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
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
The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of length...The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.展开更多
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 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Sponsored by the National Natural Science Foundation of China(Grant Nos.61372074 and 91438101)the National High Technology Research and Development Program of China(Grant No.2015AA01A709)
文摘The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.
