LDPC Research Articles

Constrained Capacity Optimal Generalized Multi-User MIMO: A Theoretical and Practical Framework

Conventional multi-user multiple-input multiple-output (MU-MIMO) mainly focused on Gaussian signaling, independent and identically distributed (IID) channels, and a limited number of users. It will be laborious to cope with the heterogeneous requirements in next-generation wireless communications, such as various transmission data, complicated communication scenarios, and unprecedented massive user access. Therefore, this paper studies a generalized MU-MIMO (GMU-MIMO) system with more generalized and practical constraints, i.e., practical channel coding, non-Gaussian signaling, right-unitarily-invariant channels (covering Rayleigh fading channel matrices, certain ill-conditioned and correlated channel matrices, etc.), and massive users and antennas. These generalized assumptions bring new challenges in theory and practice. For example, there is no accurate constrained capacity region analysis for GMU-MIMO. In addition, it is unclear how to achieve constrained-capacity-optimal performance with practical complexity. To address these challenges, a unified framework is proposed to derive the constrained capacity region of GMU-MIMO and design a constrained-capacity-optimal transceiver, which jointly considers encoding, modulation, detection, and decoding. Group asymmetry is developed to group users according to their rates, which makes a tradeoff between user rate allocation and implementation complexity. Specifically, the constrained capacity region of group-asymmetric GMU-MIMO is characterized by using the minimum mean-square error (MMSE) optimality of orthogonal/vector approximate message passing (OAMP/VAMP) and the relationship between mutual information and MMSE. Furthermore, a theoretically optimal multi-user OAMP/VAMP receiver and practical multi-user low-density parity-check (MU-LDPC) codes are proposed to achieve the constrained capacity region of group-asymmetric GMU-MIMO. Numerical results demonstrate that the proposed MU-LDPC coded GMU-MIMO systems achieve asymptotic performance within 0.2 dB from the theoretical sum capacity. Moreover, their finite-length performances are about 1~2 dB away from the associated sum capacity of GMU-MIMO.

Neural Min-Sum Decoding for Generalized LDPC Codes

In this letter, we investigate the min-sum (MS) and neural MS (NMS) decoding algorithms for generalized low-density parity-check (GLDPC) codes. Although the MS decoder is much simpler than the a posteriori probability (APP) decoder commonly used for GLDPC codes, the MS decoder has not been considered mainly due to its inferior decoding performance. However, we show that the performance can be improved by i) employing the NMS decoding algorithm and ii) optimizing the component parity check matrix (PCM). For the four representative short GLDPC codes in the literature, experimental results show that the NMS decoding performance with the optimized component PCM significantly outperforms the MS decoding performance and even outperforms the APP decoding performance for some cases.

Deep Learning-Based Authentication Framework for Secure Terrestrial Communications in Next Generation Heterogeneous Networks

Smart Grid (SG) network is growing rapidly to improve the efficiency and reliability of the power supply. It will connect billions of devices to the internet in the near future. This increase in the number of internet-connected devices has led to an exponential increase in the market size of smart meters. These smart meters and devices will generate lakhs of gigabytes of data in upcoming years. To handle this massive amount of data flow, the Information and Communication Technology (ICT) of SG will experience huge advancements in terms of 5G and 6G wireless networks. These networks will provide higher data rates by utilizing the huge bandwidth spectrum of heterogeneous networks (HetNet). As the massive amount of data will be transmitted to various components of the smart grid using the internet, an open channel. Therefore, in addition to the need for high bandwidth and low latency, HetNet security has also become a prime concern. This paper presents an efficient approach to authenticate the smart devices in SG environment by using the channel state information (CSI) of the wireless links. Firstly, Low-Density Parity-Check (LDPC) codes are used to maintain the confidentiality and reliability of data transmission in the Advanced Metering Infrastructure (AMI) of SG. Then, a Convolution Neural Network (CNN)-based authentication framework is proposed to enhance the physical layer security (PLS) of terrestrial communications in next generation SG Hetnets. Further, the proposed framework is evaluated using received Channel State Information (CSI) values from smart meters placed at different locations, while also taking the scenario of active eavesdroppers into account. Experimental analysis reveals that the proposed CNN based authentication achieves 30.76 percent better authentication rate than existing DNN based authentication scheme. Further, the LDPC coded data transmission scheme reduces the bit error rate (BER) by 20 percent as compared to uncoded data transmission.

