A new method of constructing regular low-density parity-check (LDPC) codes was proposed. And the novel class of LDPC codes was applied in a coded orthogonal frequency division multiplexing (OFDM) system. This method e...A new method of constructing regular low-density parity-check (LDPC) codes was proposed. And the novel class of LDPC codes was applied in a coded orthogonal frequency division multiplexing (OFDM) system. This method extended the class of LDPC codes which could be constructed from shifted identity matrices. The method could avoid short cycles in Tanner graphs with simple inequation in the construction of shifting identity matrices, which made the girth of Tanner graphs 8. Because of the quasicyclic structure and the inherent block configuration of parity-check matrices, the encoders and the decoders were practically feasible. They were linear-time encodable and decodable. The LDPC codes proposed had various code rates, ranging from low to high. They performed excellently with iterative decoding and demonstrate better performance than other regular LDPC codes in OFDM systems.展开更多
In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDP...In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.展开更多
This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC...This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.展开更多
In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction ...In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-Ⅱ QC-LDPC codes based on perfect cyclic difference sets(CDSs) are constructed. The parity check matrices of these type-Ⅱ QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices(CPMs) with weight of 1 and the circulant matrices with weight of 2(W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error-correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-Ⅱ QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise(AWGN) channel with sum-product algorithm(SPA) iterative decoding.展开更多
文摘A new method of constructing regular low-density parity-check (LDPC) codes was proposed. And the novel class of LDPC codes was applied in a coded orthogonal frequency division multiplexing (OFDM) system. This method extended the class of LDPC codes which could be constructed from shifted identity matrices. The method could avoid short cycles in Tanner graphs with simple inequation in the construction of shifting identity matrices, which made the girth of Tanner graphs 8. Because of the quasicyclic structure and the inherent block configuration of parity-check matrices, the encoders and the decoders were practically feasible. They were linear-time encodable and decodable. The LDPC codes proposed had various code rates, ranging from low to high. They performed excellently with iterative decoding and demonstrate better performance than other regular LDPC codes in OFDM systems.
基金supported in part by National Natural Science Foundation of China under Grants 61372074,91438101,61103143,U1504601,and U1404622Key Scientific and Technological Project of Henan under Grants 162102310589 and 172102310124
文摘In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.
基金Supported by the National Natural Science Foundation of China(No.60472053)
文摘This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.
基金supported by the National Natural Science Foundation of China(No.61472464)the Research Foundation of Education Bureau of Hunan Province in China(No.16C0686)the Key Discipline Construction Project Funding for Hunan University of Science and Engineering(Electrical systems)
文摘In view of the problems that the encoding complexity of quasi-cyclic low-density parity-check(QC-LDPC) codes is high and the minimum distance is not large enough which leads to the degradation of the error-correction performance, the new irregular type-Ⅱ QC-LDPC codes based on perfect cyclic difference sets(CDSs) are constructed. The parity check matrices of these type-Ⅱ QC-LDPC codes consist of the zero matrices with weight of 0, the circulant permutation matrices(CPMs) with weight of 1 and the circulant matrices with weight of 2(W2CMs). The introduction of W2CMs in parity check matrices makes it possible to achieve the larger minimum distance which can improve the error-correction performance of the codes. The Tanner graphs of these codes have no girth-4, thus they have the excellent decoding convergence characteristics. In addition, because the parity check matrices have the quasi-dual diagonal structure, the fast encoding algorithm can reduce the encoding complexity effectively. Simulation results show that the new type-Ⅱ QC-LDPC codes can achieve a more excellent error-correction performance and have no error floor phenomenon over the additive white Gaussian noise(AWGN) channel with sum-product algorithm(SPA) iterative decoding.
