Protograph Low-density Parity-check Research Articles

Design of double protograph LDPC codes based JSCC systems via the ACE-PEG algorithm

Design of double protograph LDPC codes based JSCC systems via the ACE-PEG algorithm

Global optimization of double protograph LDPC codes for JSCC scheme

Global optimization of double protograph LDPC codes for JSCC scheme

P-LDPC coded image transmission with OFDM over underwater acoustic channel

Underwater environment is still an attractive area to explore and exploit by human beings. However, underwater characteristics limit communications due to harsh channel conditions, and efficient channel codes are essential to deploy. This study presents an underwater system based on protograph low-density parity check (P-LDPC) codes and orthogonal frequency division multiplexing (OFDM) for image transmission. The system proves a successful reconstruction of P-LDPC coded images with different levels of comparison. The performance of the proposed system is evaluated using nine objective measures such as bit error rate (BER) and peak signal to noise ratio (PSNR). Firstly, the proposed system performance is evaluated with different block lengths of P-LDPC code. Then, the implemented system shows a coding gain of approximately 1.75 dB for applying P-LDPC when compared to polar with cyclic redundancy check at 0.0001 BER. Additionally, image subjective assessment is obtained to demonstrate how the P-LDPC outweighs polar and turbo product codes in terms of estimated image quality. Lastly, further investigation is performed to study the effect of varying fast Fourier transform (FFT) size and cyclic prefix (CP) length on image reserved quality. The results show that the received image is better reconstructed for larger FFT sizes since that produce longer CP and symbol duration, and that in turn helps the system to combat the multipath fading introduced by the underwater channel.

A Cooperative Communication System With P-LDPC For Internet of Underwater Things

The acoustic communications are extremely challenging in underwater environments due to harsh conditions of this kind of nature. That medium's harshness affects the transmission reliability which in turn crucially requires an adoption of robust channel codes based on cooperative approaches to attain a more reliable data communication. This study proposes a cooperative communication system based on a protograph low-density parity check (P-LDPC) code. The system is elaborated in an Internet of underwater things (IoUT) scenario in which a relay node is acting as a helper that provides side information to destination. Compression and channel coding are offered by the system to cope with requirements of IoT in terms of reliable communication and compressed data between nodes. Furthermore, an algorithm for joint source channel coding is presented based on a modified version of offset min-sum. Moreover, layered decoding is Implemented in order to minimize number of iterations for the P-LDPC code. The results prove that proposed design can achieve a bit error rate (BER) of 5 × 10−6 at signal to noise ratio SNR = 8 dB for a coding rate of 1/3 and block length of 1500 bits. In addition, the proposed system shows a coding gain of 3.6 dB when compared with a non cooperative (no relay) approach. Besides, the proposed cooperative design can offer reduced computations versus the non cooperative system to achieve the same BER at a fixed SNR.

Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Partial IDS decoding based on the base graph of protograph LDPC codes

AbstractThe residual belief propagation (RBP) algorithm, which is the most classic informed dynamic scheduling strategy, achieves outstanding performance in error correction and can drastically accelerate convergence speed. However, the greedy algorithmic property of this iterative decoding will inevitably cause loss of decoding performance. To address this, a novel algorithm called the partial average bundle residual belief propagation (PABRBP) is proposed in this paper. According to the construction characteristics of a base matrix of protograph‐LDPC codes, informed dynamic scheduling (IDS) strategies are applied to an edge bundle of base matrices for the first time. This edge bundle of the base matrix can be applied to a corresponding cyclic permutation matrix. Furthermore, the update level of each bundle is determined by the value of the Partially Average Bundle Residual (PABR). Therefore, the edge message with the maximum residual in each bundle is updated in order, and the process of iterative decoding is less likely to become trapped in a local optimum. Additionally, the generation of silent nodes is reduced as much as possible. To further improve the PABRBP decoding performance for medium and long codes over the fading channel, the adjusted compensation term is periodically introduced. Analysis and simulation results show that PABRBP demonstrates a notable convergence quality and decoding performance improvement over the fading channels compared to existing state‐of‐art IDS algorithms.

Belief Propagation Optimization for Lossy Compression Based on Gaussian Source

In the Internet of Things, sensor nodes collect environmental information and utilize lossy compression for saving storage space. To achieve this objective, high-efficiency compression of the continuous source should be studied. Different from existing schemes, lossy source coding is implemented based on the duality principle in this work. Referring to the duality principle between the lossy source coding and the channel decoding, the belief propagation (BP) algorithm is introduced to realize lossy compression based on a Gaussian source. In the BP algorithm, the log-likelihood ratios (LLRs) are iterated, and their iteration paths follow the connecting relation between the check nodes and the variable nodes in the protograph low-density parity-check (P-LDPC) code. During LLR iterations, the trapping set is the main factor that influences compression performance. We propose the optimized BP algorithms to weaken the impact of trapping sets. The simulation results indicate that the optimized BP algorithms obtain better distortion–rate performance.

