  Multi-dimensional (MD) mapping offers more flexibility in mapping design for
bit-interleaved coded modulation with iterative decoding (BICM-ID) and
potentially improves the bandwidth efficiency. However, for higher order signal
constellations, finding suitable MD mappings is a very complicated task due to
the large number of possible mappings. In this paper, a novel mapping method is
introduced to construct efficient MD mappings to improve the error performance
of BICM-ID over Rayleigh fading
  channels. We propose to break the MD mapping design problem into four
distinct $2$-D mapping functions. The $2$-D mappings are designed such that the
resulting MD mapping improves the BICM-ID error performance at low signal to
noise ratios (SNRs). We also develop cost functions that can be optimized to
improve the error performance at high SNRs. The proposed mapping method is very
simple compared to well-known mapping methods, and it can achieve suitable MD
mappings for different modulations including higher order modulations for
BICM-ID. Simulation results show that our mappings significantly outperform the
previously known mappings at a target bit error rate (BER) of $10^{-6}$. Our
mappings also offer a lower error-floor compared to their well-known
counterparts.
