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
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 adopt...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.展开更多
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 co...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.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 densit...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.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 progressive edge-growth(PEG)al-gorithm is a general method to construct short low-density parity-check(LDPC)codes and it is a greedy method to place each edge with large girths.In order to improve the performance ...The progressive edge-growth(PEG)al-gorithm is a general method to construct short low-density parity-check(LDPC)codes and it is a greedy method to place each edge with large girths.In order to improve the performance of LDPC codes,many im-proved PEG(IPEG)algorithms employ multi metrics to select surviving edges in turn.In this paper,the pro-posed edges metric(EM)based on message-passing algorithm(MPA)is introduced to PEG algorithm and the proposed EM constrained PEG(EM-PEG)algo-rithm mainly considers the independence of message passing from different nodes in Tanner graph.The numerical results show that our EM-PEG algorithm brings better bit error rate(BER)performance gains to LDPC codes than the traditional PEG algorithm and the powerful multi-edge multi-metric constrained PEG algorithm(MM-PEGA)proposed recently.In ad-dition,the multi-edge EM constrained PEG(M-EM-PEG)algorithm which adopts multi-edge EM may fur-ther improve the BER performance.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
A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorit...A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.展开更多
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...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.展开更多
Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first...Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.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
This paper presents a simple yet effective decoding for general quasi-cyclic low-density parity-check （QC-LDPC） codes, which not only achieves high hardware utility efficiency （HUE）, but also brings about great me...This paper presents a simple yet effective decoding for general quasi-cyclic low-density parity-check （QC-LDPC） codes, which not only achieves high hardware utility efficiency （HUE）, but also brings about great memory block reduction without any performance degradation. The main idea is to split the check matrix into several row blocks, then to perform the improved mes- sage passing computations sequentially block by block. As the decoding algorithm improves, the sequential tie between the two-phase computations is broken, so that the two-phase computations can be overlapped which bring in high HUE. Two over- lapping schemes are also presented, each of which suits a different situation. In addition, an efficient memory arrangement scheme is proposed to reduce the great memory block requirement of the LDPC decoder. As an example, for the 0.4 rate LDPC code selected from Chinese Digital TV Terrestrial Broadcasting （DTTB）, our decoding saves over 80% memory blocks com- pared with the conventional decoding, and the decoder achieves 0.97 HUE. Finally, the 0.4 rate LDPC decoder is implemented on an FPGA device EP2S30 （speed grade -5）. Using 8 row processing units, the decoder can achieve a maximum net throughput of 28.5 Mbps at 20 iterations.展开更多
If the degree distribution is chosen carefully, the irregular low-density parity-check (LDPC) codes can outperform the regular ones. An image transmission system is proposed by combining regular and irregular LDPC cod...If the degree distribution is chosen carefully, the irregular low-density parity-check (LDPC) codes can outperform the regular ones. An image transmission system is proposed by combining regular and irregular LDPC codes with 16QAM/64QAM modulation to improve both efficiency and reliability. Simulaton results show that LDPC codes are good coding schemes over fading channel in image communication with lower system complexity. More over, irregular codes can obtain a code gain of about 0.7 dB compared with regular ones when BER is 10 -4. So the irregular LDPC codes are more suitable for image transmission than the regular codes.展开更多
An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matri...An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an(n,2,n−1)code.The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory.The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding.In particular,the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.展开更多
In order to solve high encoding complexities of irregular low-density parity-check （LDPC） codes, a deterministic construction of irregular LDPC codes with low encoding complexities is proposed. The encoding algorith...In order to solve high encoding complexities of irregular low-density parity-check （LDPC） codes, a deterministic construction of irregular LDPC codes with low encoding complexities is proposed. The encoding algorithms are designed, whose complexities are linear equations of code length. The construction and encoding algorithms are derived from the effectively encoding characteristics of repeat-accumulate （RA） codes and masking technique. First, the new construction modifies parity-check matrices of RA codes to eliminate error floors of RA codes. Second, the new constructed parity-check matrices are based on Vandermonde matrices; this deterministic algebraic structure is easy for hardware implementation. Theoretic analysis and experimental results show that, at a bit-error rate of 10 × 10^-4, the new codes with lower encoding complexities outperform Mackay＇s random LDPC codes by 0.4-0.6 dB over an additive white Gauss noise （AWGN） channel.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
