Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list...Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.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
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
The 16-ary quadrature amplitude modulation （16QAM） is a high spectral efficient scheme for high-speed transmission systems. To remove the phase ambiguity in the coherent detection system, differential-encoded 16QAM ...The 16-ary quadrature amplitude modulation （16QAM） is a high spectral efficient scheme for high-speed transmission systems. To remove the phase ambiguity in the coherent detection system, differential-encoded 16QAM （DE-16QAM） is usually used, however, it will cause performance degradation about 3 dB as compared to the conventional 16QAM. To overcome the performance loss, a serial concatenated system with outer low density parity check （LDPC） codes and inner DE-16QAM is proposed. At the receiver, joint iterative differential demodulation and decoding （ID） is carried out to approach the maximum likelihood performance. Moreover, a genetic evolution algorithm based on the extrinsic information transfer chart is proposed to optimize the degree distribution of the outer LDPC codes. Both theoretical analyses and simulation results indicate that this algorithm not only compensates the performance loss, but also obtains a significant performance gain, which is up to 1 dB as compared to the conventional non-DE-16QAM.展开更多
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 Key R&D Program of China(2018YFB2101300)the National Science Foundation of China(61973056)
文摘Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.
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 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.
基金supported by the National Natural Science Foundation of China(61171101)the State Major Science and Technology Special Projects(2009ZX03003-011-03)
文摘The 16-ary quadrature amplitude modulation （16QAM） is a high spectral efficient scheme for high-speed transmission systems. To remove the phase ambiguity in the coherent detection system, differential-encoded 16QAM （DE-16QAM） is usually used, however, it will cause performance degradation about 3 dB as compared to the conventional 16QAM. To overcome the performance loss, a serial concatenated system with outer low density parity check （LDPC） codes and inner DE-16QAM is proposed. At the receiver, joint iterative differential demodulation and decoding （ID） is carried out to approach the maximum likelihood performance. Moreover, a genetic evolution algorithm based on the extrinsic information transfer chart is proposed to optimize the degree distribution of the outer LDPC codes. Both theoretical analyses and simulation results indicate that this algorithm not only compensates the performance loss, but also obtains a significant performance gain, which is up to 1 dB as compared to the conventional non-DE-16QAM.
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.
