The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,whi...The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,which results in high computational complexity.This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding.This paper proposes a hybrid technique that combines the“paritycheck”with the“G-matrix”to reduce the computational complexity of BP decoder for polar codes.The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process,which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding.We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance.Moreover,mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated.The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding.Simulation results show that the proposed hybrid technique reduces the iterations by about 90%of BP decoding in a high Signal-to-Noise Ratio(SNR)(i.e.,3.5~4 dB),and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.展开更多
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 ...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.展开更多
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 ...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.展开更多
The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication.Here we present a heralded two-photon entanglement purification protocol(EPP)usin...The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication.Here we present a heralded two-photon entanglement purification protocol(EPP)using heralded high-fidelity parity-check gate(HH-PCG),which can increase the entanglement of nonlocal two-photon polarization mixed state.The HH-PCG is constructed by the input-output process of nitrogen-vacancy(NV)center in diamond embedded in a single-sided optical cavity,where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector.As the unwanted components can be filtrated due to the heralded function,the fidelity of the EPP scheme can be enhanced considerably,which will increase the fidelity of quantum communication processing.展开更多
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 ev...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 results 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.展开更多
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-che...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.展开更多
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 ...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.展开更多
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 de...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).展开更多
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 dec...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.展开更多
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 easil...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.展开更多
Free-space optical(FSO)communication is of supreme importance for designing next-generation networks.Over the past decades,the radio frequency(RF)spectrum has been the main topic of interest for wireless technology.Th...Free-space optical(FSO)communication is of supreme importance for designing next-generation networks.Over the past decades,the radio frequency(RF)spectrum has been the main topic of interest for wireless technology.The RF spectrum is becoming denser and more employed,making its availability tough for additional channels.Optical communication,exploited for messages or indications in historical times,is now becoming famous and useful in combination with error-correcting codes(ECC)to mitigate the effects of fading caused by atmospheric turbulence.A free-space communication system(FSCS)in which the hybrid technology is based on FSO and RF.FSCS is a capable solution to overcome the downsides of current schemes and enhance the overall link reliability and availability.The proposed FSCS with regular low-density parity-check(LDPC)for coding techniques is deliberated and evaluated in terms of signal-to-noise ratio(SNR)in this paper.The extrinsic information transfer(EXIT)methodology is an incredible technique employed to investigate the sum-product decoding algorithm of LDPC codes and optimize the EXIT chart by applying curve fitting.In this research work,we also analyze the behavior of the EXIT chart of regular/irregular LDPC for the FSCS.We also investigate the error performance of LDPC code for the proposed FSCS.展开更多
This paper proposes a parallel cyclic shift structure of address decoder to realize a high-throughput encoding and decoding method for irregular-quasi-cyclic low-density parity-check(IR-QC-LDPC)codes,with a dual-diago...This paper proposes a parallel cyclic shift structure of address decoder to realize a high-throughput encoding and decoding method for irregular-quasi-cyclic low-density parity-check(IR-QC-LDPC)codes,with a dual-diagonal parity structure.A normalized min-sum algorithm(NMSA)is employed for decoding.The whole verification of the encoding and decoding algorithm is simulated with Matlab,and the code rates of 5/6 and 2/3 are selected respectively for the initial bit error ratio as 6%and 1.04%.Based on the results of simulation,multi-code rates are compatible with different basis matrices.Then the simulated algorithms of encoder and decoder are migrated and implemented on the field programmable gate array(FPGA).The 183.36 Mbps throughput of encoder and the average 27.85 Mbps decoding throughput with the initial bit error ratio 6%are realized based on FPGA.展开更多
Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rat...Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.展开更多
A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filt...A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate (BER) performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.展开更多
A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and...A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.展开更多
The existing constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead ...The existing constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate (BER) performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.展开更多