Rate-Compatible Protograph LDPC Codes for Source Coding in Joint Source—Channel Coded Modulation Systems

Using the source residual redundancy in a joint source and channel coded modulation (JSCCM) system to achieve a shaping gain has proven to be a good solution for probabilistic amplitude shaping. In a JSCCM system, rate-compatible source codes are essential for adapting to dynamically changing source probabilities. However, conventional rate-compatible source codes are not appropriate for JSCCM systems, since they may yield a loss in the shaping gain. Moreover, a code design that depends solely on the source decoding threshold appears to be ill suited, thus complicating the search for good source codes. In this paper, we propose a rate-compatible family of source codes for JSCCM systems based on an achievable system rate analysis and the source protograph extrinsic information transfer (PEXIT) algorithm. The proposed codes not only have good source decoding thresholds but also obtain shaping gains over the whole considered range of source probabilities. Numerical results show that the proposed rate-compatible family of source codes can significantly improve the bit-error-rate (BER) performance of the JSCCM system.

Asymmetric Dual-Mode Constellation and Protograph LDPC Code Design for Generalized Spatial MPPM Systems

To achieve reliable and efficient transmissions in free-space optical (FSO) communication, this paper designs a new protograph low-density parity-check (PLDPC) coded generalized spatial multipulse position modulation (GSMPPM) system over weak turbulence channels. Specifically, we investigate the PLDPC code, generalized space shift keying (GSSK) modulation, and MPPM constellation. First, we propose a type of novel GSMPPM constellations that intelligently integrates the GSSK into MPPM, referred to as asymmetric dual-mode (ADM) constellations, so as to improve the performance of the PLDPC-coded GSMPPM system. Furthermore, exploiting a protograph extrinsic information transfer (PEXIT) algorithm, we construct a type of improved PLDPC code, referred to as I-PLDPC code, which outperforms the existing PLDPC codes over weak turbulence channels. Analytical and simulation results show that the proposed ADM constellations and the proposed I-PLDPC code can obtain noticeable performance gains over their counterparts. Therefore, the proposed PLDPC-coded GSMPPM system with ADM constellations is competent to satisfy the high-reliability requirement for FSO applications.

Construction of protograph LDPC codes based on the convolution neural network

This paper presents an intelligent protograph construction algorithm. Protograph LDPC codes have shown excellent error correction performance and play an important role in wireless communications. Random search or manual construction are often used to obtain a good protograph, but the efficiency is not high enough and many experience and skills are needed. In this paper, a fast searching algorithm is proposed using the convolution neural network to predict the iterative decoding thresholds of protograph LDPC codes effectively. A special input data transformation rule is applied to provide stronger generalization ability. The proposed algorithm converges faster than other algorithms. The iterative decoding threshold of the constructed proto-graph surpasses greedy algorithm and random search by about 0.53 dB and 0.93 dB respectively under 100 times of density evolution. Simulation results show that quasi-cyclic LDPC (QC-LDPC) codes constructed from the proposed algorithm have competitive performance compared to other papers.

Designing Protograph LDPC Codes for Differential Chaotic Bit-Interleaved Coded Modulation System for Underwater Acoustic Communications

Underwater acoustic (UWA) communications face many challenges, such as large multipath delay, severe fading and the time-varying distortions. Chaotic modulations have shown advantages in UWA communications, but the reliability of current chaotic modulations is still not guaranteed. In this paper, a short-length protograph low-density parity-check (P-LDPC) code design framework for the differential chaotic bit-interleaved coded modulation (DC-BICM) system for UWA communication is proposed. This design framework, considering the requirements of short codes in UWA communications, integrates the DC-BICM system, UWA channel and the differential evolutionary code searching algorithm. Through this design framework, the optimized short P-LDPC code can be obtained. Simulation results show that the DC-BICM system with the proposed P-LDPC code can obtain more than 0.48 dB coding gain and reduce 32.6%~69.5% of the average number of iterations compared with the counterparts. Moreover, the reconstructed underwater image with the proposed P-LDPC code is clearest with the highest peak-signal-noise ratio value when compared with counterparts.

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.

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.

A New Transceiver Design for Protograph LDPC-Coded LACO-OFDM VLC Systems With Deep Learning

As a spectral-efficient and transmission-reliable technique, channel coded layered asymmetrically clipped optical orthogonal frequency-division multiplexing (LACO-OFDM) has attracted considerable interest in visible light communications. In this letter, we investigate the protograph low-density parity-check (LDPC)-coded LACO-OFDM VLC systems. Specially, we design a novel type of interleaving scheme, referred to as “variable-node subcarrier matched mapping (VNSMM)” to optimize the performance of protograph-coded LACO-OFDM VLC systems. In such scenario, the conventional iterative detection framework cannot completely eliminate the inter-layer interference (ILI), which degrades the system performance. To further suppress the ILI at the receiver, we propose a deep learning (DL)-based detection framework, called “DeepLACO”, to simultaneously obtain the log-likelihood ratios (LLRs) used for the protograph decoders in all layers without the knowledge of channel state information (CSI). Analyses and simulations demonstrate that the protograph-coded LACO-OFDM exploiting the proposed interleaving scheme and detection framework can achieve excellent performance in VLC systems.

