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
In this article, we consider the faster than Nyquist(FTN) technology in aspects of the application of the Viterbi algorithm(VA). Finite in time optimal FTN signals are used to provide a symbol rate higher than the &qu...In this article, we consider the faster than Nyquist(FTN) technology in aspects of the application of the Viterbi algorithm(VA). Finite in time optimal FTN signals are used to provide a symbol rate higher than the "Nyquist barrier" without any encoding. These signals are obtained as the solutions of the corresponding optimization problem. Optimal signals are characterized by intersymbol interference(ISI). This fact leads to significant bit error rate(BER) performance degradation for "classical" forms of signals. However, ISI can be controlled by the restriction of the optimization problem. So we can use optimal signals in conditions of increased duration and an increased symbol rate without significant energy losses. The additional symbol rate increase leads to the increase of the reception algorithm complexity. We consider the application of VA for optimal FTN signals reception. The application of VA for receiving optimal FTN signals with increased duration provides close to the potential performance of BER,while the symbol rate is twice above the Nyquist limit.展开更多
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 Grant of the President of the Russian Federation for state support of young Russian scientists(agreementМК-1571.2019.8 No.075-15-2019-1155)。
文摘In this article, we consider the faster than Nyquist(FTN) technology in aspects of the application of the Viterbi algorithm(VA). Finite in time optimal FTN signals are used to provide a symbol rate higher than the "Nyquist barrier" without any encoding. These signals are obtained as the solutions of the corresponding optimization problem. Optimal signals are characterized by intersymbol interference(ISI). This fact leads to significant bit error rate(BER) performance degradation for "classical" forms of signals. However, ISI can be controlled by the restriction of the optimization problem. So we can use optimal signals in conditions of increased duration and an increased symbol rate without significant energy losses. The additional symbol rate increase leads to the increase of the reception algorithm complexity. We consider the application of VA for optimal FTN signals reception. The application of VA for receiving optimal FTN signals with increased duration provides close to the potential performance of BER,while the symbol rate is twice above the Nyquist limit.
