Threshold of Protograph-Based LDPC Coded BICM for Rayleigh Fading

Protograph-based bit-interleaved coded modulation (BICM) provides an elegant way of designing coded modulation over Rayleigh faded channels, however, to date the available designs have been limited to specific modulations and the corresponding decoding thresholds have not been known for Rayleigh faded channels. In this work, we present a simple method for designing protograph-based BICM that is general and applies to any modulation, and furthermore we calculate the iterative decoding thresholds of the protograph codes while mapped to higher order modulations. This general coding framework can support not only multiple rates but also adaptive modulation. We report that certain families of protograph codes achieve a threshold within a gap of approximately 0.2 - 0.4 dB of BICM capacity limit across a wide range of rates and modulations.