Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

Implementation of low-density parity-check codes decoder for CCSDS standard

The complexity/performance balanced decoder for low-density parity-check （LDPC） codes is preferred in practical wireless communication systems. A low complexity LDPC decoder for the Consultative Committee for Space Data Systems （CCSDS） standard is achieved in DSP. An ap- proximate decoding algorithm, normalized rain-sum algorithm, is used in the implementation for its low amounts of computation. To reduce the performance loss caused by the approximation, the pa- rameters of the normalized min-sum algorithm are determined by calculating and finding the mini- mum value of thresholds through density evolution. The minimum value which indicates the best per- formance of the decoding algorithm is corresponding with the optimized parameters. In implementa- tion, the memory cost is saved by decomposing the parity-check matrix into submatrices to store and the computation of passing message in decoding is accelerated by using the intrinsic function of DSP. The performance of the decoder with optimized factors is simulated and compared with the ideal BP decoder. The result shows they have about the same performance.

THE Q-MATRIX LOW-DENSITY PARITY-CHECK CODES

This paper presents a matrix permuting approach to the construction of Low-Density Parity-Check (LDPC) code. It investigates the structure of the sparse parity-check matrix defined by Gallager. It is discovered that the problem of constructing the sparse parity-check matrix requires an algorithm that is efficient in search environments and also is able to work with constraint satisfaction problem. The definition of Q-matrix is given, and it is found that the queen algorithm enables to search the Q-matrix. With properly permuting Q-matrix as sub-matrix, the sparse parity-check matrix which satisfied constraint condition is created, and the good regular-LDPC code that is called the Q-matrix LDPC code is generated. The result of this paper is significant not only for designing low complexity encoder, improving performance and reducing complexity of iterative decoding arithmetic, but also for building practical system of encodable and decodable LDPC code.

REGULAR LOW-DENSITY PARITY-CHECK CODES BASED ON SHIFTED IDENTITY MATRICES

This paper extends the class of Low-Density Parity-Check (LDPC) codes that can be constructed from shifted identity matrices. To construct regular LDPC codes, a new method is proposed. Two simple inequations are adopted to avoid the short cycles in Tanner graph, which makes the girth of Tanner graphs at least 8. Because their parity-check matrices are made up of circulant matrices, the new codes are quasi-cyclic codes. They perform well with iterative decoding.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

Low-Complexity Optimization Algorithm for Irregular Low-Density Parity-Check Codes

A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check （LDPC） codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation resuits show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.

Effect of temperature and time on the precipitation ofκ-carbides in Fe-28Mn-10Al-0.8C low-density steels:Aging mechanism and its impact on material properties

In low-density steel,κ-carbides primarily precipitate in the form of nanoscale particles within austenite grains.However,their precipitation within ferrite matrix grains has not been comprehensively explored,and the second-phase evolution mechanism during aging remains unclear.In this study,the crystallographic characteristics and morphological evolution ofκ-carbides in Fe-28Mn-10Al-0.8C(wt%)low-density steel at different aging temperatures and times and the impacts of these changes on the steels’microhardness and properties were comprehensively analyzed.Under different heat treatment conditions,intragranularκ-carbides exhibited various morpho-logical and crystallographic characteristics,such as acicular,spherical,and short rod-like shapes.At the initial stage of aging,acicularκ-carbides primarily precipitated,accompanied by a few spherical carbides.κ-Carbides grew and coarsened with aging time,the spherical carbides were considerably reduced,and rod-like carbides coarsened.Vickers hardness testing demonstrated that the material’s hardness was affected by the volume fraction,morphology,and size ofκ-carbides.Extended aging at higher temperatures led to an increase in carbide size and volume fraction,resulting in a gradual rise in hardness.During deformation,the primary mechanisms for strengthening were dislocation strengthening and second-phase strengthening.Based on these findings,potential strategies for improving material strength are proposed.

