  In this paper, we represent Raptor codes as multi-edge type low-density
parity-check (MET-LDPC) codes, which gives a general framework to design them
for higher-order modulation using MET density evolution. We then propose an
efficient Raptor code design method for higher-order modulation, where we
design distinct degree distributions for distinct bit levels. We consider a
joint decoding scheme based on belief propagation for Raptor codes and also
derive an exact expression for the stability condition. In several examples, we
demonstrate that the higher-order modulated Raptor codes designed using the
multi-edge framework outperform previously reported higher-order modulation
codes in literature.
