In the bit-interleaved coded modulation with iterative decoding,it is desired that any two Hamming neighbors,i.e..signal constellation points whose binary labels are at unit Hamming distance,be separated by a large Eu...In the bit-interleaved coded modulation with iterative decoding,it is desired that any two Hamming neighbors,i.e..signal constellation points whose binary labels are at unit Hamming distance,be separated by a large Euclidean distance.This paper determines the mappings for the 32-ary fourdimensional generalized cross constellation（32-4D-GCC） so that the minimum squared Euclidean distance d_（min）~2 between Hamming neighbors is maximized.Among such mappings,those with minimum multiplicity N（d_（min）~2） are selected.To reduce the large search space,a set of ＂mapping templates,＂ each producing a collection of mappings with the same set partitions of binary labels,is introduced.Via enumeration of mapping templates,it is shown that the optimum d_（min）~2=16and the optimum N（d_（min）~2）=16.Among thousands optimum mappings found by computer search,two of the best performance are presented.展开更多
We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two...We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni （2014） in an earlier paper.展开更多
基金supported by the National Key Basic Research Program of China(973 program) under grant No.2010CB328206NSFC under grants No.60837002+3 种基金60807003and 61102048the Fundamental Research Funds for the Central Universities under grant No.2011JBM208NSF under grant CCF-0952711
文摘In the bit-interleaved coded modulation with iterative decoding,it is desired that any two Hamming neighbors,i.e..signal constellation points whose binary labels are at unit Hamming distance,be separated by a large Euclidean distance.This paper determines the mappings for the 32-ary fourdimensional generalized cross constellation（32-4D-GCC） so that the minimum squared Euclidean distance d_（min）~2 between Hamming neighbors is maximized.Among such mappings,those with minimum multiplicity N（d_（min）~2） are selected.To reduce the large search space,a set of ＂mapping templates,＂ each producing a collection of mappings with the same set partitions of binary labels,is introduced.Via enumeration of mapping templates,it is shown that the optimum d_（min）~2=16and the optimum N（d_（min）~2）=16.Among thousands optimum mappings found by computer search,two of the best performance are presented.
基金supported by National Science Foundation of USA(Grant No.DMS1252992)an Alfred P.Sloan Research Fellowship
文摘We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni （2014） in an earlier paper.