An adaptive modulation (AM) algorithm is proposed and the application of the adapting algorithm together with low-density parity-check (LDPC) codes in multicarrier systems is investigated. The AM algorithm is base...An adaptive modulation (AM) algorithm is proposed and the application of the adapting algorithm together with low-density parity-check (LDPC) codes in multicarrier systems is investigated. The AM algorithm is based on minimizing the average bit error rate (BER) of systems, the combination of AM algorithm and LDPC codes with different code rates (half and three-fourths) are studied. The proposed AM algorithm with that of Fischer et al is compared. Simulation results show that the performance of the proposed AM algorithm is better than that of the Fischer's algorithm. The results also show that application of the proposed AM algorithm together with LDPC codes can greatly improve the performance of multicarrier systems. Results also show that the performance of the proposed algorithm is degraded with an increase in code rate when code length is the same.展开更多
In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destinatio...In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.展开更多
A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbo...A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern's order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.展开更多
Reconciliation is a necessary step in postprocessing of continuous-variable quantum key distribution(CV-QKD)system.We use globally coupled low-density parity-check(GC-LDPC)codes in reconciliation to extract a precise ...Reconciliation is a necessary step in postprocessing of continuous-variable quantum key distribution(CV-QKD)system.We use globally coupled low-density parity-check(GC-LDPC)codes in reconciliation to extract a precise secret key from the raw keys over the authenticated classical public channel between two users.GC-LDPC codes have excellent performance over both the additive Gaussian white noise and binary-erasure channels.The reconciliation based on GC-LDPC codes can improve the reconciliation efficiency to 95.42% and reduce the frame error rate to 3.25×10^-3.Using distillation,the decoding speed can achieve 23.8 Mbits/s and decrease the cost of memory.Given decoding speed and low memory usage,this makes the proposed reconciliation method viable approach for high-speed CV-QKD system.展开更多
基金This work is partially supported by the National Key Research and Development Project under Grant 2018YFB1802402.
文摘The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,which results in high computational complexity.This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding.This paper proposes a hybrid technique that combines the“paritycheck”with the“G-matrix”to reduce the computational complexity of BP decoder for polar codes.The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process,which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding.We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance.Moreover,mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated.The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding.Simulation results show that the proposed hybrid technique reduces the iterations by about 90%of BP decoding in a high Signal-to-Noise Ratio(SNR)(i.e.,3.5~4 dB),and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.
文摘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.
基金Supported by the National Natural Science Foundation of China (61205116)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grants Nos.11674033,11474026,11604226,and 11475021)Science and Technology Program Foundation of the Beijing Municipal Commission of Education of China(Grant Nos.KM201710028005 and CIT&TCD201904080)
文摘The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication.Here we present a heralded two-photon entanglement purification protocol(EPP)using heralded high-fidelity parity-check gate(HH-PCG),which can increase the entanglement of nonlocal two-photon polarization mixed state.The HH-PCG is constructed by the input-output process of nitrogen-vacancy(NV)center in diamond embedded in a single-sided optical cavity,where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector.As the unwanted components can be filtrated due to the heralded function,the fidelity of the EPP scheme can be enhanced considerably,which will increase the fidelity of quantum communication processing.
基金Leading Academic Discipline Project of Shanghai Municipal Education Commission,China(No.J51801)Shanghai Second Polytechnic University Foundation,China(No.QD209008)Leading Academic Discipline Project of Shanghai Second Polytechnic University,China(No.XXKZD1302)
文摘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 results 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.
基金supported by the National Natural Science Foundation of China (Nos. 61101072 and 61132002)
文摘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.
基金This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11271004, 11371121, 11471096).
文摘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.
基金the National Natural Science Foundation of China(Nos.61401164,61471131 and 61201145)the Natural Science Foundation of Guangdong Province(No.2014A030310308)
文摘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).
基金Supported by the National Key Basic Research and Development (973) Program of China (No.2009CB320300)
文摘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.
文摘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.
文摘Free-space optical(FSO)communication is of supreme importance for designing next-generation networks.Over the past decades,the radio frequency(RF)spectrum has been the main topic of interest for wireless technology.The RF spectrum is becoming denser and more employed,making its availability tough for additional channels.Optical communication,exploited for messages or indications in historical times,is now becoming famous and useful in combination with error-correcting codes(ECC)to mitigate the effects of fading caused by atmospheric turbulence.A free-space communication system(FSCS)in which the hybrid technology is based on FSO and RF.FSCS is a capable solution to overcome the downsides of current schemes and enhance the overall link reliability and availability.The proposed FSCS with regular low-density parity-check(LDPC)for coding techniques is deliberated and evaluated in terms of signal-to-noise ratio(SNR)in this paper.The extrinsic information transfer(EXIT)methodology is an incredible technique employed to investigate the sum-product decoding algorithm of LDPC codes and optimize the EXIT chart by applying curve fitting.In this research work,we also analyze the behavior of the EXIT chart of regular/irregular LDPC for the FSCS.We also investigate the error performance of LDPC code for the proposed FSCS.