A class of Quasi-Systematic Block-Circulant Low-Density Parity-Check(QSBC-LDPC) codes is proposed.Block-circulant LDPC codes have been studied a lot recently,because the simple structures of their parity-check matrice...A class of Quasi-Systematic Block-Circulant Low-Density Parity-Check(QSBC-LDPC) codes is proposed.Block-circulant LDPC codes have been studied a lot recently,because the simple structures of their parity-check matrices are very helpful to reduce the implementation complexities.QSBC-LDPC codes are special block-circulant LDPC codes with quasi-systematic parity-check ma-trices.The memories for encoders of QSBC-LDPC codes are limited,and the encoding process can be carried out in a simple recursive way with low complexities.Researches show that the QSBC-LDPC codes can provide remarkable performances with low encoding complexities.展开更多
This letter proposes a novel and simple construction of regular Low-Density Parity-Check (LDPC) codes using sparse binary sequences. It utilizes the cyclic cross correlation function of sparse sequences to generate co...This letter proposes a novel and simple construction of regular Low-Density Parity-Check (LDPC) codes using sparse binary sequences. It utilizes the cyclic cross correlation function of sparse sequences to generate codes with girth8. The new codes perform well using the sumproduct decoding. Low encodingcomplexity can also be achieved due to the inherent quasi-cyclic structure of the codes.展开更多
For one class of Low-Density Parity-Check(LDPC)codes with low row weight in theirparity check matrix,a new Syndrome Decoding(SD)based on the heuristic Beam Search(BS),labeledas SD-BS,is put forward to improve the erro...For one class of Low-Density Parity-Check(LDPC)codes with low row weight in theirparity check matrix,a new Syndrome Decoding(SD)based on the heuristic Beam Search(BS),labeledas SD-BS,is put forward to improve the error performance.First,two observations are made andverified by simulation results.One is that in the SNR region of interest,the hard-decision on thecorrupted sequence yields only a handful of erroneous bits.The other is that the true error pattern forthe nonzero syndrome has a high probability to survive the competition in the BS,provided sufficientbeam width.Bearing these two points in mind,the decoding of LDPC codes is transformed into seekingan error pattern with the known decoding syndrome.Secondly,the effectiveness of SD-BS dependsclosely on how to evaluate the bit reliability.Enlightened by a bit-flipping definition in the existingliterature,a new metric is employed in the proposed SD-BS.The strength of SD-BS is demonstrated viaapplying it on the corrupted sequences directly and the decoding failures of the Belief Propagation(BP),respectively.展开更多
By exploiting the structural features of L1C messages,a novel Early Termination( ET) strategy is proposed to speed up the decoding of low-density parity-check( LDPC) codes in the GPS system. The proposed strategy is b...By exploiting the structural features of L1C messages,a novel Early Termination( ET) strategy is proposed to speed up the decoding of low-density parity-check( LDPC) codes in the GPS system. The proposed strategy is based on the cyclic redundancy check( CRC) of the messages in the subframes 2 and 3. The simulation results show that average number of iterations of the proposed strategy is less than that of the standard ET strategy,with nearly no degradation in decoding performance. Besides,the proposed ET strategy can be efficiently implemented in a sequential or parallel manner. Thus,the proposed ET strategy is attractive for practical purposes.展开更多
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 Key Project of National Nature Science Foundation of China(No.60390540)
文摘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.
基金the National Natural Science Foundation of China(No.60272009,No.60472045,and No.60496313).
文摘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.
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 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.
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.
文摘The progressive edge-growth(PEG)al-gorithm is a general method to construct short low-density parity-check(LDPC)codes and it is a greedy method to place each edge with large girths.In order to improve the performance of LDPC codes,many im-proved PEG(IPEG)algorithms employ multi metrics to select surviving edges in turn.In this paper,the pro-posed edges metric(EM)based on message-passing algorithm(MPA)is introduced to PEG algorithm and the proposed EM constrained PEG(EM-PEG)algo-rithm mainly considers the independence of message passing from different nodes in Tanner graph.The numerical results show that our EM-PEG algorithm brings better bit error rate(BER)performance gains to LDPC codes than the traditional PEG algorithm and the powerful multi-edge multi-metric constrained PEG algorithm(MM-PEGA)proposed recently.In ad-dition,the multi-edge EM constrained PEG(M-EM-PEG)algorithm which adopts multi-edge EM may fur-ther improve the BER performance.
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Supported by the National High Technology Research and Development Programme of China(No.2009AAJ128,2009AAJ208,2010AA7010422)
文摘A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.
基金Supported by the National Natural Science Foundation of China (No. 60772061)Science Foundation of Nanjing University of Posts and Telecommunications (No. NY207132)
文摘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.
基金The National Key Technology R&D Program of China during the 12th Five-Year Plan Period(No.2012BAH15B00)
文摘Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.