A Residual CNN-Based Denoiser for Reliable Recovery of Bit Stream With Applications to Soft Channel Decoding

The noise existent in practical systems degrades reliability performances, especially when delivering data over fast fading channels with the correlated noise. To address this issue, we propose a residual convolutional neural network aided denoiser (ResCNND) to suppress the noise for more reliable information recovery. The intelligent ResCNND is composed by convolutional layers, batch normalization layers and nonlinear activation functions. The ResCNND aided denoiser is then integrated with different types of channel decoders, and we propose a data preprocessing module to embed the statistical characteristics of channel conditions in terms of channel state information (CSI) as inputs to the neural network. Additionally, we propose the loss function by combining the mean square error loss and the normality test loss to simultaneously reduce the noise power and preserve the Gaussian distribution of residual noises. Then the well trained ResCNND can be used to suppress the noise in real time. In simulations, three types of channel codes, including LDPC, Polar and Turbo codes, are considered. The results demonstrate that the proposed ResCNND-aided receiver can effectively improve the signal-to-noise ratio and bit error rate performances with no requirement of perfect CSI, thereby achieving better reliability and robustness performances than benchmark schemes.

Performance Comparison of Channel Coding Techniques for OFDM System

Wireless communication is one of the speedily evolving and dynamic technology areas in the realm of communication. OFDM is an acronym for Orthogonal Frequency Division Multiplexing. It is a version of FDM in which orthogonal subcarriers are closely spaced to maximize bandwidth consumption. By decreasing Inter Symbol Interference (ISI) and increasing the Signal-to-Noise ratio (SNR), it has enhanced the quality of long-distance communication. It’s commonly employed in digital communication systems to safeguard digital data from noise and interference while also reducing bit mistakes. Convolutional codes, Block codes, are the two fundamental forms of channel codes. Block codes are based on abstract algebra and finite field arithmetic. They are capable of detecting and correcting faults. This category includes LDPC and Reed Solomon codes. Convolution codes, alternatively are created using a distinct strong mathematical framework and are generally utilised for real-time error correction. They combine all of the data into a single codeword. Reed-Solomon codes are block-based error correcting codes used in digital communications, storage, and ADSL, among other uses. The BER performance of an OFDM system is investigated in this paper using various channel coding algorithms.

Conservation Laws and Quantum Error Correction: Toward a Generalized Matching Decoder

Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the leading efforts to demonstrate scalable quantum computing. Central to our discussion is the minimum-weight perfect-matching decoder. The decoder works by exploiting underlying structure that arises due to materialised symmetries among surface-code stabilizer elements. By concentrating on these symmetries, we begin to address the question of how a minimum-weight perfect-matching decoder might be generalised for other families of codes. We approach this question first by investigating examples of matching decoders for other codes. These include decoding algorithms that have been specialised to correct for noise models that demonstrate a particular structure or bias with respect to certain codes. In addition to this, we propose a systematic way of constructing a minimum-weight perfect-matching decoder for codes with certain characteristic properties. The properties we make use of are common among topological codes. We discuss the broader applicability of the proposal, and we suggest some questions we can address that may show us how to design a generalised matching decoder for arbitrary stabilizer codes.

Side Information-based distributed source coding with Low-Density Parity-Check code

Considering the shortcomings of the existing Distributed Source Coding schemes on the bit error rate and the compression ratio, a side information-based distributed source coding scheme with Low-Density Parity-Check code is proposed. In the design of source encoder, redundancy is used to provide error protection, which is similar to insert redundancy to error protection in convolution coding; Set redundancy and Side Information approach is applied in the paper. Because of the correlation along the source, Low-Density Parity-Check code based Slepian-Wolf bound is adopted to implement the distributed source coding strategy. Experimental results are shown that the proposed method in paper can reach high compression ratio when the correlation among neighboring symbols is strong. The bit error rate of the sequence can be kept low between the sources are weak. It is an efficient distributed source coding scheme and is easy to be implemented.