基金supported by the National Natural Science Foundation of China(11705191)the Anhui Provincial Natural Science Foundation(1808085QF180)the Natural Science Foundation of Shanghai(18ZR1443600)
文摘This paper proposes a parallel cyclic shift structure of address decoder to realize a high-throughput encoding and decoding method for irregular-quasi-cyclic low-density parity-check(IR-QC-LDPC)codes,with a dual-diagonal parity structure.A normalized min-sum algorithm(NMSA)is employed for decoding.The whole verification of the encoding and decoding algorithm is simulated with Matlab,and the code rates of 5/6 and 2/3 are selected respectively for the initial bit error ratio as 6%and 1.04%.Based on the results of simulation,multi-code rates are compatible with different basis matrices.Then the simulated algorithms of encoder and decoder are migrated and implemented on the field programmable gate array(FPGA).The 183.36 Mbps throughput of encoder and the average 27.85 Mbps decoding throughput with the initial bit error ratio 6%are realized based on FPGA.
基金This work was supported in part by National Natural Science Foundation of China(No.61671324)the Director’s Funding from Pilot National Laboratory for Marine Science and Technology(Qingdao)(QNLM201712).
文摘Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.
基金supported by the National Natural Science Foundation of China (60572093)Specialized Research Fund for the Doctoral Program of Higher Education (20050004016)
文摘A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate (BER) performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.
基金Supported by the National Key Basic Research Program (973) Project (No. 2010CB328300)the 111 Project (No. B08038)
文摘A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.
基金supported by the National Natural Science Foundation of China (60572093)Specialized Research Fund for the Doctoral Program of Higher Education (20050004016)
文摘The existing constructions of quasi-cyclic low-density parity-check (QC-LDPC) codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate (BER) performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.
基金the National Natural Science Foundation of China (60496313)
文摘An adaptive modulation (AM) algorithm is proposed and the application of the adapting algorithm together with low-density parity-check (LDPC) codes in multicarrier systems is investigated. The AM algorithm is based on minimizing the average bit error rate (BER) of systems, the combination of AM algorithm and LDPC codes with different code rates (half and three-fourths) are studied. The proposed AM algorithm with that of Fischer et al is compared. Simulation results show that the performance of the proposed AM algorithm is better than that of the Fischer's algorithm. The results also show that application of the proposed AM algorithm together with LDPC codes can greatly improve the performance of multicarrier systems. Results also show that the performance of the proposed algorithm is degraded with an increase in code rate when code length is the same.
基金Supported by the Open Research Fund of National Moblie Communications Research Laboratory of Southeast Uni-versity (No. W200704)
文摘In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.
文摘A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern's order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61801522,61972418,and 61872390)the Natural Science Foundation of Hunan Province,China(Grant Nos.2019JJ40352 and 2017JJ3415)the Special Foundation for Distinguished Young Scientists of Changsha City,China(Grant No.kq1905058)。
文摘Reconciliation is a necessary step in postprocessing of continuous-variable quantum key distribution(CV-QKD)system.We use globally coupled low-density parity-check(GC-LDPC)codes in reconciliation to extract a precise secret key from the raw keys over the authenticated classical public channel between two users.GC-LDPC codes have excellent performance over both the additive Gaussian white noise and binary-erasure channels.The reconciliation based on GC-LDPC codes can improve the reconciliation efficiency to 95.42% and reduce the frame error rate to 3.25×10^-3.Using distillation,the decoding speed can achieve 23.8 Mbits/s and decrease the cost of memory.Given decoding speed and low memory usage,this makes the proposed reconciliation method viable approach for high-speed CV-QKD system.