This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check(NB-QC-LDPC)codes with short block lengths.In our scheme,the initial template base matrices and...This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check(NB-QC-LDPC)codes with short block lengths.In our scheme,the initial template base matrices and the corresponding non-binary replacement matrices are constructed by the progressive edge growth algorithm and randomly generated,respectively.The genetic algorithm is then utilized to optimize the base matrices and the replacement ones.The simulation results show that the NB-QC-LDPC codes constructed by the proposed method achieve better decoding performance and lower implementation complexity compared to the existing NB-LDPC codes such as consultative committee for space data system and Bei Dou satellite navigation system.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
This paper introduces a novel blind recognition of non-binary low-density parity-check(LDPC)codes without a candidate set,using ant colony optimization(ACO)algorithm over additive white Gaussian noise(AWGN)channels.Sp...This paper introduces a novel blind recognition of non-binary low-density parity-check(LDPC)codes without a candidate set,using ant colony optimization(ACO)algorithm over additive white Gaussian noise(AWGN)channels.Specifically,the scheme that effectively combines the ACO algorithm and the non-binary elements over finite fields is proposed.Furthermore,an improved,simplified elitist ACO algorithm based on soft decision reliability is introduced to recognize the parity-check matrix over noisy channels.Simulation results show that the recognition rate continuously increases with an increased signalto-noise ratio(SNR)over the AWGN channel.展开更多
This paper proposes a family of raptor-like rate-compatible spatially coupled low-density parity-check(RL-RC-SC-LDPC)codes from RL-RC-LDPC block codes.There are two important keys.One is the performance of the base ma...This paper proposes a family of raptor-like rate-compatible spatially coupled low-density parity-check(RL-RC-SC-LDPC)codes from RL-RC-LDPC block codes.There are two important keys.One is the performance of the base matrix.RL-LDPC codes have been adopted in the technical specification of 5G new radio(5G-NR).We use the 5G NR LDPC code as the base matrix.The other is the edge coupling design.In this regard,we have designed a rate-compatible coupling algorithm,which can improve performance under multiple code rates.The constructed RL-RC-SC-LDPC code property requires a large coupling length L and thus we improved the reciprocal channel approximation(RCA)algorithm and proposed a sliding window RCA algorithm.It can provide lower com-plexity and latency than RCA algorithm.The code family shows improved thresholds close to the Shannon limit and finite-length performance compared with 5G NR LDPC codes for the additive white Gaussian noise(AWGN)channel.展开更多
This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID ...This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.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
According to large coverage of satellites, there are various channel states in a satellite broadcasting network. In order to introduce an efficient rateless transmission method to satellite multimedia broadcasting/mul...According to large coverage of satellites, there are various channel states in a satellite broadcasting network. In order to introduce an efficient rateless transmission method to satellite multimedia broadcasting/multicast services with finite-length packets, a cross-layer packet transmission method is proposed with Luby transform （LT） codes for efficiency in the network layer and low density parity check （LDPC） codes for reliability in the physical layer jointly. The codewords generated from an LT encoder are divided into finite-length packets, which are encoded by an LDPC encoder subsequently. Based on noise and fading effects of satellite channels, the LT packets received from an LDPC decoder either have no error or are marked as erased, which can be mod- eled as a binary erasure channels （BECs）. By theoretical analysis on LT parameters and LDPC parameters, the relationships between LDPC code rates in the physical layer and LT codes word lengths in the network layer are investigated. With tradeoffs between the LT codes word lengths and the LDPC code rates, optimized cross-layer solutions are achieved with a binary search algorithm. Verified by simulations, the proposed solution for cross-layer parameters design can provide the best transmission mode according to satellite states, so as to improve throughput performance for satellite multimedia transmission.展开更多
The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder nee...The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder needs to store every ＂1＂ of the generator matrices by using huge chip area. In order to solve this problem, we need to design the protograph LDPC codes with circular generator matrices. A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed. The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix. This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices, and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem. Simulation results in ad- ditive white Gaussian noise （AWGN） channels show that the bit error rate （BER） performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.展开更多
