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
In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all ...In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.展开更多
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
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 in part by National Basic Research Program of China under Grant No.2012CB316100National Natural Science Foundation of China under Grants 61372074 and 91438101+1 种基金Joint Funds of the National Natural Science Foundation of China under Grant No.U1504601Science and Technology on Communication Networks Laboratory under Grant KX132600032
文摘In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.
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.
