Raptor Codes for Higher-Order Modulation Using a Multi-Edge Framework

In this letter, we represent Raptor codes using a multi-edge framework, which gives a general framework to design them for higher-order modulation using multi-edge type 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.