Performance analysis and design of quasi-cyclic LDPC codes for underwater magnetic induction communications

Magnetic induction (MI) communication is an effective scheme for underwater wireless communication. In this paper, we aim to design an underwater MI communication system based on Quasi-cyclic LDPC (QC-LDPC) codes. Firstly, for a given QC-LDPC code used in underwater MI communication, we propose a novel algorithm to evaluate its performance, which is named as underwater magnetic induction protograph (UWMIP) extrinsic information transfer algorithm. Furthermore, we present a differential evolution UWMIP (DE-UWMIP) algorithm, which incorporates the differential evolution method and the UWMIP algorithm. By this algorithm, we search the optimized QC-LDPC codes with best distance threshold. Simulation results show that the proposed algorithm is effective and provide a good guidance to design the underwater MI communication system.

Energy consumption modeling and analysis for short-reach optical transmissions using irregular LDPC codes.

As the transmission rate of data center (DC) related short-reach optical transmissions quickly increases to keep up with internet services' data demand pace, advanced FEC technology starts to establish its key role in short reach optical transmission systems. Coding strategy using Quasi-Cyclic LDPC (QC-LDPC) codes with hard-decision (HD) decoders stands out due to its excellent error correction ability and simple hardware implementation. Meanwhile, with the introduction of green communication concept and increasingly extensive applications of DC, energy consumption of short-reach links has become an urgent problem to be studied. Based on tanner-graph, energy consumption models of regular LDPC codes' HD decoding circuits over AWGN channel have been proposed. In this work, for the first time, we introduce energy consumption of optical transmitters and characteristics of short reach optical channels into energy consumption modeling. Besides, probability distributions of flipping operation as well as bit errors during irregular QC-LDPC codes' HD decoding iterations are analytically derived using density evolution algorithm. Based on our proposed model and post-layout circuit simulation, systems' total power when using four QC-LDPC codes in IEEE and 3GPP with Gallager A/B decoders together with the case of using no FEC are analyzed in two typical scenarios. Numerical results show that, in short range scenario with slight bandwidth limit, uncoded strategy is much more energy-saving than all adopted LDPC-coded strategies in 50Gbaud OOK and 25Gbaud PAM4 transmissions. While in severely band-limited case when FEC is necessary, a tradeoff between energy consumption of transmitters and decoders occurs in 70Gbaud OOK and 35Gbaud PAM4 transmissions. Besides, LDPC codes with longer length at similar rate are proved to consume less power for their better error correction ability. And in long range scenario, power differences among coding strategies grow significantly when pre-bit error rate (BER) approaches their error correction threshold, reflecting the great influence of error correction threshold on the energy consumption of LDPC decoders. Among all adopted coding strategies, a (19200, 15872) LDPC code with Gallager B decoder consumes minimum power in both two scenarios. However, it is also found that decoding algorithm minimizing the total power differs at different pre-BER if we concentrate on decoding algorithm, justifying the significance of our modeling in minimizing system energy consumption.

Low power, less occupying area, and improved speed of a 4-bit router/rerouter circuit for low-density parity-check (LDPC) decoders.

Background: Low-density parity-check (LDPC) codes are more error-resistant than other forward error-correcting codes. Existing circuits give high power dissipation, less speed, and more occupying area. This work aimed to propose a better design and performance circuit, even in the presence of noise in the channel. Methods: In this research, the design of the multiplexer and demultiplexer were achieved using pass transistor logic. The target parameters were low power dissipation, improved throughput, and more negligible delay with a minimum area. One of the essential connecting circuits in a decoShder architecture is a multiplexer (MUX) and a demultiplexer (DEMUX) circuit. The design of the MUX and DEMUX contributes significantly to the performance of the decoder. The aim of this paper was the design of a 4 × 1 MUX to route the data bits received from the bit update blocks to the parallel adder circuits and a 1 × 4 DEMUX to receive the input bits from the parallel adder and distribute the output to the bit update blocks in a layered architecture LDPC decoder. The design uses pass transistor logic and achieves the reduction of the number of transistors used. The proposed circuit was designed using the Mentor Graphics CAD tool for 180 nm technology. Results: The parameters of power dissipation, area, and delay were considered crucial parameters for a low power decoder. The circuits were simulated using computer-aided design (CAD) tools, and the results depicted a significantly low power dissipation of 7.06 nW and 5.16 nW for the multiplexer and demultiplexer, respectively. The delay was found to be 100.5 ns (MUX) and 80 ns (DEMUX). Conclusion: This decoder's potential use may be in low-power communication circuits such as handheld devices and Internet of Things (IoT) circuits.

