Broadcast Coded Modulation: Multilevel and Bit-Interleaved Construction

The capacity of the AWGN broadcast channel is achieved by superposition coding, but the superposition of individual coded modulations expands the modulation alphabet and distorts its configuration. Hierarchical modulations, which appear in the literature mostly in the context of unequal error protection, can approach only a few isolated points on the boundary of the broadcast capacity region. This paper studies multilevel coding (MLC) for constellation-constrained broadcast-coded modulation. The conditions under which multilevel codes can achieve the constellation-constrained capacity of the AWGN broadcast channel are derived. We propose a pragmatic multilevel design technique with near-constellation-constrained-capacity performance where the coupling of the superposition inner and outer codes is localized to each bit-level. It is shown that this can be further relaxed to a code coupling on only one bit-level, with a 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-bit-interleaved-coded modulation 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.