This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant...This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.展开更多
In conventional string theory with fixed space-time dimension number, the extra space dimensions are compactized. In string theory with oscillating space-time dimension number, dimension number oscillates between 11D ...In conventional string theory with fixed space-time dimension number, the extra space dimensions are compactized. In string theory with oscillating space-time dimension number, dimension number oscillates between 11D and 10D and between 10D and 4D reversibly, and there is no compactization. Dimension number decreases with decreasing speed of light and increasing rest mass. The 4D particle has the lowest speed of light and the highest rest mass. The two different oscillations between 10D and 4D are the stepwise oscillation passing through every dimension number and the direct oscillation oscillating directly between 10D and 4D without the intermediate dimension numbers. Dark energy represents the stepwise oscillation, and dark energy becomes observable only when it has 4D space-time. 4D baryonic matter and 4D dark matter represent the direct oscillation directly from 10D to 4D. Our universe is the dual cyclic universe of the dark energy universe and the baryonic-dark matter universe. The Big Bang in the baryonicdark matter universe produced irreversible kinetic energy that stopped the reversible direct oscillation. The reversible direct oscillation will resume after the Big Crush to remove irreversible kinetic energy. Our cyclic universe started from the zero-energy universe through the four-stage transformation. The theoretical calculated percentages of dark energy, dark matter, and baryonic matter are 68.3, 26.4, and 5.3, respectively, in agreement with observed 68.3, 26.8, and 4.9, respectively. According to the calculation, dark energy started in 4.28 billion years ago in agreement with the observed 4.71 ± 0.98 billion years ago.展开更多
基金supported by the National Natural Science Foundation of China under Grants No.61172085,No.61103221,No.61133014,No.11061130539 and No.61021004
文摘This paper is concerned with (3,n) and (4,n) regular quasi-cyclic Low Density Parity Check (LDPC) code constructions from elementary number theory.Given the column weight,we determine the shift values of the circulant permutation matrices via arithmetic analysis.The proposed constructions of quasi-cyclic LDPC codes achieve the following main advantages simultaneously:1) our methods are constructive in the sense that we avoid any searching process;2) our methods ensure no four or six cycles in the bipartite graphs corresponding to the LDPC codes;3) our methods are direct constructions of quasi-cyclic LDPC codes which do not use any other quasi-cyclic LDPC codes of small length like component codes or any other algorithms/cyclic codes like building block;4)the computations of the parameters involved are based on elementary number theory,thus very simple and fast.Simulation results show that the constructed regular codes of high rates perform almost 1.25 dB above Shannon limit and have no error floor down to the bit-error rate of 10-6.
基金supported by National Natural Science Foundation of China,China(No.52101138)Natural Science Foundation of Hubei Province,China(No.2020CFB259)+7 种基金Shenzhen Science and Technology Program,China(No.JCYJ20220530160813032)State Key Lab of Advanced Metals and Materials,China(No.2020-Z01)State Key Laboratory for Mechanical Behavior of Materials,China(No.20202205)Guangdong Basic and Applied Basic Research Foundation,China(Nos.2020A1515110531,2021A1515111122)State Key Laboratory of Materials Processing and Die&Mold Technology,Huazhong University of Science and Technology,China(No.P2021-021)support from the National Natural Science Foundation of China(No.12004294)National Youth Talents Programsupport by Center for Alloy Innovation and Design(CAID)and HPC platform of Xi’an Jiaotong University。
文摘In conventional string theory with fixed space-time dimension number, the extra space dimensions are compactized. In string theory with oscillating space-time dimension number, dimension number oscillates between 11D and 10D and between 10D and 4D reversibly, and there is no compactization. Dimension number decreases with decreasing speed of light and increasing rest mass. The 4D particle has the lowest speed of light and the highest rest mass. The two different oscillations between 10D and 4D are the stepwise oscillation passing through every dimension number and the direct oscillation oscillating directly between 10D and 4D without the intermediate dimension numbers. Dark energy represents the stepwise oscillation, and dark energy becomes observable only when it has 4D space-time. 4D baryonic matter and 4D dark matter represent the direct oscillation directly from 10D to 4D. Our universe is the dual cyclic universe of the dark energy universe and the baryonic-dark matter universe. The Big Bang in the baryonicdark matter universe produced irreversible kinetic energy that stopped the reversible direct oscillation. The reversible direct oscillation will resume after the Big Crush to remove irreversible kinetic energy. Our cyclic universe started from the zero-energy universe through the four-stage transformation. The theoretical calculated percentages of dark energy, dark matter, and baryonic matter are 68.3, 26.4, and 5.3, respectively, in agreement with observed 68.3, 26.8, and 4.9, respectively. According to the calculation, dark energy started in 4.28 billion years ago in agreement with the observed 4.71 ± 0.98 billion years ago.
