Design of low-density parity-check codes for bandwidth efficient modulation

We design low-density parity-check (LDPC) codes for bandwidth efficient modulation using a multilevel coding (MLC) technique. We develop a method to analyze the asymptotic performance of the LDPC codes using message-passing decoding at each level of the MLC scheme as the codeword length goes to infinity. Simulation of very large block size LDPC codes verifies the accuracy of the analytical results. We jointly optimize the code rates and code parameters of the LDPC codes at each level of the MLC scheme, and the asymptotic performance of the optimized irregular LDPC codes is very close to the channel capacity of the additive white Gaussian noise (AWGN) channel.