Effects of heating temperature and atmosphere on element distribution and microstructure in high-Mn/Al austenitic low-density steel

The elemental distribution and microstructure near the surface of high-Mn/Al austenitic low-density steel were investigated after isothermal holding at temperatures of 900-1200℃ in different atmospheres,including air,N_(2),and N_(2)+CO_(2).No ferrite was formed near the surface of the experimental steel during isothermal holding at 900 and 1000℃ in air,while ferrite was formed near the steel sur-face at holding temperatures of 1100 and 1200℃.The ferrite fraction was larger at 1200℃ because more C and Mn diffused to the sur-face,exuded from the steel,and then reacted with N and O to form oxidation products.The thickness of the compound scale increased owing to the higher diffusion rate at higher temperatures.In addition,after isothermal holding at 1100℃ in N_(2),the Al content near the surface slightly decreased,while the C and Mn contents did not change.Therefore,no ferrite was formed near the surface.However,the near-surface C and Al contents decreased after holding at 1100℃in the N_(2)+CO_(2)mixed atmosphere,resulting in the formation of a small amount of ferrite.The compound scale was thickest in N_(2),followed by the N_(2)+CO_(2)mixed atmosphere,and thinnest in air.Overall,the element loss and ferrite fraction were largest after holding in air at the same temperature.The differences in element loss and ferrite frac-tion between in N_(2) and N_(2)+CO_(2)atmospheres were small,but the compound scale formed in N_(2) was significantly thicker.According to these results,N_(2)+CO_(2)is the ideal heating atmosphere for the industrial production of high-Mn/Al austenitic low-density steel.

Low-density lipoprotein receptor-related protein 2(LRP2)is required for lipid export in the midgut of the migratory locust,Locusta migratoria

Low-density lipoprotein receptor-related protein 2(LRP2)is a multifunctional endocytic receptor expressed in epithelial cells.In mammals,it acts as an endocytic receptor that mediates the cellular uptake of cholesterol-containing apolipoproteins to maintain lipid homeostasis.However,little is known about the role of LRP2 in lipid homeostasis in insects.In the present study,we investigated the function of LRP2 in the migratory locust Locusta migratoria(LmLRP2).The mRNA of LmLRP2 is widely distributed in various tissues,including integument,wing pads,foregut,midgut,hindgut,Malpighian tubules and fat body,and the amounts of LmLRP2 transcripts decreased gradually in the early stages and then increased in the late stages before ecdysis during the nymphal developmental stage.Fluorescence immunohistochemistry revealed that the LmLRP2 protein is mainly located in cellular membranes of the midgut and hindgut.Using RNAi to silence LmLRP2 caused molting defects in nymphs(more than 60%),and the neutral lipid was found to accumulate in the midgut and surface of the integument,but not in the fat body,of dsLmLRP2-treated nymphs.The results of a lipidomics analysis showed that the main components of lipids(diglyceride and triglyceride)were significantly increased in the midgut,but decreased in the fat body and hemolymph.Furthermore,the content of total triglyceride was significantly increased in the midgut,but markedly decreased in the fat body and hemolymph in dsLmLRP2-injected nymphs.Our results indicate that LmLRP2 is located in the cellular membranes of midgut cells,and is required for lipid export from the midgut to the hemolymphand fat body in locusts.

Overexpression of low-density lipoprotein receptor prevents neurotoxic polarization of astrocytes via inhibiting NLRP3 inflammasome activation in experimental ischemic stroke

Neurotoxic astrocytes are a promising therapeutic target for the attenuation of cerebral ischemia/reperfusion injury.Low-density lipoprotein receptor,a classic cholesterol regulatory receptor,has been found to inhibit NLR family pyrin domain containing protein 3(NLRP3)inflammasome activation in neurons following ischemic stroke and to suppress the activation of microglia and astrocytes in individuals with Alzheimer’s disease.However,little is known about the effects of low-density lipoprotein receptor on astrocytic activation in ischemic stroke.To address this issue in the present study,we examined the mechanisms by which low-density lipoprotein receptor regulates astrocytic polarization in ischemic stroke models.First,we examined low-density lipoprotein receptor expression in astrocytes via immunofluorescence staining and western blotting analysis.We observed significant downregulation of low-density lipoprotein receptor following middle cerebral artery occlusion reperfusion and oxygen-glucose deprivation/reoxygenation.Second,we induced the astrocyte-specific overexpression of low-density lipoprotein receptor using astrocyte-specific adeno-associated virus.Low-density lipoprotein receptor overexpression in astrocytes improved neurological outcomes in middle cerebral artery occlusion mice and reversed neurotoxic astrocytes to create a neuroprotective phenotype.Finally,we found that the overexpression of low-density lipoprotein receptor inhibited NLRP3 inflammasome activation in oxygen-glucose deprivation/reoxygenation injured astrocytes and that the addition of nigericin,an NLRP3 agonist,restored the neurotoxic astrocyte phenotype.These findings suggest that low-density lipoprotein receptor could inhibit the NLRP3-meidiated neurotoxic polarization of astrocytes and that increasing low-density lipoprotein receptor in astrocytes might represent a novel strategy for treating cerebral ischemic stroke.

