Multi-dimensional mapping for bit-interleaved coded modulation with BPSK/QPSK signaling

In recent years, it has been recognized that bit-interleaved coded modulation with iterative decoding (BICM-ID) achieves excellent performance on virtually any channel, provided the signal mapping is carefully designed. In this paper, we introduce multi-dimensional mapping for BICM-ID, where a group of bits is mapped to a vector of symbols, rather than a single symbol. This allows for more flexibility and potential performance improvements. Our analysis shows that multidimensional mapping leads to an increase in Euclidean distance, thus boosting the performance compared to conventional mapping schemes. We derive a design criterion for optimal mappings, and we provide such optimal mappings for BPSK and QPSK constellations.