Design of low-density parity-check (LDPC) codes for high order constellations

In this paper, we propose a simple design of LDPC codes which combines the good properties of multilevel coding (MLC) and bit-interleaved coded modulation (BICM) schemes with Gray-mapped PAM constellations and one-shot demodulation. Through simulations, we show that it performs better than MLC/parallel independent decoding for short-medium lengths, which is required for most applications, on AWGN and block-fading channels. Since 2^m-PAM represents one quadrature component of 2^2m-QAM, the optimization holds true for QAM too. In general, this idea can be extended to other modulation schemes like 2^m-PSK very easily.