modified method also provides for an ordered enumeration over subgraphs containing cycles.Results. The proposed method made it possible to speed up the search for trapping sets in Mackay's PEG(1008, 504) LDPC code by 5027 times compared to the Velasquez-Subramani method, and 43 times faster compared to the original Cole method. In the case of (2640, 1320) LDPC Margulis code, the proposed method is 28 times faster than the Velasquez-Subramani quasi-cyclic method and 134 times faster than the original Cole method.Conclusion. The result of experimental studies showed the possibility of using the developed method to improve the connectivity spectrum, increase the code distance of QC-LDPC codes. This made it possible to reduce the probability of a bit error at the decoder output by orders of magnitude at high signal-to-noise ratios in the AWGN channel.

On the Performance of LDPC-Coded Large Intelligent Antenna System

This article studies Large Intelligent Systems (LIS) along with Single Carrier with Frequency Domain Equalization (SC-FDE), utilizing Low-Density Parity-Check (LDPC). Four different receivers are studied in the scenarios described above, namely Equal Gain Combining (EGC), Maximum Ratio Combining (MRC), Zero Forcing (ZF), and Minimum Mean Squared Error (MMSE). The results of this article show that the use of LDPC codes leads to an improvement of performance by about 2 dB for a 4X25 LIS system and by 3 dB for a 4X225 LIS system, as compared to similar systems without LDPC codes. Moreover, for all simulations, the MMSE receiver achieves the best overall performance, while EGC performs the worst.

Delayed Bit-Interleaved Coded Transmission for Spatial Modulation

It has been shown that delayed bit-interleaved coded modulation (BICM) performs better than the original BICM in some scenarios. This paper is intended to enhance the performance of low-density parity-check (LDPC) coded spatial modulation. To this end, we present the delayed bit-interleaved coded spatial modulation (DBICSM) when LDPC codes are employed. The resulting transmission scheme is termed LDPC-DBICSM. Firstly, we present the encoding structure of the LDPC-DBICSM. Secondly, we present a non-iterative decoder that works only on two blocks of received sequences for the LDPC-BICSM. Thirdly, we present an estimated lower bound on the performance of the LDPC-DBICSM. Finally, we present extensive simulation results to show the performance advantages of the LDPC-DBICSM when compared to the LDPC-BICSM. Particularly, a performance gain of about 1.25 dB is obtained at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> .

An investigation of low-density parity-check codes and polar codes for future communication systems

In the fifth-generation (5G) era and future, mobile internet and internet of things (IoT) are the driving forces for mobile communications’ development. The three main 5G usage scenarios: enhanced mobile broadband (eMBB), massive machine-type communication (mMTC), and ultra-reliable and low-latency communications (URLLC), require improvement in throughput, reliability, and latency as compared with the previous fourth generation (4G) system. In this paper, an investigation is done on the coding part of the wireless communication systems. Two channel coding types; low-density parity-check (LDPC) code which is used as the coding scheme for data transmission, and Polar code which is utilized for control in 5G are discussed. Moreover, simulations are performed to assess their performance. The simulation results revealed the superiority of polar code for transmitting short information messages and LDPC for transmitting long data messages. The use of LDPC and polar codes in 5G communication systems is justified by their ability to accommodate a wide range of data lengths and code rates, as well as their good bit error rate (BER) performance. Furthermore, the effect of the number of iterations on the BER performance of LDPC code and different decoding algorithms of polar code are considered.

Multicarrier Acoustic Communications in Multiuser and Interference-Limited Regimes

In this article, we address the design of a multicarrier communication system based on orthogonal frequency-division multiplexing and direct sequence spread spectrum. The design targets operation in the low-signal-to-noise-ratio regimes and multiuser settings. Specifically, coding is employed across carriers such that channel estimation and signal detection are coupled. We consider both coherent and differentially coherent detection and extend the principles to multichannel reception. A custom-designed frequency synchronization technique is proposed to counteract the motion-induced Doppler frequency shifting effect. Using the recordings from the 2010 Mobile Acoustic Communication Experiment, where signals were transmitted in the 10.5–15.5-kHz acoustic band in shallow water, with relative motion up to 1.5 m/s, we demonstrate the system performance in terms of the mean squared error and bit error rate in data detection. Further employing Polar and low-density parity-check coding, we show that the proposed methods provide excellent performance while maintaining low computational complexity, making them suitable for a practical implementation.

