A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check （QC-LDPC） codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filt...A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check （QC-LDPC） codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate （BER） performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.展开更多
The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead ...The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate （BER） performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.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 (60572093)Specialized Research Fund for the Doctoral Program of Higher Education (20050004016)
文摘A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check （QC-LDPC） codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate （BER） performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.
基金supported by the National Natural Science Foundation of China (60572093)Specialized Research Fund for the Doctoral Program of Higher Education (20050004016)
文摘The existing constructions of quasi-cyclic low-density parity-check （QC-LDPC） codes do not consider the problems of small stopping sets and small girth together in the Tanner graph, while their existences will lead to the bit error rate （BER） performance of QC-LDPC codes being much poorer than that of randomly constructed LDPC codes even decoding failure. To solve the problem, some theorems of the specific chosen parity-check matrix of QC-LDPC codes without small stopping sets and small girth are proposed. A novel construction for QC-LDPC codes with long block lengths is presented by multiplying mmin or the multiple of mmin, which is the minimum order of the identity matrix for the chosen parity-check matrix. The simulation results show that the specific chosen parity-check matrix of QC-LDPC codes can effectively avoid specified stopping sets and small girth and exhibit excellent BER performance than random LDPC codes with the same longer codes length.
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.
