A superposition bit-interleaved coded modulation (BICM) with successive cancellation decoding for Gaussian broadcast channel is considered. An upper bound for the bit error rate based on converting the multilevel channel of the BICM into a number of parallel equivalent binary-input channels is derived. This bound is applied to illustrate the performance of the high-rate superposition BICM employing product accumulate codes. For a two-user transmission at overall rate of 6 bits per channel use, the proposed transmission scheme performs within 2.8 dB of constrained capacity.