New low-density-parity-check decoding approach based on the hard and soft decisions algorithms

&lt;span lang="EN-US"&gt;It is proved that hard decision algorithms are more appropriate than a soft decision for low-density parity-check (LDPC) decoding since they are less complex at the decoding level. On the other hand, it is notable that the soft decision algorithm outperforms the hard decision one in terms of the bit error rate (BER) gap. In order to minimize the BER and the gap between these two families of LDPC codes, a new LDPC decoding algorithm is suggested in this paper, which is based on both the normalized min-sum (NMS) and modified-weighted bit-flipping (MWBF). The proposed algorithm is named normalized min sum- modified weighted bit flipping (NMSMWBF). The MWBF is executed after the NMS algorithm. The simulations show that our algorithm outperforms the NMS in terms of BER at 10-8 over the additive white gaussian noise (AWGN) channel by 0.25 dB. Furthermore, the proposed NMSMWBF and the NMS are both at the same level of decoding difficulty.&lt;/span&gt;

Trapping and Absorbing Set Enumerators for Nonbinary Protograph-Based Low-Density Parity-Check Code Ensembles

The finite-length trapping and (elementary) absorbing set enumerators for nonbinary protograph-based LDPC code ensembles are derived. Both constrained and unconstrained edge labeling approaches are considered. The normalized logarithmic asymptotic distributions of trapping and (elementary) absorbing sets are obtained through an efficient method that requires solving a system of equations. Using these results, the asymptotic distributions of trapping and (elementary) absorbing sets are evaluated for some example nonbinary protograph-based LDPC code ensembles.

A Review of Modern and Recent Studies on the Low-Density Parity-Check Technology Approach

Data theory coding is an excellent and well-known branch of study that has produced various crucial solutions to the insoluble challenges of safe data transfers. Last improvements in detecting error techniques have resulted in a significant increase in the use of low-density parity-check (LDPC) code to address critical concerns connected to secure data transfer. Until now, decent efforts have been performed on LDPC codes that target low complexity, high performance, and low bit error rate goals. The final aim of this review is to provide a recent literature understanding of modern improvements previously mentioned and in LDPC encoding and decoding (applicative and theoretical) techniques. A comparative scan of many remarkable LDPC decoding algorithms, 5G standard requirements, popular power management methods, and low-energy LDPC design studies is also shown. Lastly, conclusions are presented by outlining key study results, current concerns, and general thoughts on new research directions possibilities. Index Terms— low-density parity-check encoder/decoder (LDPC), error correction codes (ECC), forward error correction codes (FEC), parity check matrix(PCM).

Performance Analysis of LDPC-Coded OFDM in Underwater Wireless Optical Communications

The performance of Low-Density Parity-Check (LDPC)-coded Orthogonal Frequency Division Multiplexing (OFDM) is investigated over turbulence channels in underwater wireless optical communications (UWOC). The relation between the bit error ratio (BER) and parameters such as the scintillation coefficient, signal-to-noise ratio (SNR), length of LDPC code, and order of OFDM is quantified by simulation. Results show that while the OFDM with subcarrier quadrature amplitude modulation (QAM-OFDM) has slightly better anti-turbulence performance than the OFDM with subcarrier phase shift keying modulation (PSK-OFDM), the LDPC-coded QAM-OFDM has a much better performance than the QAM-OFDM and the LDPC-coded PSK-OFDM, and, at SNR = 12, it decreases the BER by four orders of magnitude compared to the 16QAM-OFDM system when the scintillation coefficient σξ2 = 0.05.

An Improved Marker Code Scheme Based on Nucleotide Bases for DNA Data Storage

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.

FPGA-based burst-error performance analysis and optimization of regular and irregular SD-LDPC codes for 50G-PON and beyond.

We evaluate the burst-error performance of the regular low-density parity-check (LDPC) code and the irregular LDPC code that has been considered for ITU-T's 50G-PON standard via experimental measurements in FPGA. By using intra codeword interleaving and parity-check matrix rearrangement, we demonstrate that the BER performance can be improved under ∼44-ns-duration burst errors for 50-Gb/s upstream signals.

Comparison between dicode PPM and offset PPM enhancement with different error correction codes

AbstractOffset pulse position modulation (OPPM) and Dicode pulse position modulation (DiPPM) have been introduced as new attractive modulation techniques, however, they are suffering from erasure, wrong slot, and false alarm errors. in this paper, two types of error correction (EC) codes, Low‐Density Parity Check (LDPC) code and Reed Solomon (RS) code, where paired the OPPM and DiPPM systems to reduce bugs, analyze the best EC parameters, and choose the superlative EC system. In other words, the performance of OPPM engaging LDPC codes and DiPPM employing LDPC codes will be compared against the OPPM engaging RS codes and DiPPM employing RS codes. To systematically carry out this comparison, numbers of photons, transmission efficiency, and the code rate are computed. The evaluation has stated that the data transmission rate at the start has indicated that OPPM with LDPC requires only 1.2 × 103 photons/pulse compared to the necessity of 1.821 × 103 photons/pulse when the DiPPM used LDPC. Accordingly, the transmission efficiency has been increased due to a reduction of number of photons. Also, the coded OPPM with LDPC codes is better than the coded DiPPM with LDPC codes when operating at a code rate that is approximately 0.7.

