Labeling and decoding schemes for backward-compatible hierarchical coded modulation

Labeling and decoding schemes are compared for a backward-compatible hierarchical coded modulation system. This system, which is typical of recent proposals, uses two convolutional encoders (and two Viterbi decoders) with a hierarchical 16-QAM constellation, and is compatible with an existing QPSK based coded system. We derive upper bounds for four different schemes (two decoding schemes, multi-stage decoding and independent decoding, and two labeling schemes, Gray labeling and non-Gray labeling) in the AWGN channel. We show that the performance of the simple Gray labeling with independent decoding scheme is nearly optimum in the AWGN channel. Simulation results are given for comparison with the bounds