Two Relative-Residual-based Dynamic Schedules(RRDS) for Belief Propagation(BP) decoding of Low-Density Parity-Check(LDPC) codes are proposed,in which the Variable code-RRDS(VN-RRDS) is a greediness-reduced version of ...Two Relative-Residual-based Dynamic Schedules(RRDS) for Belief Propagation(BP) decoding of Low-Density Parity-Check(LDPC) codes are proposed,in which the Variable code-RRDS(VN-RRDS) is a greediness-reduced version of the Check code-RRDS(CN-RRDS).The RRDS only processes the variable(or check) node,which has the maximum relative residual among all the variable(or check) nodes in each decoding iteration,thus keeping less greediness and decreased complexity in comparison with the edge-based Variable-to-Check Residual Belief Propagation(VC-RBP) algorithm.Moreover,VN-RRDS propagates first the message which has the largest residual based on all check equations.For different types of LDPC codes,simulation results show that the convergence rate of RRDS is higher than that of VC-RBP while keeping very low computational complexity.Furthermore,VN-RRDS achieves faster convergence as well as better performance than CN-RRDS.展开更多
In this paper,we propose a doping approach to lower the error floor of Low-Density Parity-Check(LDPC)codes.The doping component is a short block code in which the information bits are selected from the coded bits of t...In this paper,we propose a doping approach to lower the error floor of Low-Density Parity-Check(LDPC)codes.The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code.Accordingly,an algorithm for selecting the information bits of the short code is proposed,and a specific two-stage decoding algorithm is presented.Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 dB gain compared with the original LDPC code at a frame error rate of 10^(-6)Furthermore,the proposed design can lower the error floor of original LDPC Codes.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 proposes a scheme to construct time- frequency codes based on protograph low density parity check （LDPC） codes in orthogonal frequency division multiplexing （OFDM） communication systems. This approach s...This paper proposes a scheme to construct time- frequency codes based on protograph low density parity check （LDPC） codes in orthogonal frequency division multiplexing （OFDM） communication systems. This approach synthesizes two techniques： protograph LDPC codes and OFDM. One symbol of encoded information by protograph LDPC codes corresponds to one sub-carrier, namely the length of encoded information equals to the number of sub-carriers. The design of good protograph LDPC codes with short lengths is given, and the proposed proto- graph LDPC codes can be of fast encoding, which can reduce the encoding complexity and simplify encoder hardware implementa- tion. The proposed approach provides a higher coding gain in the Rayleigh fading channel. The simulation results in the Rayleigh fading channel show that the bit error rate （BER） performance of the proposed time-frequency codes is as good as random LDPC- OFDM codes and is better than Tanner LDPC-OFDM codes under the condition of different fading coefficients.展开更多
A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the enco...A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.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
基金supported by the National Natural Science Foundation of China under Grants 62331002。
文摘This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check(NB-QC-LDPC)codes with short block lengths.In our scheme,the initial template base matrices and the corresponding non-binary replacement matrices are constructed by the progressive edge growth algorithm and randomly generated,respectively.The genetic algorithm is then utilized to optimize the base matrices and the replacement ones.The simulation results show that the NB-QC-LDPC codes constructed by the proposed method achieve better decoding performance and lower implementation complexity compared to the existing NB-LDPC codes such as consultative committee for space data system and Bei Dou satellite navigation system.
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This paper introduces a novel blind recognition of non-binary low-density parity-check(LDPC)codes without a candidate set,using ant colony optimization(ACO)algorithm over additive white Gaussian noise(AWGN)channels.Specifically,the scheme that effectively combines the ACO algorithm and the non-binary elements over finite fields is proposed.Furthermore,an improved,simplified elitist ACO algorithm based on soft decision reliability is introduced to recognize the parity-check matrix over noisy channels.Simulation results show that the recognition rate continuously increases with an increased signalto-noise ratio(SNR)over the AWGN channel.
