Multi-dimensional mapping for bit-interleaved coded modulation

In recent years, it has been recognized that the error-rate performance of bit-interleaved coded modulation (BICM) can be improved by exchanging soft-information between the demapper and decoder. This so-called 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 a multi-dimensional mapping strategy for BICM-ID. The basic idea is to map a group of bits to a vector of symbols, rather than to a single symbol. This allows for more flexibility and potential performance improvements. Our analysis shows that multi-dimensional mapping leads to an increase in Euclidean distance, thus boosting the performance compared to conventional mapping schemes. We derive a design criterion yielding optimal mappings in an asymptotic sense, and we provide such optimal mappings for BPSK and QPSK constellations. To illustrate the flexibility of the multi-dimensional mapping concept, we also examine some random mappings. These mappings illustrate the trade-off between asymptotic error-rate performance and convergence threshold.