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Science and Technology on Avionics Integration Laboratory and Aeronautical Science Foundation of China (20115551022)
文摘This paper presents a simple yet effective decoding for general quasi-cyclic low-density parity-check （QC-LDPC） codes, which not only achieves high hardware utility efficiency （HUE）, but also brings about great memory block reduction without any performance degradation. The main idea is to split the check matrix into several row blocks, then to perform the improved mes- sage passing computations sequentially block by block. As the decoding algorithm improves, the sequential tie between the two-phase computations is broken, so that the two-phase computations can be overlapped which bring in high HUE. Two over- lapping schemes are also presented, each of which suits a different situation. In addition, an efficient memory arrangement scheme is proposed to reduce the great memory block requirement of the LDPC decoder. As an example, for the 0.4 rate LDPC code selected from Chinese Digital TV Terrestrial Broadcasting （DTTB）, our decoding saves over 80% memory blocks com- pared with the conventional decoding, and the decoder achieves 0.97 HUE. Finally, the 0.4 rate LDPC decoder is implemented on an FPGA device EP2S30 （speed grade -5）. Using 8 row processing units, the decoder can achieve a maximum net throughput of 28.5 Mbps at 20 iterations.
文摘If the degree distribution is chosen carefully, the irregular low-density parity-check (LDPC) codes can outperform the regular ones. An image transmission system is proposed by combining regular and irregular LDPC codes with 16QAM/64QAM modulation to improve both efficiency and reliability. Simulaton results show that LDPC codes are good coding schemes over fading channel in image communication with lower system complexity. More over, irregular codes can obtain a code gain of about 0.7 dB compared with regular ones when BER is 10 -4. So the irregular LDPC codes are more suitable for image transmission than the regular codes.
基金the National Natural Science Foundation of China(No.61401164)。
文摘An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an(n,2,n−1)code.The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory.The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding.In particular,the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.
基金Supported by the National Natural Science Foundation of China(60496315, 60572050)
文摘In order to solve high encoding complexities of irregular low-density parity-check （LDPC） codes, a deterministic construction of irregular LDPC codes with low encoding complexities is proposed. The encoding algorithms are designed, whose complexities are linear equations of code length. The construction and encoding algorithms are derived from the effectively encoding characteristics of repeat-accumulate （RA） codes and masking technique. First, the new construction modifies parity-check matrices of RA codes to eliminate error floors of RA codes. Second, the new constructed parity-check matrices are based on Vandermonde matrices; this deterministic algebraic structure is easy for hardware implementation. Theoretic analysis and experimental results show that, at a bit-error rate of 10 × 10^-4, the new codes with lower encoding complexities outperform Mackay＇s random LDPC codes by 0.4-0.6 dB over an additive white Gauss noise （AWGN） channel.
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A class of Quasi-Systematic Block-Circulant Low-Density Parity-Check(QSBC-LDPC) codes is proposed.Block-circulant LDPC codes have been studied a lot recently,because the simple structures of their parity-check matrices are very helpful to reduce the implementation complexities.QSBC-LDPC codes are special block-circulant LDPC codes with quasi-systematic parity-check ma-trices.The memories for encoders of QSBC-LDPC codes are limited,and the encoding process can be carried out in a simple recursive way with low complexities.Researches show that the QSBC-LDPC codes can provide remarkable performances with low encoding complexities.
基金Supported by Key Project of the National Natural Science Foundation of China (No.60496311).
文摘This letter proposes a novel and simple construction of regular Low-Density Parity-Check (LDPC) codes using sparse binary sequences. It utilizes the cyclic cross correlation function of sparse sequences to generate codes with girth8. The new codes perform well using the sumproduct decoding. Low encodingcomplexity can also be achieved due to the inherent quasi-cyclic structure of the codes.
基金the National Science Foundation of China(No.60472104).
文摘For one class of Low-Density Parity-Check(LDPC)codes with low row weight in theirparity check matrix,a new Syndrome Decoding(SD)based on the heuristic Beam Search(BS),labeledas SD-BS,is put forward to improve the error performance.First,two observations are made andverified by simulation results.One is that in the SNR region of interest,the hard-decision on thecorrupted sequence yields only a handful of erroneous bits.The other is that the true error pattern forthe nonzero syndrome has a high probability to survive the competition in the BS,provided sufficientbeam width.Bearing these two points in mind,the decoding of LDPC codes is transformed into seekingan error pattern with the known decoding syndrome.Secondly,the effectiveness of SD-BS dependsclosely on how to evaluate the bit reliability.Enlightened by a bit-flipping definition in the existingliterature,a new metric is employed in the proposed SD-BS.The strength of SD-BS is demonstrated viaapplying it on the corrupted sequences directly and the decoding failures of the Belief Propagation(BP),respectively.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61271423)
文摘By exploiting the structural features of L1C messages,a novel Early Termination( ET) strategy is proposed to speed up the decoding of low-density parity-check( LDPC) codes in the GPS system. The proposed strategy is based on the cyclic redundancy check( CRC) of the messages in the subframes 2 and 3. The simulation results show that average number of iterations of the proposed strategy is less than that of the standard ET strategy,with nearly no degradation in decoding performance. Besides,the proposed ET strategy can be efficiently implemented in a sequential or parallel manner. Thus,the proposed ET strategy is attractive for practical purposes.