Generalized Low-Density Parity-Check Coding Scheme with Partial-Band Jamming

In this study, a class of Generalized Low-Density Parity-Check （GLDPC） codes is designed for data transmission over a Partial-Band Jamming （PBJ） environment. The GLDPC codes are constructed by replacing parity-check code constraints with those of nonsystematic Bose-Chaudhuri-Hocquenghem （BCH）, referred to as Low-Density Parity-Check （LDPC）-BCH codes. The rate of an LDPC-BCH code is adjusted by selecting the transmission length of the nonsystematic BCH code, and a low-complexity decoding algorithm based on message- passing is presented that employs A Posteriori Probability （APP） fast BCH transform for decoding the BCH check nodes at each decoding iteration. Simulation results show that the LDPC-BCH codes with a code rate of 1/8.5 have a bit error rate performance of 1 x10-8 at signal-noise-ratios of -6.97 dB, -4.63 dB, and 2.48 dB when the fractions of the band jammed are 30%, 50%, and 70%, respectively.

Minimum distances of three families of low-density parity-check codes based on finite geometries

Three families of low-density parity-check （LDPC） codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.

Construction of Rate-Compatible(RC) Low-Density Parity-Check(LDPC) Convolutional Codes Based on RC-LDPC Block Codes

In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).

Multistep Linear Programming Approaches for Decoding Low-Density Parity-Check Codes

The problem of improving the performance of linear programming（LP） decoding of low-density parity-check（LDPC） codes is considered in this paper.A multistep linear programming（MLP） algorithm was developed for decoding LDPC codes that includes a slight increase in computational complexity.The MLP decoder adaptively adds new constraints which are compatible with a selected check node to refine the results when an error is reported by the original LP decoder.The MLP decoder result is shown to have the maximum-likelihood（ML） certificate property.Simulations with moderate block length LDPC codes suggest that the MLP decoder gives better performance than both the original LP decoder and the conventional sum-product（SP） decoder.

An improved low-complexity sum-product decoding algorithm for low-density parity-check codes

In this paper, an improved low-complexity sum-product decoding algorithm is presented for low-density parity-check （LDPC） codes. In the proposed algorithm, reduction in computational complexity is achieved by utilizing fast Fourier transform （FFT） with time shift in the check node process. The improvement in the decoding performance is achieved by utilizing an op- timized integer constant in the variable node process. Simulation results show that the proposed algorithm achieves an overall coding gain improvement ranging from 0.04 to 0.46 dB. Moreover, when compared with the sum-product algorithm （SPA）, the proposed decoding algorithm can achieve a reduction of 42%-67% of the total number of arithmetic operations required for the decoding process.

Quad-Level Cell NAND Design and Soft-Bit Generation for Low-Density Parity-Check Decoding in System-Level Application

QLC（Quad-Level Cell） NAND flash will be one of the future technologies for next generation memory chip after three-dimensional（3D） TLC（Triple-Level Cell） stacked NAND flash. In QLC device, data errors will easily occur because of 2~4 data levels in the limited voltage range. This paper studies QLC NAND technology which is 4 bits per cell. QLC programming methods based on 16 voltage levels and reading method based on ＂half-change＂ Gray coding are researched. Because of the probable error impact of QLC NAND cell＇s voltage change, the solution of generating the soft information after XOR（exclusive OR） the soft bits by internal read mechanism is presented for Low-Density Parity-Check（LDPC） Belief Propagation（BP） decoding in QLC design for its system level application.