Novel construction of quasi‐cyclic low‐density parity‐check codes with variable code rates for cloud data storage systems

AbstractThis paper proposed a novel method for constructing quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes of medium to high code rates that can be applied in cloud data storage systems, requiring better error correction capabilities. The novelty of this method lies in the construction of sparse base matrices, using a girth greater than 4 that can then be expanded with a lift factor to produce high code rate QC‐LDPC codes. Investigations revealed that the proposed large‐sized QC‐LDPC codes with high code rates displayed low encoding complexities and provided a low bit error rate (BER) of 10−10 at 3.5 dB Eb/N0 than conventional LDPC codes, which showed a BER of 10−7 at 3 dB Eb/N0. Subsequently, implementation of the proposed QC‐LDPC code in a software‐defined radio, using the NI USRP 2920 hardware platform, was conducted. As a result, a BER of 10−6 at 4.2 dB Eb/N0 was achieved. Then, the performance of the proposed codes based on their encoding–decoding speeds and storage overhead was investigated when applied to a cloud data storage (GCP). Our results revealed that the proposed codes required much less time for encoding and decoding (of data files having a 10 MB size) and produced less storage overhead than the conventional LDPC and Reed–Solomon codes.

On the Performance of Rate-Compatible LDPC Codes under All-Integer Quantization Decoding

From a practical point of view, quantization is necessary for the design of any low-complexity LDPC decoder. However, the quantization scheme with the minimum computational complexity called all-integer quantization has not been well investigated since, intuitively, it seems to significantly degrade the decoding performance. It is found in this work that the utilization of 4-bit all-integer quantization for MSA-based LDPC decoder is adequate to achieve the decoding performance of the nonquantized case which can be considered as the lower bound on the decoding performance. Moreover, this simple quantization scheme can also be applied to the hardware and cost-efficient rate-compatible LDPC codes.

Efficient Decoder for Turbo Product Codes Based on Quadratic Residue Codes

In this letter, we study turbo product codes with quadratic residue codes (called QR-TPCs) as the component codes. We propose an efficient decoder based on Chase-II algorithm with two convergence conditions for the iterative decoding of QR-TPCs. For each row and column, the Chase-II decoder will stop immediately when one of the conditions is met. The simulation results show that the proposed algorithm has a lower computational complexity compared with existing decoding methods. Moreover, a comparison with 5G low-density parity-check codes shows that the proposed turbo product codes have better performance for short code lengths.

Rate‐compatible spatially coupled LDPC code ensembles by partial repetition extension

Herein, one partial repetition extension method is proposed to construct the rate-compatible spatially coupled low-density parity-check (RC-SCLDPC) codes. For each position of the base SCLDPC code, a certain proportion of the variable nodes are first selected randomly and then repeated a certain number of times. By adjusting the selection proportions and the repetition times, a family of RC-SCLDPC codes with arbitrary rates from 0 to the rate of the base SCLDPC code can be obtained and the rate-compatibility is realized. Threshold analysis results show that all member codes in the proposed RC-SCLDPC code family display capacity-approaching thresholds over the binary erasure channel and additive white Gaussian noise channel. Finite length simulation results also confirm their excellent thresholds. Moreover, the decoding complexity can be significantly decreased using this partial repetition extension method.

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.

A Semi Linear State Space Model for Error Floor Estimation of LDPC Codes Over the AWGN Channel

In this paper, we propose a novel state-space model to represent the behavior of sum-product algorithm (SPA) in the vicinity of a trapping set (TS) of a low-density parity-check (LDPC) code over the additive white Gaussian noise (AWGN) channel in the error floor region. The proposed model takes into account the non-linear behavior of SPA in the initial iterations using a quadratic approximation, and dynamically adjusts the operating point of the model in accordance to the statistical properties of TS messages. This is in contrast to the existing linear state-space models which linearly approximate the non-linear behavior of SPA at around the operating point of zero in all iterations. Simulation results are provided to demonstrate the higher accuracy of the proposed model in estimating the error floor of LDPC codes compared to the linear state-space model. We also make connections to the semi-analytical code-dependent technique proposed by Richardson for the error floor estimation of LDPC codes, and demonstrate that the proposed state-space model not only is a fully-analytical code-independent counterpart to that method, but also has less complexity and, in some cases, more accuracy.