文摘This paper proposes a family of raptor-like rate-compatible spatially coupled low-density parity-check(RL-RC-SC-LDPC)codes from RL-RC-LDPC block codes.There are two important keys.One is the performance of the base matrix.RL-LDPC codes have been adopted in the technical specification of 5G new radio(5G-NR).We use the 5G NR LDPC code as the base matrix.The other is the edge coupling design.In this regard,we have designed a rate-compatible coupling algorithm,which can improve performance under multiple code rates.The constructed RL-RC-SC-LDPC code property requires a large coupling length L and thus we improved the reciprocal channel approximation(RCA)algorithm and proposed a sliding window RCA algorithm.It can provide lower com-plexity and latency than RCA algorithm.The code family shows improved thresholds close to the Shannon limit and finite-length performance compared with 5G NR LDPC codes for the additive white Gaussian noise(AWGN)channel.
基金supported in part by the NSF of China under Grant 62322106,62071131the Guangdong Basic and Applied Basic Research Foundation under Grant 2022B1515020086+2 种基金the International Collaborative Research Program of Guangdong Science and Technology Department under Grant 2022A0505050070in part by the Open Research Fund of the State Key Laboratory of Integrated Services Networks under Grant ISN22-23the National Research Foundation,Singapore University of Technology Design under its Future Communications Research&Development Programme“Advanced Error Control Coding for 6G URLLC and mMTC”Grant No.FCP-NTU-RG-2022-020.
文摘This paper investigates the bit-interleaved coded generalized spatial modulation(BICGSM) with iterative decoding(BICGSM-ID) for multiple-input multiple-output(MIMO) visible light communications(VLC). In the BICGSM-ID scheme, the information bits conveyed by the signal-domain(SiD) symbols and the spatial-domain(SpD) light emitting diode(LED)-index patterns are coded by a protograph low-density parity-check(P-LDPC) code. Specifically, we propose a signal-domain symbol expanding and re-allocating(SSER) method for constructing a type of novel generalized spatial modulation(GSM) constellations, referred to as SSERGSM constellations, so as to boost the performance of the BICGSM-ID MIMO-VLC systems.Moreover, by applying a modified PEXIT(MPEXIT) algorithm, we further design a family of rate-compatible P-LDPC codes, referred to as enhanced accumulate-repeat-accumulate(EARA) codes,which possess both excellent decoding thresholds and linear-minimum-distance-growth property. Both analysis and simulation results illustrate that the proposed SSERGSM constellations and P-LDPC codes can remarkably improve the convergence and decoding performance of MIMO-VLC systems. Therefore, the proposed P-LDPC-coded SSERGSM-mapped BICGSMID configuration is envisioned as a promising transmission solution to satisfy the high-throughput requirement of MIMO-VLC applications.
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 Natural Science Foundation of China (No.61101125)
文摘According to large coverage of satellites, there are various channel states in a satellite broadcasting network. In order to introduce an efficient rateless transmission method to satellite multimedia broadcasting/multicast services with finite-length packets, a cross-layer packet transmission method is proposed with Luby transform （LT） codes for efficiency in the network layer and low density parity check （LDPC） codes for reliability in the physical layer jointly. The codewords generated from an LT encoder are divided into finite-length packets, which are encoded by an LDPC encoder subsequently. Based on noise and fading effects of satellite channels, the LT packets received from an LDPC decoder either have no error or are marked as erased, which can be mod- eled as a binary erasure channels （BECs）. By theoretical analysis on LT parameters and LDPC parameters, the relationships between LDPC code rates in the physical layer and LT codes word lengths in the network layer are investigated. With tradeoffs between the LT codes word lengths and the LDPC code rates, optimized cross-layer solutions are achieved with a binary search algorithm. Verified by simulations, the proposed solution for cross-layer parameters design can provide the best transmission mode according to satellite states, so as to improve throughput performance for satellite multimedia transmission.