Code Optimization, Frozen Glassy Phase and Improved Decoding Algorithms for Low-Density Parity-Check Codes

The statistical physics properties of low-density parity-cheek codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check （bit） nodes have higher decoding thresholds compared to regular counterparts with homo- geneous degree distribution. We also show that the instability of the mean-field caiculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed （searching for the ground state）, we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is dose to the dynamicai transition where all local search heuristics fail to identify the true message （codeword or the ferromagnetic state）. After the dynamical transition, the number of metastable states with larger energy density （than the ferromagnetic state） becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentiaily numerous codewords sharing the identical ferromagnetic energy.

Emerging low-density polyethylene/paraffin wax/aluminum composite as a form-stable phase change thermal interface material

Thermal interface materials(TIMs) play a vital role in the thermal management of electronic devices and can significantly reduce thermal contact resistance(TCR). The TCR between the solid–liquid contact surface is much smaller than that of the solid–solid contact surface, but conventional solid–liquid phase change materials are likely to cause serious leakage. Therefore, this work has prepared a new formstable phase change thermal interface material. Through the melt blending of paraffin wax(PW) and low-density polyethylene(LDPE), the stability is improved and it has an excellent coating effect on PW. The addition of aluminum(Al) powder improves the low thermal conductivity of PW/LDPE, and the addition of 15wt% Al powder improves the thermal conductivity of the internal structure of the matrix by 67%. In addition, the influence of the addition of Al powder on the internal structure, thermal properties, and phase change behavior of the PW/LDPE matrix was systematically studied. The results confirmed that the addition of Al powder improved the thermal conductivity of the material without a significant impact on other properties, and the thermal conductivity increased with the increase of Al addition. Therefore, morphologically stable PW/LDPE/Al is an important development direction for TIMs.

DESIGN OF LOW-DENSITY PARITY CHECK CODES FOR MIMO SYSTEMS WITH DOUBLY-ITERATIVE RECEIVERS

In this paper, the Multiple Input Multiple Output (MIMO) doubly-iterative receiver which consists of the Probabilistic Data Association detector (PDA) and Low-Density Parity-Check Code (LDPC) decoder is developed. The receiver performs two iterative decoding loops. In the outer loop, the soft information is exchanged between the PDA detector and the LDPC decoder. In the inner loop, it is exchanged between variable node and check node decoders inside the LDPC decoder. On the light of the Extrinsic Information Transfer (EXIT) chart technique, an LDPC code degree profile optimization algorithm is developed for the doubly-iterative receiver. Simulation results show the doubly-receiver with optimized irregular LDPC code can have a better performance than the one with the regular one.

Inhibitory Effect of Isorhapontigenin on Copper-Mediated Peroxidation of Human Low-Density Lipoprotein in vitro

Aim To study the effect of Isorhapontigenin (Iso) on copper-mediatedperoxidation of human low-density lipoprotein (LDL) and on the toxicity of oxidized LDL (ox-LDL) tomouse macrophages in vitro. Methods Human LDL from sera df normal lipidemic donors was separated bysequential ultracentrifugation. The separated human IDL 1 mg·mL^(-1) in phosphate buffer saline, pH7.4, was incubated with cupric sulfate (10 μmol·L^(-1) ) at 37℃ for 10 h in the presence orabsence of various concentrations of Iso. Malondialdehyde (MDA) formation, vitamin E consumption,electrophoretic mobility of LDL, mitochondria] membrane potential of mouse peritoneal macrophages,phagocytosis of neutral red, and release of nitric oxide (NO) from macrophages were determined byvarious methods. Results Iso 1 - 100 μmol·L^(-1) significantly inhibited the increase of MDAformation, vitamin E consumption and electrophoretic mobility of LDL induced by Cu^(2+) in aconcentration-dependent manner. The injury of the mitochondrial membrane potential of mouseperitoneal macrophages due to incubation with ox-LDL (0.1 mg·mL^(-1)) at 37℃ for 12 h was markedlyprotected by 10 μmol·L^(-1) Iso. After pretreat-ment of the macrophages with 10 μmol · L^(-1)of Iso and then exposure to ox-LDL for 4 h, the reduction of phagocytosis of neutral red and releaseof NO in response to lipopolysaccharide (IPS) stimulation were significantly prevented. ConclusionIso has protective action against Cu^(2+) - mediated LDL peroxidation and ox-LDL induced toxicity tomacrophages in vitro.