Signal constellations for bit-interleaved coded modulation

Bit-interleaved coded modulation (BICM) is a bandwidth-efficient coding technique consisting of serial concatenation of binary error-correcting coding, bit-by-bit interleaving, and high-order modulation. BICM is capable of achieving excellent error performance provided that powerful codes, such as for example turbo codes or low-density parity-check (LDPC) codes, are employed. In this correspondence, we address the problem of finding the signal sets that are the most suitable ones for designing power-efficient BICM schemes over an additive white Gaussian noise (AWGN) channel. To this end, we exploit the expression of the BICM capacity limit, and evaluate it for several 8- and 16-ary constellations. The bit-error rate (BER) performance of some BICM schemes made up of turbo codes and various signal sets is also investigated by computer simulations so as to illustrate the theoretical results. We show that, for spectral efficiencies of practical interest, the most attractive signal sets are those for which Gray mapping is possible, provided that their symbol error rate performance is "sufficiently close" to the optimum. This explains why some constellations having a simple structure, such as 8-PSK and 16-QAM, perform very well when combined with a powerful code. At the same time, the constellations displaying optimal error performance without coding are, generally, not of interest for BICM.