Two-stage frequency compensation for Doppler shift on BPSK transceiver with LDPC codes for free-space optical communication systems

The deployment of low earth orbits is seen as a promising way of enlarging data capacities as well as high data rates. Catering to these interests, optical communication presents possible ways of larger bandwidth than microwave communication. The current generation of mainstream communication systems are classified as coherent systems and incoherent systems, and in particular, coherent systems have received more attention owing to their high receiving sensitivity. This study investigates a digital coherent transceiver, based on binary phase-shift keying technology. As coherent demodulation will be affected by considering the Doppler shift effect in digital demodulation, Doppler shift of ± GHz can be compensated by adopting a two-stage frequency offset compensation. Moreover, by leveraging a fast filtering algorithm a considerable amount of resource consumption is saved in its engineering implementation, and its sensitivity can be significantly enhanced via a high-speed parallel error-correction codec based on low-density parity-check technology.

Free-Ride Coding for Constructions of Coupled LDPC Codes

Free-ride coding, as an approach that admits transmission of a few extra bits over a low-density parity-check (LDPC) coded link without bandwidth expansion, is applied in this paper to construct coupled LDPC codes. Firstly, we present a syndrome channel model and derive the lower and upper bounds on its capacity (referred to as accessible capacity), indicating the feasibility of the reliable transmission of extra bits. Secondly, we present the performance evaluation on both the word error rate (WER) and the bit error rate (BER) for the free-ride codes with simple lower and upper bounds. Then we propose three applications of free-ride coding to construct coupled LDPC codes, including implicit globally-coupled LDPC (GC-LDPC) codes, partial product-LDPC codes, and terminated spatially-coupled LDPC (SC-LDPC) codes, all of which have the figure of merits that they share the same code rates with the basic component LDPC codes. Simulation results show that: 1) the proposed GC-LDPC codes can outperform the component LDPC codes, yielding a coding gain of up to 0.8 dB; 2) the proposed product codes with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(3,6)$ </tex-math></inline-formula> -regular LDPC component codes of length 1024 can lower the WER from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-2}$ </tex-math></inline-formula> down to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-6}$ </tex-math></inline-formula> at the SNR around 2 dB; 3) the proposed terminated SC-LDPC codes can perform as well as the conventional terminated SC-LDPC codes but without any rate loss.

Proximal Decoding for LDPC Codes

This paper presents a novel optimization-based decoding algorithm for LDPC codes. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea of the proposed algorithm is the use of a code-constraint polynomial to penalize a vector far from a codeword as a regularizer in the approximate MAP objective function. A code proximal operator is naturally derived from a code-constraint polynomial. The proposed algorithm, called proximal decoding, can be described by a simple recursive formula consisting of the gradient descent step for a negative log-likelihood function corresponding to the channel conditional probability density function and the code proximal operation regarding the code-constraint polynomial. Proximal decoding is experimentally shown to be applicable to several non-trivial channel models such as LDPC-coded massive MIMO channels, correlated Gaussian noise channels, and nonlinear vector channels. In particular, in MIMO channels, proximal decoding outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding. The simple optimization-based formulation of proximal decoding allows a way for developing novel signal processing algorithms involving LDPC codes.

Performance Evaluation of Burst Error Correction by LDPC Coding and Iterative Decoding System in Magnetic Tape Drive

The tolerance for burst error of interleaved low-density parity-check (LDPC) code is evaluated with the cross-interleaved Reed–Solomon code (CIRC) in the magnetic tape drive using a BaFe magnetic tape. We evaluate the interleaved LDPC coding and iterative decoding system with burst error detector (LDPC-BD) system by the required signal-to-noise ratio (SNR) to achieve “No errors” for the burst-like deterioration such as media defects to the CIRC with erasure error correction (CIRC-EC) system by computer simulation. The results clarify that the LDPC-BD system tolerates the longer burst errors than the CIRC-EC system and the LDPC-BD system achieves “No errors” with the 3.0–4.5 dB lower SNR than the CIRC-EC system.