Global Design of Double Protograph LDPC Codes for Joint Source-Channel Coding

In this letter, a global design of double protograph low-density parity-check (DP-LDPC) codes is proposed for joint source-channel coding (JSCC) system. The maximum number of degree-2 variable nodes (VNs), which is very important for the performance of the system, is determined from a global perspective that considers the joint protograph as a whole. Based on the allocation of degree-2 VNs, the new guidelines with this more comprehensive perspective are summarized and the global optimized DP-LDPC codes are designed. The simulation results that are in consistent with the joint protograph extrinsic information transfer (P-EXIT) analysis indicate that the optimized DP-LDPC codes have better performance compared with the existing re-designed DP-LDPC codes.

Protograph Designing of P-LDPC Codes via M3 Method

Recently, a mesh model-based merging (M3) method and four basic graph models were proposed to construct the double protograph low-density parity-check (P-LDPC) code pair of the joint source channel coding (JSCC). Designing the protograph (mother code) of the P-LDPC code with both a good waterfall region and lower error floor is a challenge, and few works have existed until now. In this paper, the single P-LDPC code is improved to further verify the availability of the M3 method, and its structure is different from the channel code in the JSCC. This construction technique yields a family of new channel codes with lower power consumption and higher reliability. The structured design and better performance demonstrate that the proposed code is hardware-friendly.

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.

Designing a Common DP-LDPC Code Pair for Variable On-Body Channels

The joint source channel coding (JSCC) system is sensitive to the changing channel characteristics, because the optimally designed source-channel code pair always needs to be redesigned when the transmission environment is updated. A solution is to seek a common code pair for variable channels. Channel model 3 (CM3) is a variable on-body channel following the Weibull distribution, which is analyzed in four conditions due to varying shape factors, namely with exponential, Rayleigh, log-normal and normal distributions. The JSCC system is considered in this paper based on double protograph low-density parity-check (DP-LDPC) code pair over the variable CM3 channel. Firstly, four DP-LDPC code pairs are searched by the conventional differential evolution (DE) algorithm with four distributions of the Weibull model, respectively. However, these four code pairs only present good bit-error ratio performance in their own distribution, and have error floors in the other three. To resolve the problem, an artificial intelligence method based on principle component analysis (PCA) algorithm is designed to extract the common code pair. It is demonstrated that the common code pair performs well in noise-varying and practical-parameter transmissions. Instead of four DE code pairs, the designed one PCA code pair provides a strong technical support to low-complexity manufacturing such as eHealthcare.

Protograph bit-interleaved coded modulation: A bandwidth-efficient design paradigm for 6G wireless communications

Bit-interleaved coded modulation (BICM) has attracted considerable attention from the research community in the past three decades, because it can achieve desirable error performance with relatively low implementation complexity for a large number of communication and storage systems. By exploiting the iterative demapping and decoding (ID), the BICM is able to approach capacity limits of coded modulation over various channels. In recent years, protograph low-density parity-check (PLDPC) codes and their spatially-coupled (SC) variants have emerged to be a pragmatic forward-error-correction (FEC) solution for BICM systems due to their tremendous error-correction capability and simple structures, and found widespread applications such as deep-space communication, satellite communication, wireless communication, optical communication, and data storage. This article offers a comprehensive survey on the state-of-the-art development of PLDPC-BICM and its innovative SC variants over a variety of channel models, e.g., additive white Gaussian noise (AWGN) channels, fading channels, Poisson pulse position modulation (PPM) channels, and flash-memory channels. Of particular interest is code construction, constellation shaping, as well as bit-mapper design, where the receiver is formulated as a serially-concatenated decoding framework consisting of a soft-decision demapper and a belief-propagation decoder. Finally, several promising research directions are discussed, which have not been adequately addressed in the current literature.

Redesign of Channel Codes for Joint Source-Channel Coding Systems over One-Dimensional Inter-Symbol-Interference Magnetic Recording Channels

Although the joint source-channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) codes has been shown to possess excellent error performance over additive white Gaussian noise (AWGN) channels, it cannot perform well over one-dimensional inter-symbol-interference (OD-ISI) magnetic recording channels. In this study, a new JSCC system with a three-stage serially concatenated framework of Turbo equalization is firstly proposed for OD-ISI magnetic recording channels. Then, a modified joint protograph extrinsic information transfer (M-JPEXIT) algorithm is put forward to analyze the convergence-performance of the proposed system. By applying the M-JPEXIT algorithm, the channel codes are redesigned for this system to improve the error performance. Both the M-JPEXIT analysis and the bit-error-rate (BER) simulation results show the performance improvement of the proposed channel codes, especially in the water-fall region.