  Bit-interleaved coded modulation (BICM) transceivers often use equally spaced
constellations and a random interleaver. In this paper, we propose a new BICM
design, which considers hierarchical (nonequally spaced) constellations, a
bit-level multiplexer, and multiple interleavers. It is shown that this new
scheme increases the degrees of freedom that can be exploited in order to
improve its performance. Analytical bounds on the bit error rate (BER) of the
system in terms of the constellation parameters and the multiplexing rules are
developed for the additive white Gaussian Noise (AWGN) and Nakagami-$m$ fading
channels. These bounds are then used to design the BICM transceiver. Numerical
results show that, compared to conventional BICM designs, and for a target BER
of $10^{-6}$, gains up to 3 dB in the AWGN channel are obtained. For fading
channels, the gains depend on the fading parameter, and reach 2 dB for a target
BER of $10^{-7}$ and $m=5$.
