Global design methods for raptor codes using binary and higher-order modulations

Abstract

We develop accurate and robust one-dimensional EXIT chart methods to design raptor codes with binary and higher-order modulations on AWGN channels over any desired range of SNRs. We formulate the check-node degree distribution optimization as a linear program that optimizes a suitable objective function of the desired operating points. The throughput curves predicted by the analysis are easily compared across different pre-code rates and pre-code error-correcting capabilities. For higher-order modulations we employ BICM on standard Gray-mapped constellations. We further enhance the optimization by applying separate check-node degree distributions to the mapped MSBs and LSBs. Simulated throughput curves using the designed codes for QPSK and 16-QAM modulations on the AWGN channel show marked improvement over previously reported raptor code designs.