Mapping Design of a Four-Dimensional 32-ary Signal Constellation over an AWGN Channel

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.