基金supported by Beijing Natural Science Foundation(4102050)the National Natural Science of Foundation of China(NSFC)-Korea Science and Engineering Foundation (KOSF) Joint Research Project of China and Korea (60811140343)
文摘The application of protograph low density parity check （LDPC） codes involves the encoding complexity problem. Since the generator matrices are dense, and if the positions of ＂1＂ s are irregularity, the encoder needs to store every ＂1＂ of the generator matrices by using huge chip area. In order to solve this problem, we need to design the protograph LDPC codes with circular generator matrices. A theorem concerning the circulating property of generator matrices of nonsingular protograph LDPC codes is proposed. The circulating property of generator matrix of nonsingular protograph LDPC codes can be obtained from the corresponding quasi-cyclic parity check matrix. This paper gives a scheme of constructing protograph LDPC codes with circulating generator matrices, and it reveals that the fast encoding algorithm of protograph LDPC codes has lower encoding complexity under the condition of the proposed theorem. Simulation results in ad- ditive white Gaussian noise （AWGN） channels show that the bit error rate （BER） performance of the designed codes based on the proposed theorem is much better than that of GB20600 LDPC codes and Tanner LDPC codes.
基金supported by the Fundamental Research Funds for the Central Universities
文摘Two Relative-Residual-based Dynamic Schedules(RRDS) for Belief Propagation(BP) decoding of Low-Density Parity-Check(LDPC) codes are proposed,in which the Variable code-RRDS(VN-RRDS) is a greediness-reduced version of the Check code-RRDS(CN-RRDS).The RRDS only processes the variable(or check) node,which has the maximum relative residual among all the variable(or check) nodes in each decoding iteration,thus keeping less greediness and decreased complexity in comparison with the edge-based Variable-to-Check Residual Belief Propagation(VC-RBP) algorithm.Moreover,VN-RRDS propagates first the message which has the largest residual based on all check equations.For different types of LDPC codes,simulation results show that the convergence rate of RRDS is higher than that of VC-RBP while keeping very low computational complexity.Furthermore,VN-RRDS achieves faster convergence as well as better performance than CN-RRDS.
基金supported in part by China NSF under Grants No.61771081 and 62072064the Fundamental Research Funds for the Central Universities(China)under Grant cstc2019jcyjmsxmX0110+2 种基金the Project of Chongqing Natural Science Foundation under Grant CSTB2022NSCQ-MSX0990Science and Technology Research Project of Chongqing Education Commission under Grant KJQN202000612the Venture and Innovation Support Program for Chongqing Overseas Returnees under Grant cx2020070.
文摘In this paper,we propose a doping approach to lower the error floor of Low-Density Parity-Check(LDPC)codes.The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code.Accordingly,an algorithm for selecting the information bits of the short code is proposed,and a specific two-stage decoding algorithm is presented.Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 dB gain compared with the original LDPC code at a frame error rate of 10^(-6)Furthermore,the proposed design can lower the error floor of original LDPC Codes.
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 Beijing Natural Science Foundation of China (4102050)the National Natural Science of Foundation of China (NSFC)-Korea Science and Engineering Foundation (KOSF) Joint Research Project of China and Korea (60811140343)
文摘This paper proposes a scheme to construct time- frequency codes based on protograph low density parity check （LDPC） codes in orthogonal frequency division multiplexing （OFDM） communication systems. This approach synthesizes two techniques： protograph LDPC codes and OFDM. One symbol of encoded information by protograph LDPC codes corresponds to one sub-carrier, namely the length of encoded information equals to the number of sub-carriers. The design of good protograph LDPC codes with short lengths is given, and the proposed proto- graph LDPC codes can be of fast encoding, which can reduce the encoding complexity and simplify encoder hardware implementa- tion. The proposed approach provides a higher coding gain in the Rayleigh fading channel. The simulation results in the Rayleigh fading channel show that the bit error rate （BER） performance of the proposed time-frequency codes is as good as random LDPC- OFDM codes and is better than Tanner LDPC-OFDM codes under the condition of different fading coefficients.
文摘A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.
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.