Effects of Rosa roxburghii on insulin resistance in obese rats and its mechanisms

Objective: To investigate the effects of Rosa roxburghii on insulin resistance in obese rats and the regulation of phosphatidylinositol 3-kinase (PI3K)/ protein kinase Bβ(PKBβ/Akt2)/ glucose transporter 4(GLUT4) signaling pathway. Methods: Five-week-old male SD rats were randomly divided into normal control group (NC), model group (M), positive control group (PC), low-dose rosa roxburghii group (LD) and high-dose rosa roxburghii group (HD), with 10 rats in each group. The rats in the NC group were fed with normal diet, while those in the M, PC, LD and HD groups were fed with high-fat diet. From the 13th week, according to the dose standard of 6 ml/kg, rats in the LD group were intragastrically administered with 100 mg/kg Rosa roxburghii Tratt, the HD group were treated with 300 mg/kg Rosa roxburghii Tratt, the PC group were treated with 0.11 g/kg Chiglitazar sodium, and the NC and M groups were intragastrically administered with the same volume of normal saline. The body weight was measured every week until 20 weeks. The rats were sacrificed 24 h after the last experiment. Blood and skeletal muscle were collected. Serum total cholesterol (TC) and triglyceride (TG) contents were detected by colorimetric method, serum superoxide dismutase (SOD) activity was detected by xanthine oxidase method, serum malondialdehyde (MDA) content was detected by thiobarbituric acid method, blood glucose (FBG) value was detected by glucose oxidase method, insulin (FINS) content was detected by ELISA, and PI3K, Akt2, and GLUT4 protein and gene expressions were detected by Western blot and reverse transcription-polymerase chain reaction (RT-PCR). Results: Compared with the NC group, the body weight, serum MDA, TG, TC, FBG, FINS, HOMA-IR levels in the M group were significantly increased (P＜0.01), while SOD activity, PI3K、Akt2、GLUT4 protein and mRNA expression levels were significantly increased(P＜ 0.01). Compared with group M, the body weight, serum MDA, TG, TC, FBG, FINS, and HOMA-IR were decreased significantly in LD group, HD group and PC group (P＜0.05 or P＜0.01), while SOD activity, PI3K, Akt2, GLUT4 protein and mRNA expression levels were increased significantly (P＜0.05 or P＜0.01). Conclusion: Rosa roxburghii can improve insulin resistance in obese rats by antioxidant stress and up-regulating the expressions of PI3K, Akt2, and GLUT4 proteins and genes, which may be related to the PI3K/Akt2/GLUT4 signaling pathway.

PDD-Based Decoder for LDPC Codes With Model-Driven Neural Networks

In this work, we develop a double-loop iterative decoding algorithm for low density parity check (LDPC) codes based on the penalty dual decomposition (PDD) framework. We utilize the linear programming (LP) relaxation and the penalty method to handle the discrete constraints and the over-relaxation method is employed to improve convergence. Then, we unfold the proposed PDD decoding algorithm into a model-driven neural network, namely the learnable PDD decoding network (LPDN). We turn the tunable coefficients and parameters in the proposed PDD decoder into layer-dependent trainable parameters which can be optimized by gradient descent-based methods during network training. Simulation results demonstrate that the proposed LPDN with well-trained parameters is able to provide superior error-correction performance with much lower computational complexity as compared to the PDD decoder.

Block-Based Scheduling Algorithm for Layered Decoding of Block LDPC Codes

Block-Based Scheduling Algorithm for Layered Decoding of Block LDPC Codes

A Neural Network-based approach for Decoding of an Image of Low-Girth LDPC Code

A Neural Network-based approach for Decoding of an Image of Low-Girth LDPC Code