A Novel Multi-Dimensional Mapping of 8-PSK for BICM-ID

Employing multi-dimensional constellation and mapping to improve the error performance of bit-interleaved coded modulation with iterative decoding (BICM-ID) has recently received a lot of attention, both in single-antenna and multiple-antenna systems. To date, except for the cases of BPSK and QPSK constellations, good multi-dimensional mappings have only been found by computer searching techniques. This paper introduces an explicit algorithm to construct a good multi-dimensional mapping of 8-PSK for improving the asymptotic performance of BICM-ID systems. By comparing the performance of the proposed mapping with an unachievable lower bound, it is conjectured that the proposed mapping is the globally optimal mapping. The superiority of the proposed mapping over the best conventional (two-dimensional) mapping and the multi-dimensional mapping found previously by computer search is also demonstrated.