  The capacity of the AWGN broadcast channel is achieved by superposition
coding, but superposition of individual coded modulations expands the
modulation alphabet and distorts its configuration. Coded modulation over a
broadcast channel subject to a specific channel-input modulation constraint
remains an important open problem. Some progress has been made in the related
area of unequal-error protection modulations which can be considered
single-user broadcast transmission, but it does not approach all points on the
boundary of the capacity region. This paper studies broadcast coded modulation
using multilevel coding (MLC) subject to a specific channel input
constellation. The conditions under which multilevel codes can achieve the
constellation-constrained capacity of the AWGN broadcast channel are derived.
For any given constellation, we propose a pragmatic multilevel design technique
with near constellation-constrained-capacity performance where the coupling of
the superposition inner and outer codes are localized to each bit-level. It is
shown that this can be further relaxed to a code coupling on only one bit
level, with little or no penalty under natural labeling. The rate allocation
problem between the bit levels of the two users is studied and a pragmatic
method is proposed, again with near-capacity performance. In further pursuit of
lower complexity, a hybrid MLC-BICM is proposed, whose performance is shown to
be very close to the boundary of the constellation-constrained capacity region.
Simulation results show that good point-to-point LDPC codes produce excellent
performance in the proposed coded modulation framework.