Mesh Model-Based Merging Method for DP-LDPC Code Pair

For the double protograph low-density parity-check (DP-LDPC) code pair, indicating the source and channel codes utilized in the joint source channel coding, the coding optimization is generally implemented by the differential evolution searching with high complexity. In this paper, a new structured design of the DP-LDPC code pair is proposed based on Graph theory to reduce the searching complexity, namely mesh model-based merging (M3) method. Firstly, four basic mesh models are designed to merge the protographs at any dimension. According to the different structures of the source and channel codes, the merging boundary constraint is statistically established to limit the using number of basic models. Then, a prior sorting algorithm is proposed to arrange the selection priorities of basic models for source and channel codes, respectively, which greatly refines the merging accuracy. Since most of the degrees are symmetric and predetermined in the merged protographs, the searching complexity is significantly reduced when the merged protographs are used as the initial input. Finally, simulation results demonstrate that the merging DP-LDPC code pairs show better performances compared to the existing code pairs. Furthermore, the proposed M3 method is hardware-friendly in Internet of Things because of its simple structure.

Energy-Efficient Backscatter-Assisted Coded Cooperative NOMA for B5G Wireless Communications

In this manuscript, we propose an alternating optimization framework to maximize the energy efficiency of a backscatter-enabled cooperative Non-orthogonal multiple access (NOMA) system by optimizing the transmit power of the source, power allocation coefficients (PAC), and power of the relay node under imperfect successive interference cancellation (SIC) decoding. A three-stage low-complexity energy-efficient alternating optimization algorithm is introduced which optimizes the transmit power, PAC, and relay power by considering the quality of service (QoS), power budget, and cooperation constraints. Subsequently, a joint channel coding framework is introduced to enhance the performance of far user which has no direct communication link with the base station (BS) and has bad channel conditions. In the destination node, the far user data is jointly decoded using a Sum-product algorithm (SPA) based joint iterative decoder realized by jointly-designed Quasi-cyclic Low-density parity-check (QC-LDPC) codes. Simulation results evince that the proposed backscatter-enabled cooperative NOMA system outperforms its counterpart by providing an efficient performance in terms of energy efficiency. Also, proposed jointly-designed QC-LDPC codes provide an excellent bit-error-rate (BER) performance by jointly decoding the far user data for considered BSC cooperative NOMA system with only a few decoding iterations.

Optimization of Protograph LDPC Codes via Surrogate Channel for Unequal Power Allocation

This paper investigates the possibilities of optimizing existing protograph low-density parity-check (PLDPC) codes and designing optimal PLDPC codes on both AWGN and Rayleigh channels under binary modulation with unequal power allocation (UPA) for nonuniform sources. While the binary UPA modulation achieves a power gain, it also results in unequal error protection on the coded bits in systematic codewords during transmission. For irregular codes, it is possible to best protect the information bits by optimizing the classification of variable nodes (VNs). Those VNs represent the coded bits in protograph that allows exploiting jointly the degree irregularity and the power differentiation. An algorithm for UPA-based protograph extrinsic information transfer (UPA-PEXIT) analysis on the Rayleigh channel is proposed with the concept of surrogate channel which circumvents the channel asymmetry problem with UPA. With the RJA code as example, it is shown that classification optimization does improve the decoding threshold when the source entropy is small. To design optimal codes, a UPA-based differential evolution (UPA-DE) algorithm is proposed in conjunction with the UPA-PEXIT analysis. A family of optimized codes are illustrated for three typical nonuniform source distributions and compared with the RJA and NND codes by simulations in error rate performance.

A Unified, SNR-Aware SC-LDPC Code Design With Applications to Magnetic Recording

Spatially coupled (SC)-low-density parity-check (LDPC) codes are known to have outstanding error-correction performance and low decoding latency, which make them an excellent choice for high-density magnetic recording (MR) technologies. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, we propose a unified framework for jointly optimizing the codes’ thresholds and cycle counts to address both regimes. We focus on circulant-based (CB) SC-LDPC code family as a representative, high-performance exemplar of structured SC-LDPC codes. The framework is based on efficient traversal and pruning of the code search space, building on the fact that the performance of a CB SC-LDPC code depends on some characteristics of the code’s partitioning matrix, which by itself is much smaller than the code’s full parity-check matrix. We then propose an algorithm that traverses all non-equivalent partitioning matrices and outputs a list of codes, each offering an attractive point on the trade-off between asymptotic and finite-length performance. Our simulations show that our framework results in SC-LDPC codes that outperform the state-of-the-art constructions, over both additive white Gaussian noise (AWGN) and partial response (PR) channel models, and that it offers the flexibility to choose low-signal-to-noise ratio (SNR), high-SNR, or in- between SNR region considering system requirements, e.g., that of the MR device.